Stevanović, Nevena

(Sage Publications Ltd, London, 2022)

TY  - JOUR
AU  - Milićev, Snežana
AU  - Stevanović, Nevena
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3728
AB  - The paper presents an analytical solution for the non-isothermal compressible gas flow in a slide microbearing with different temperatures of walls. The gas flow is defined by the Navier-Stokes-Fourier system of the continuum equations and first order boundary conditions. Knudsen number corresponds to the slip and continuum flow (Kn  lt = 10(-1)) and Reynolds number is moderately high, so inertia needs to be included. The solution is obtained by perturbations with the first approximation that relates to the continuum flow and the second one that involves second-order effects: the rarefaction, inertia, convection, dissipation, and rate at which work is done in compressing the element of fluid. The presented model analyzes the influence of the dependence of transport coefficients on temperature. The obtained analytical solution for the pressure, velocity, and temperature is approved by a comparison with the results of other authors. The microbearings can often be a part of MEMS, so the presented method and the obtained analytical solution can serve for solving similar non-isothermal shear-driven or pressure-driven problems. The paper gives an estimation about the error in values for microbearing mass flow and load capacity if the dependence of transport coefficients on temperature are neglected.
PB  - Sage Publications Ltd, London
T2  - Advances in Mechanical Engineering
T1  - Influence of transport coefficients' dependence on temperature for gas flow in microbearing
IS  - 6
VL  - 14
DO  - 10.1177/16878132221103942
ER  -

@article{
author = "Milićev, Snežana and Stevanović, Nevena",
year = "2022",
abstract = "The paper presents an analytical solution for the non-isothermal compressible gas flow in a slide microbearing with different temperatures of walls. The gas flow is defined by the Navier-Stokes-Fourier system of the continuum equations and first order boundary conditions. Knudsen number corresponds to the slip and continuum flow (Kn  lt = 10(-1)) and Reynolds number is moderately high, so inertia needs to be included. The solution is obtained by perturbations with the first approximation that relates to the continuum flow and the second one that involves second-order effects: the rarefaction, inertia, convection, dissipation, and rate at which work is done in compressing the element of fluid. The presented model analyzes the influence of the dependence of transport coefficients on temperature. The obtained analytical solution for the pressure, velocity, and temperature is approved by a comparison with the results of other authors. The microbearings can often be a part of MEMS, so the presented method and the obtained analytical solution can serve for solving similar non-isothermal shear-driven or pressure-driven problems. The paper gives an estimation about the error in values for microbearing mass flow and load capacity if the dependence of transport coefficients on temperature are neglected.",
publisher = "Sage Publications Ltd, London",
journal = "Advances in Mechanical Engineering",
title = "Influence of transport coefficients' dependence on temperature for gas flow in microbearing",
number = "6",
volume = "14",
doi = "10.1177/16878132221103942"
}

Milićev, S.,& Stevanović, N.. (2022). Influence of transport coefficients' dependence on temperature for gas flow in microbearing. in Advances in Mechanical Engineering
Sage Publications Ltd, London., 14(6).
https://doi.org/10.1177/16878132221103942

Milićev S, Stevanović N. Influence of transport coefficients' dependence on temperature for gas flow in microbearing. in Advances in Mechanical Engineering. 2022;14(6).
doi:10.1177/16878132221103942 .

Milićev, Snežana, Stevanović, Nevena, "Influence of transport coefficients' dependence on temperature for gas flow in microbearing" in Advances in Mechanical Engineering, 14, no. 6 (2022),
https://doi.org/10.1177/16878132221103942 . .

	2
	2

Influence of second order effects on pressure distribution in microtubes

(Serbian Society of Mechanics, 2021)

TY  - CONF
AU  - Guranov, Iva
AU  - Milićev, Snežana
AU  - Stevanović, Nevena
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3978
PB  - Serbian Society of Mechanics
C3  - Proceedings of the The 8th International Congress of Serbian Society of Mechanics, Kragujevac, June 28-30, 2021
T1  - Influence of second order effects on pressure distribution in microtubes
EP  - 94
SP  - 93
UR  - https://hdl.handle.net/21.15107/rcub_machinery_3978
ER  -

@conference{
author = "Guranov, Iva and Milićev, Snežana and Stevanović, Nevena",
year = "2021",
publisher = "Serbian Society of Mechanics",
journal = "Proceedings of the The 8th International Congress of Serbian Society of Mechanics, Kragujevac, June 28-30, 2021",
title = "Influence of second order effects on pressure distribution in microtubes",
pages = "94-93",
url = "https://hdl.handle.net/21.15107/rcub_machinery_3978"
}

Guranov, I., Milićev, S.,& Stevanović, N.. (2021). Influence of second order effects on pressure distribution in microtubes. in Proceedings of the The 8th International Congress of Serbian Society of Mechanics, Kragujevac, June 28-30, 2021
Serbian Society of Mechanics., 93-94.
https://hdl.handle.net/21.15107/rcub_machinery_3978

Guranov I, Milićev S, Stevanović N. Influence of second order effects on pressure distribution in microtubes. in Proceedings of the The 8th International Congress of Serbian Society of Mechanics, Kragujevac, June 28-30, 2021. 2021;:93-94.
https://hdl.handle.net/21.15107/rcub_machinery_3978 .

Guranov, Iva, Milićev, Snežana, Stevanović, Nevena, "Influence of second order effects on pressure distribution in microtubes" in Proceedings of the The 8th International Congress of Serbian Society of Mechanics, Kragujevac, June 28-30, 2021 (2021):93-94,
https://hdl.handle.net/21.15107/rcub_machinery_3978 .

Non-isothermal rarefied gas flow in microtube with constant wall temperature

(Sage Publications Ltd, London, 2021)

TY - JOUR
AU - Guranov, Iva
AU - Milićev, Snežana
AU - Stevanović, Nevena
PY - 2021
UR - https://machinery.mas.bg.ac.rs/handle/123456789/3553
AB - In this paper, pressure-driven gas flow through a microtube with constant wall temperature is considered. The ratio of the molecular mean free path and the diameter of the microtube cannot be negligible. Therefore, the gas rarefaction is taken into account. A solution is obtained for subsonic as well as slip and continuum gas flow. Velocity, pressure, and temperature fields are analytically attained by macroscopic approach, using continuity, Navier-Stokes, and energy equations, with the first order boundary conditions for velocity and temperature. Characteristic variables are expressed in the form of perturbation series. The first approximation stands for solution to the continuum flow. The second one reveals the effects of gas rarefaction, inertia, and dissipation. Solutions for compressible and incompressible gas flow are presented and compared with the available results from the literature. A good matching has been achieved. This enables using proposed method for solving other microtube gas flows, which are common in various fields of engineering, biomedicine, pharmacy, etc. The main contribution of this paper is the integral treatment of several important effects such as rarefaction, compressibility, temperature field variability, inertia, and viscous dissipation in the presented solutions. Since the solutions are analytical, they are useful and easily applicable.
PB - Sage Publications Ltd, London
T2 - Advances in Mechanical Engineering
T1 - Non-isothermal rarefied gas flow in microtube with constant wall temperature
IS - 11
VL - 13
DO - 10.1177/16878140211065147
ER -

@article{
author = "Guranov, Iva and Milićev, Snežana and Stevanović, Nevena",
year = "2021",
abstract = "In this paper, pressure-driven gas flow through a microtube with constant wall temperature is considered. The ratio of the molecular mean free path and the diameter of the microtube cannot be negligible. Therefore, the gas rarefaction is taken into account. A solution is obtained for subsonic as well as slip and continuum gas flow. Velocity, pressure, and temperature fields are analytically attained by macroscopic approach, using continuity, Navier-Stokes, and energy equations, with the first order boundary conditions for velocity and temperature. Characteristic variables are expressed in the form of perturbation series. The first approximation stands for solution to the continuum flow. The second one reveals the effects of gas rarefaction, inertia, and dissipation. Solutions for compressible and incompressible gas flow are presented and compared with the available results from the literature. A good matching has been achieved. This enables using proposed method for solving other microtube gas flows, which are common in various fields of engineering, biomedicine, pharmacy, etc. The main contribution of this paper is the integral treatment of several important effects such as rarefaction, compressibility, temperature field variability, inertia, and viscous dissipation in the presented solutions. Since the solutions are analytical, they are useful and easily applicable.",
publisher = "Sage Publications Ltd, London",
journal = "Advances in Mechanical Engineering",
title = "Non-isothermal rarefied gas flow in microtube with constant wall temperature",
number = "11",
volume = "13",
doi = "10.1177/16878140211065147"
}

Guranov, I., Milićev, S.,& Stevanović, N.. (2021). Non-isothermal rarefied gas flow in microtube with constant wall temperature. in Advances in Mechanical Engineering
Sage Publications Ltd, London., 13(11).
https://doi.org/10.1177/16878140211065147

Guranov I, Milićev S, Stevanović N. Non-isothermal rarefied gas flow in microtube with constant wall temperature. in Advances in Mechanical Engineering. 2021;13(11).
doi:10.1177/16878140211065147 .

Guranov, Iva, Milićev, Snežana, Stevanović, Nevena, "Non-isothermal rarefied gas flow in microtube with constant wall temperature" in Advances in Mechanical Engineering, 13, no. 11 (2021),
https://doi.org/10.1177/16878140211065147 . .

	4
	3

Gas Flow in Microchannels and Nanochannels With Variable Cross Section for All Knudsen and All Mach Number Values

(ASME, New York, 2021)

TY - JOUR
AU - Milićev, Snežana
AU - Stevanović, Nevena
PY - 2021
UR - https://machinery.mas.bg.ac.rs/handle/123456789/3611
AB - The analytical solution for steady viscous pressure-driven compressible isothermal gas flow through micro- and nanochannels with variable cross section for all Knudsen and all Mach number values is presented in this paper. The continuum one-dimensional governing equations are solved using the friction factor that is established in a special way to provide solutions for mass flow rate, pressure, and velocity distribution through the microchannels and nanochannels in the entire rarefaction regime. The friction factor, defined by the general boundary condition and generalized diffusion coefficient proposed by Beskok and Karniadakis (1999, "A Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales," J. Microscale Thermophys. Eng., 3, pp. 43-77), spreads the solution application to all rarefaction regimes from continuum to free molecular flow. The correlation between the product of friction factor and Reynolds number (Poiseuille number) and Knudsen number is established explicitly in the paper. Moreover, the obtained solution includes the inertia effect, which allows the application of the solution to both subsonic and supersonic gas flows, which was not shown earlier. The presented solution confirms the existence of the Knudsen minimum in the diverging, converging, and microchannels and nanochannels with constant cross section. The proposed solution is verified by comparison with experimental, analytical, and numerical results available in literature.
PB - ASME, New York
T2 - Journal of Fluids Engineering-Transactions of The Asme
T1 - Gas Flow in Microchannels and Nanochannels With Variable Cross Section for All Knudsen and All Mach Number Values
IS - 2
VL - 143
DO - 10.1115/1.4048288
ER -

@article{
author = "Milićev, Snežana and Stevanović, Nevena",
year = "2021",
abstract = "The analytical solution for steady viscous pressure-driven compressible isothermal gas flow through micro- and nanochannels with variable cross section for all Knudsen and all Mach number values is presented in this paper. The continuum one-dimensional governing equations are solved using the friction factor that is established in a special way to provide solutions for mass flow rate, pressure, and velocity distribution through the microchannels and nanochannels in the entire rarefaction regime. The friction factor, defined by the general boundary condition and generalized diffusion coefficient proposed by Beskok and Karniadakis (1999, "A Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales," J. Microscale Thermophys. Eng., 3, pp. 43-77), spreads the solution application to all rarefaction regimes from continuum to free molecular flow. The correlation between the product of friction factor and Reynolds number (Poiseuille number) and Knudsen number is established explicitly in the paper. Moreover, the obtained solution includes the inertia effect, which allows the application of the solution to both subsonic and supersonic gas flows, which was not shown earlier. The presented solution confirms the existence of the Knudsen minimum in the diverging, converging, and microchannels and nanochannels with constant cross section. The proposed solution is verified by comparison with experimental, analytical, and numerical results available in literature.",
publisher = "ASME, New York",
journal = "Journal of Fluids Engineering-Transactions of The Asme",
title = "Gas Flow in Microchannels and Nanochannels With Variable Cross Section for All Knudsen and All Mach Number Values",
number = "2",
volume = "143",
doi = "10.1115/1.4048288"
}

Milićev, S.,& Stevanović, N.. (2021). Gas Flow in Microchannels and Nanochannels With Variable Cross Section for All Knudsen and All Mach Number Values. in Journal of Fluids Engineering-Transactions of The Asme
ASME, New York., 143(2).
https://doi.org/10.1115/1.4048288

Milićev S, Stevanović N. Gas Flow in Microchannels and Nanochannels With Variable Cross Section for All Knudsen and All Mach Number Values. in Journal of Fluids Engineering-Transactions of The Asme. 2021;143(2).
doi:10.1115/1.4048288 .

Milićev, Snežana, Stevanović, Nevena, "Gas Flow in Microchannels and Nanochannels With Variable Cross Section for All Knudsen and All Mach Number Values" in Journal of Fluids Engineering-Transactions of The Asme, 143, no. 2 (2021),
https://doi.org/10.1115/1.4048288 . .

	8
	6

Pressure distribution in microtubes with variable cross section

(Serbian Society of Mechanics, 2019)

TY - CONF
AU - Guranov, Iva
AU - Milićev, Snežana
AU - Stevanović, Nevena
PY - 2019
UR - https://machinery.mas.bg.ac.rs/handle/123456789/3973
AB - A steady compressible isothermal slip gas flow in a microtube is analyzed for low Reynolds
numbers. The microtube is with varying cross-section, which from the standpoint of geometry
gives three considered cases: convergent microtube, divergent microtube and microtube with
constant radius. The gas flow is caused by the pressure difference between the inlet and the outlet
cross-section. The solution for pressure and mass flow rate is obtained by macroscopic approach
from Navier-Stokes equations with the second order velocity slip boundary condition. Analysis of
the order of dimensionless terms in governing equations is possible with the usage of exact
relation between Reynolds, Mach and Knudsen numbers. The solution procedure for this flow
model is based on perturbation approach, where significant variables are assumed in the form of
perturbation series. The first approximation represents the solution for the continuum flow
conditions, and the second approximation incorporates the effect of gas rarefaction. The obtained
solution is compared with verified results of numerical experiment found in literature and good
agreement is achieved. Hence, the reliability of obtained solution and presented method is
confirmed.
PB - Serbian Society of Mechanics
C3 - Proceedings of the The 7th International Congress of Serbian Society of Mechanics, Sremski Karlovci, June 24-26, 2019
T1 - Pressure distribution in microtubes with variable cross section
EP - 8
SP - 1
UR - https://hdl.handle.net/21.15107/rcub_machinery_3973
ER -

@conference{
author = "Guranov, Iva and Milićev, Snežana and Stevanović, Nevena",
year = "2019",
abstract = "A steady compressible isothermal slip gas flow in a microtube is analyzed for low Reynolds 
numbers. The microtube is with varying cross-section, which from the standpoint of geometry 
gives three considered cases: convergent microtube, divergent microtube and microtube with 
constant radius. The gas flow is caused by the pressure difference between the inlet and the outlet 
cross-section. The solution for pressure and mass flow rate is obtained by macroscopic approach 
from Navier-Stokes equations with the second order velocity slip boundary condition. Analysis of 
the order of dimensionless terms in governing equations is possible with the usage of exact 
relation between Reynolds, Mach and Knudsen numbers. The solution procedure for this flow 
model is based on perturbation approach, where significant variables are assumed in the form of 
perturbation series. The first approximation represents the solution for the continuum flow 
conditions, and the second approximation incorporates the effect of gas rarefaction. The obtained 
solution is compared with verified results of numerical experiment found in literature and good 
agreement is achieved. Hence, the reliability of obtained solution and presented method is 
confirmed.",
publisher = "Serbian Society of Mechanics",
journal = "Proceedings of the The 7th International Congress of Serbian Society of Mechanics, Sremski Karlovci, June 24-26, 2019",
title = "Pressure distribution in microtubes with variable cross section",
pages = "8-1",
url = "https://hdl.handle.net/21.15107/rcub_machinery_3973"
}

Guranov, I., Milićev, S.,& Stevanović, N.. (2019). Pressure distribution in microtubes with variable cross section. in Proceedings of the The 7th International Congress of Serbian Society of Mechanics, Sremski Karlovci, June 24-26, 2019
Serbian Society of Mechanics., 1-8.
https://hdl.handle.net/21.15107/rcub_machinery_3973

Guranov I, Milićev S, Stevanović N. Pressure distribution in microtubes with variable cross section. in Proceedings of the The 7th International Congress of Serbian Society of Mechanics, Sremski Karlovci, June 24-26, 2019. 2019;:1-8.
https://hdl.handle.net/21.15107/rcub_machinery_3973 .

Guranov, Iva, Milićev, Snežana, Stevanović, Nevena, "Pressure distribution in microtubes with variable cross section" in Proceedings of the The 7th International Congress of Serbian Society of Mechanics, Sremski Karlovci, June 24-26, 2019 (2019):1-8,
https://hdl.handle.net/21.15107/rcub_machinery_3973 .

An isothermal compressible slip gas flow through microtube

Radenković, Darko; Milićev, Snežana; Stevanović, Nevena

(UNIVERSITY OF BANJA LUKA FACULTY OF MECHANICAL ENGINEERING, 2018)

TY  - CONF
AU  - Guranov, Iva
AU  - Milićev, Snežana
AU  - Stevanović, Nevena
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3975
AB  - In this paper the authors considered compressible isothermal steady subsonic slip 
gas flow through microtube at low Reynolds numbers. The dimensions of the 
components in microelectromechanical systems (MEMS) are very small (the order of 
magnitude is 1 µm), and because of that the effect of gas rarefaction cannot be 
neglected, so it should be taken into account. In the analyzed problem gas flow occurs 
due to the pressure difference at the inlet and outlet section of the circular microtube, 
with the variable cross-section (convergent case, divergent case, case with constant 
radius). 
The solving approach in the paper is macroscopic, so the fluid flow is defined by the 
continuity and Navier-Stokes equations. The rarefaction effect is taken into account by
the velocity slip boundary condition at the walls. The solution process is based on a 
perturbation analysis where the order of the terms in the governing equations and 
boundary conditions is determined by using the exact relation between Mach, Reynolds 
and Knudsen numbers. Therefore, with this problem-solving procedure, two 
approximations for the pressure and velocity fields are obtained. The first 
approximation of the characteristic variables corresponds to the conditions of 
continuum flow, while the second approximation shows the effects of rarefied gas flow.
PB  - UNIVERSITY OF BANJA LUKA FACULTY OF MECHANICAL ENGINEERING
C3  - Book of abstracts - 6th International conference of applied science (ICAS 2018), University of Banja Luka, Faculty of Mechanical Engineering, Banja Luka, May 09-11, 2018
T1  - An isothermal compressible slip gas flow through microtube
EP  - 35
SP  - 35
UR  - https://hdl.handle.net/21.15107/rcub_machinery_3975
ER  -

@conference{
author = "Guranov, Iva and Milićev, Snežana and Stevanović, Nevena",
year = "2018",
abstract = "In this paper the authors considered compressible isothermal steady subsonic slip 
gas flow through microtube at low Reynolds numbers. The dimensions of the 
components in microelectromechanical systems (MEMS) are very small (the order of 
magnitude is 1 µm), and because of that the effect of gas rarefaction cannot be 
neglected, so it should be taken into account. In the analyzed problem gas flow occurs 
due to the pressure difference at the inlet and outlet section of the circular microtube, 
with the variable cross-section (convergent case, divergent case, case with constant 
radius). 
The solving approach in the paper is macroscopic, so the fluid flow is defined by the 
continuity and Navier-Stokes equations. The rarefaction effect is taken into account by
the velocity slip boundary condition at the walls. The solution process is based on a 
perturbation analysis where the order of the terms in the governing equations and 
boundary conditions is determined by using the exact relation between Mach, Reynolds 
and Knudsen numbers. Therefore, with this problem-solving procedure, two 
approximations for the pressure and velocity fields are obtained. The first 
approximation of the characteristic variables corresponds to the conditions of 
continuum flow, while the second approximation shows the effects of rarefied gas flow.",
publisher = "UNIVERSITY OF BANJA LUKA FACULTY OF MECHANICAL ENGINEERING",
journal = "Book of abstracts - 6th International conference of applied science (ICAS 2018), University of Banja Luka, Faculty of Mechanical Engineering, Banja Luka, May 09-11, 2018",
title = "An isothermal compressible slip gas flow through microtube",
pages = "35-35",
url = "https://hdl.handle.net/21.15107/rcub_machinery_3975"
}

Guranov, I., Milićev, S.,& Stevanović, N.. (2018). An isothermal compressible slip gas flow through microtube. in Book of abstracts - 6th International conference of applied science (ICAS 2018), University of Banja Luka, Faculty of Mechanical Engineering, Banja Luka, May 09-11, 2018
UNIVERSITY OF BANJA LUKA FACULTY OF MECHANICAL ENGINEERING., 35-35.
https://hdl.handle.net/21.15107/rcub_machinery_3975

Guranov I, Milićev S, Stevanović N. An isothermal compressible slip gas flow through microtube. in Book of abstracts - 6th International conference of applied science (ICAS 2018), University of Banja Luka, Faculty of Mechanical Engineering, Banja Luka, May 09-11, 2018. 2018;:35-35.
https://hdl.handle.net/21.15107/rcub_machinery_3975 .

Guranov, Iva, Milićev, Snežana, Stevanović, Nevena, "An isothermal compressible slip gas flow through microtube" in Book of abstracts - 6th International conference of applied science (ICAS 2018), University of Banja Luka, Faculty of Mechanical Engineering, Banja Luka, May 09-11, 2018 (2018):35-35,
https://hdl.handle.net/21.15107/rcub_machinery_3975 .

Strujanje razređenog gasa u mikrocevima pri malim Rejnoldsovim brojevima

(Univerzitet u Beogradu - Mašinski fakultet, Beograd, 2016)

TY  - JOUR
AU  - Radenković, Darko
AU  - Milićev, Snežana
AU  - Stevanović, Nevena
PY  - 2016
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2368
AB  - U radu se proučava osnosimetrično, izotermsko, stišljivo strujanje gasa sa klizanjem, pri malim vrednostima Rejnoldsovog broja. Problem je rešen primenom jednačine kontinuiteta i Navije-Stoksovih jednačina, zajedno sa Maksvelovim graničnim uslovom prvog reda. Analitički rezultati su dobijeni primenom perturbacione metode. Dobijena rešenja se dobro slažu sa poznatim eksperimentalnim rezultatima drugih autora.
AB  - Low Reynolds number, axisymmetric, isothermal, compressible, slip gas flow in microtubes is investigated in this paper. The problem is solved by the continuum equations, continuity and Navier-Stokes, along with Maxwell first order boundary condition. The analytical results are obtained by perturbation method. The solutions show a good agreement with experimental results.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - Strujanje razređenog gasa u mikrocevima pri malim Rejnoldsovim brojevima
T1  - Rarefied gas flow in microtubes at low Reynolds numbers
EP  - 15
IS  - 1
SP  - 10
VL  - 44
DO  - 10.5937/fmet1601010R
ER  -

@article{
author = "Radenković, Darko and Milićev, Snežana and Stevanović, Nevena",
year = "2016",
abstract = "U radu se proučava osnosimetrično, izotermsko, stišljivo strujanje gasa sa klizanjem, pri malim vrednostima Rejnoldsovog broja. Problem je rešen primenom jednačine kontinuiteta i Navije-Stoksovih jednačina, zajedno sa Maksvelovim graničnim uslovom prvog reda. Analitički rezultati su dobijeni primenom perturbacione metode. Dobijena rešenja se dobro slažu sa poznatim eksperimentalnim rezultatima drugih autora., Low Reynolds number, axisymmetric, isothermal, compressible, slip gas flow in microtubes is investigated in this paper. The problem is solved by the continuum equations, continuity and Navier-Stokes, along with Maxwell first order boundary condition. The analytical results are obtained by perturbation method. The solutions show a good agreement with experimental results.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Strujanje razređenog gasa u mikrocevima pri malim Rejnoldsovim brojevima, Rarefied gas flow in microtubes at low Reynolds numbers",
pages = "15-10",
number = "1",
volume = "44",
doi = "10.5937/fmet1601010R"
}

Radenković, D., Milićev, S.,& Stevanović, N.. (2016). Strujanje razređenog gasa u mikrocevima pri malim Rejnoldsovim brojevima. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 44(1), 10-15.
https://doi.org/10.5937/fmet1601010R

Radenković D, Milićev S, Stevanović N. Strujanje razređenog gasa u mikrocevima pri malim Rejnoldsovim brojevima. in FME Transactions. 2016;44(1):10-15.
doi:10.5937/fmet1601010R .

Radenković, Darko, Milićev, Snežana, Stevanović, Nevena, "Strujanje razređenog gasa u mikrocevima pri malim Rejnoldsovim brojevima" in FME Transactions, 44, no. 1 (2016):10-15,
https://doi.org/10.5937/fmet1601010R . .

	3
	3

Navier-stokes-fourier analytic solutions for non-isothermal couette slip gas flow

Stevanović, Nevena; Đorđević, Vladan D.

(Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd, 2016)

TY  - JOUR
AU  - Milićev, Snežana
AU  - Stevanović, Nevena
PY  - 2016
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2303
AB  - The explicit and reliable analytical solutions for steady plane compressible non-isothermal Couette gas flow are presented These solutions for velocity and temperature are developed by macroscopic approach from Navier-Stokes-Fourier system of continuum equations and the velocity slip and the temperature jump first order boundary conditions. Variability of the viscosity and thermal conductivity with temperature is involved in the model. The known result for the gas flow with constant and equal temperatures of the walls (isothermal walls) is verified and a new solution for the case of different temperature of the walls is obtained Evan though the solution for isothermal walls correspond to the gas flow of the Knudsen number (Kn  lt = 0.1), i. e. to the slip and continuum flow, it is shown that the gas velocity and related shear stress are also valid for the whole range of the Knudsen number. The deviation from numerical results for the same system is less than 1%. The reliability of the solution is confirmed by comparing with results of other authors which are obtained numerically by microscopic approach. The advantage of the presented solution compared to previous is in a very simple applicability along with high accuracy.
PB  - Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd
T2  - Thermal Science
T1  - Navier-stokes-fourier analytic solutions for non-isothermal couette slip gas flow
EP  - 1833
IS  - 6
SP  - 1825
VL  - 20
DO  - 10.2298/TSCI160423221M
ER  -

@article{
author = "Milićev, Snežana and Stevanović, Nevena",
year = "2016",
abstract = "The explicit and reliable analytical solutions for steady plane compressible non-isothermal Couette gas flow are presented These solutions for velocity and temperature are developed by macroscopic approach from Navier-Stokes-Fourier system of continuum equations and the velocity slip and the temperature jump first order boundary conditions. Variability of the viscosity and thermal conductivity with temperature is involved in the model. The known result for the gas flow with constant and equal temperatures of the walls (isothermal walls) is verified and a new solution for the case of different temperature of the walls is obtained Evan though the solution for isothermal walls correspond to the gas flow of the Knudsen number (Kn  lt = 0.1), i. e. to the slip and continuum flow, it is shown that the gas velocity and related shear stress are also valid for the whole range of the Knudsen number. The deviation from numerical results for the same system is less than 1%. The reliability of the solution is confirmed by comparing with results of other authors which are obtained numerically by microscopic approach. The advantage of the presented solution compared to previous is in a very simple applicability along with high accuracy.",
publisher = "Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd",
journal = "Thermal Science",
title = "Navier-stokes-fourier analytic solutions for non-isothermal couette slip gas flow",
pages = "1833-1825",
number = "6",
volume = "20",
doi = "10.2298/TSCI160423221M"
}

Milićev, S.,& Stevanović, N.. (2016). Navier-stokes-fourier analytic solutions for non-isothermal couette slip gas flow. in Thermal Science
Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd., 20(6), 1825-1833.
https://doi.org/10.2298/TSCI160423221M

Milićev S, Stevanović N. Navier-stokes-fourier analytic solutions for non-isothermal couette slip gas flow. in Thermal Science. 2016;20(6):1825-1833.
doi:10.2298/TSCI160423221M .

Milićev, Snežana, Stevanović, Nevena, "Navier-stokes-fourier analytic solutions for non-isothermal couette slip gas flow" in Thermal Science, 20, no. 6 (2016):1825-1833,
https://doi.org/10.2298/TSCI160423221M . .

Tačno analitičko rešenje Rejnoldsove jednačine podmazivanja za strujanje gasa sa klizanjem

(Univerzitet u Beogradu - Mašinski fakultet, Beograd, 2015)

TY  - JOUR
AU  - Stevanović, Nevena
AU  - Đorđević, Vladan D.
PY  - 2015
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2155
AB  - Izvedena je opšta Rejnoldsova jednačina podmazivanja za uslove strujanja sa klizanjem primenom opštih graničnih uslova klizanja drugog reda i pokazano je da ona ima tačno analitičko rešenje. Rešenje je dobijeno tansformacijom zavisno promenljive što je dovelo do mogućnosti analitičkog proračuna raspodele pritiska i masenog protoka u mikroležaju. Na taj način, poređenjem sa datim analitičkim rešenjem omogućena je provera eksperimentalnih i numeričkih rezultata za strujanje gasa u mikroležajima.
AB  - We derive a general slip-corrected compressible Reynolds lubrication equation, valid for any choice of the slip velocities, and show that it possesses the exact analytical solution. It is obtained by a suitable transformation of the dependent variable, and it yields both the pressure distribution in the bearing and the mass flow rate through it. It can be usefully applied for testing the other, experimental or numerical results obtained under the same or similar physical conditions, against this solution.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - Tačno analitičko rešenje Rejnoldsove jednačine podmazivanja za strujanje gasa sa klizanjem
T1  - An exact analytical solution for the second order slip-corrected Reynolds lubrication equation
EP  - 20
IS  - 1
SP  - 16
VL  - 43
DO  - 10.5937/fmet1501016S
ER  -

@article{
author = "Stevanović, Nevena and Đorđević, Vladan D.",
year = "2015",
abstract = "Izvedena je opšta Rejnoldsova jednačina podmazivanja za uslove strujanja sa klizanjem primenom opštih graničnih uslova klizanja drugog reda i pokazano je da ona ima tačno analitičko rešenje. Rešenje je dobijeno tansformacijom zavisno promenljive što je dovelo do mogućnosti analitičkog proračuna raspodele pritiska i masenog protoka u mikroležaju. Na taj način, poređenjem sa datim analitičkim rešenjem omogućena je provera eksperimentalnih i numeričkih rezultata za strujanje gasa u mikroležajima., We derive a general slip-corrected compressible Reynolds lubrication equation, valid for any choice of the slip velocities, and show that it possesses the exact analytical solution. It is obtained by a suitable transformation of the dependent variable, and it yields both the pressure distribution in the bearing and the mass flow rate through it. It can be usefully applied for testing the other, experimental or numerical results obtained under the same or similar physical conditions, against this solution.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Tačno analitičko rešenje Rejnoldsove jednačine podmazivanja za strujanje gasa sa klizanjem, An exact analytical solution for the second order slip-corrected Reynolds lubrication equation",
pages = "20-16",
number = "1",
volume = "43",
doi = "10.5937/fmet1501016S"
}

Stevanović, N.,& Đorđević, V. D.. (2015). Tačno analitičko rešenje Rejnoldsove jednačine podmazivanja za strujanje gasa sa klizanjem. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 43(1), 16-20.
https://doi.org/10.5937/fmet1501016S

Stevanović N, Đorđević VD. Tačno analitičko rešenje Rejnoldsove jednačine podmazivanja za strujanje gasa sa klizanjem. in FME Transactions. 2015;43(1):16-20.
doi:10.5937/fmet1501016S .

Stevanović, Nevena, Đorđević, Vladan D., "Tačno analitičko rešenje Rejnoldsove jednačine podmazivanja za strujanje gasa sa klizanjem" in FME Transactions, 43, no. 1 (2015):16-20,
https://doi.org/10.5937/fmet1501016S . .

	1
	3

An analysis of the Different Parameters influence on the Microbearing load carrying capacity

Stevanović, Nevena; Milićev, Snežana

(International Association for Applied Mathematics and Mechanics, Nemačka, 2014)

TY - CONF
AU - Stevanović, Nevena
AU - Milićev, Snežana
PY - 2014
UR - https://enauka.gov.rs/handle/123456789/305842
UR - https://machinery.mas.bg.ac.rs/handle/123456789/6066
AB - An analytical solution for the two-dimensional non-isothermal compressible gas flow in a slider micro-bearing is presented in this paper. It is shear-driven subsonic slip gas flow. In view of the fact that a fluid flow in a micro system is rarefied, the model takes into account this influence. The slip gas flow is defined by the continuity, Navier-Stokes and energy continuum equations, along with the velocity slip and the temperature jump Maxwell-Smoluchowski first order boundary conditions. Knudsen number is in the range of 0-10-1, which corresponds to the continuum and slip gas flow. The analytical solutions of the pressure, velocity and temperature are obtained. The results are of the order of Navier-Stokes equations, i.e., O(Kn) and they agree well with those found in the open literature.
The solutions enable analysis of the relevant parameters influences on the load carrying capacity of the micro-bearing. Hence, the influences of the flow conditions expressed by Mach, Reynolds and Knudsen numbers, the ratio of the inlet to outlet heights, bearing number, as well as temperature field are investigated. Moreover, obtained analytical solutions comprise second order effects for gas flows in micro-systems such as inertia and dissipation which enabled the assessment of their impact on the load carrying capacity of the micro-bearing, i.e. estimation of the calculations safety when these effects are neglected.
PB - International Association for Applied Mathematics and Mechanics, Nemačka
C3 - 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)
T1 - An analysis of the Different Parameters influence on the Microbearing load carrying capacity
EP - 451
SP - 451
UR - https://hdl.handle.net/21.15107/rcub_machinery_6066
ER -

@conference{
author = "Stevanović, Nevena and Milićev, Snežana",
year = "2014",
abstract = "An analytical solution for the two-dimensional non-isothermal compressible gas flow in a slider micro-bearing is presented in this paper. It is shear-driven subsonic slip gas flow. In view of the fact that a fluid flow in a micro system is rarefied, the model takes into account this influence. The slip gas flow is defined by the continuity, Navier-Stokes and energy continuum equations, along with the velocity slip and the temperature jump Maxwell-Smoluchowski first order boundary conditions. Knudsen number is in the range of 0-10-1, which corresponds to the continuum and slip gas flow. The analytical solutions of the pressure, velocity and temperature are obtained. The results are of the order of Navier-Stokes equations, i.e., O(Kn) and they agree well with those found in the open literature.
The solutions enable analysis of the relevant parameters influences on the load carrying capacity of the micro-bearing. Hence, the influences of the flow conditions expressed by Mach, Reynolds and Knudsen numbers, the ratio of the inlet to outlet heights, bearing number, as well as temperature field are investigated. Moreover, obtained analytical solutions comprise second order effects for gas flows in micro-systems such as inertia and dissipation which enabled the assessment of their impact on the load carrying capacity of the micro-bearing, i.e. estimation of the calculations safety when these effects are neglected.",
publisher = "International Association for Applied Mathematics and Mechanics, Nemačka",
journal = "85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)",
title = "An analysis of the Different Parameters influence on the Microbearing load carrying capacity",
pages = "451-451",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6066"
}

Stevanović, N.,& Milićev, S.. (2014). An analysis of the Different Parameters influence on the Microbearing load carrying capacity. in 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)
International Association for Applied Mathematics and Mechanics, Nemačka., 451-451.
https://hdl.handle.net/21.15107/rcub_machinery_6066

Stevanović N, Milićev S. An analysis of the Different Parameters influence on the Microbearing load carrying capacity. in 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM). 2014;:451-451.
https://hdl.handle.net/21.15107/rcub_machinery_6066 .

Stevanović, Nevena, Milićev, Snežana, "An analysis of the Different Parameters influence on the Microbearing load carrying capacity" in 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) (2014):451-451,
https://hdl.handle.net/21.15107/rcub_machinery_6066 .

An analysis of the different parameters influence on the microbearing load carrying capacity

Stevanović, Nevena; Milićev, Snežana

(Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2014)

TY  - JOUR
AU  - Stevanović, Nevena
AU  - Milićev, Snežana
PY  - 2014
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5989
AB  - An analytical solution for the two-dimensional non-isothermal compressible gas flow in a slider microbearing is presented in this paper. The solutions enable analysis of the relevant parameters influences on the load carrying capacity of the microbearing. Hence, the influences of the flow conditions expressed by Mach, Reynolds and Knudsen numbers, the ratio of the inlet to outlet heights, bearing number, as well as temperature field are investigated.
PB  - Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
T2  - PAMM
T1  - An analysis of the different parameters influence on the microbearing load carrying capacity
EP  - 614
IS  - 1
SP  - 613
VL  - 14
DO  - 10.1002/pamm.201410294
ER  -

@article{
author = "Stevanović, Nevena and Milićev, Snežana",
year = "2014",
abstract = "An analytical solution for the two-dimensional non-isothermal compressible gas flow in a slider microbearing is presented in this paper. The solutions enable analysis of the relevant parameters influences on the load carrying capacity of the microbearing. Hence, the influences of the flow conditions expressed by Mach, Reynolds and Knudsen numbers, the ratio of the inlet to outlet heights, bearing number, as well as temperature field are investigated.",
publisher = "Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim",
journal = "PAMM",
title = "An analysis of the different parameters influence on the microbearing load carrying capacity",
pages = "614-613",
number = "1",
volume = "14",
doi = "10.1002/pamm.201410294"
}

Stevanović, N.,& Milićev, S.. (2014). An analysis of the different parameters influence on the microbearing load carrying capacity. in PAMM
Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim., 14(1), 613-614.
https://doi.org/10.1002/pamm.201410294

Stevanović N, Milićev S. An analysis of the different parameters influence on the microbearing load carrying capacity. in PAMM. 2014;14(1):613-614.
doi:10.1002/pamm.201410294 .

Stevanović, Nevena, Milićev, Snežana, "An analysis of the different parameters influence on the microbearing load carrying capacity" in PAMM, 14, no. 1 (2014):613-614,
https://doi.org/10.1002/pamm.201410294 . .

Osnove mikrofluidike i nanofluidike

(Mašinski fakultet Univerziteta u Beogradu, 2014)

TY  - BOOK
AU  - Stevanović, Nevena
PY  - 2014
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5979
PB  - Mašinski fakultet Univerziteta u Beogradu
T1  - Osnove mikrofluidike i nanofluidike
UR  - https://hdl.handle.net/21.15107/rcub_machinery_5979
ER  -

@book{
author = "Stevanović, Nevena",
year = "2014",
publisher = "Mašinski fakultet Univerziteta u Beogradu",
title = "Osnove mikrofluidike i nanofluidike",
url = "https://hdl.handle.net/21.15107/rcub_machinery_5979"
}

Stevanović, N.. (2014). Osnove mikrofluidike i nanofluidike. 
Mašinski fakultet Univerziteta u Beogradu..
https://hdl.handle.net/21.15107/rcub_machinery_5979

Stevanović N. Osnove mikrofluidike i nanofluidike. 2014;.
https://hdl.handle.net/21.15107/rcub_machinery_5979 .

Stevanović, Nevena, "Osnove mikrofluidike i nanofluidike" (2014),
https://hdl.handle.net/21.15107/rcub_machinery_5979 .

Non-isothermal gas flow in microchannel with equal wall temperatures

(Gesellschaft für Angewandte Mathematik und Mechanik, Republika Srbija, 2013)

TY - CONF
AU - Milićev, Snežana
AU - Stevanović, Nevena
PY - 2013
UR - https://enauka.gov.rs/handle/123456789/126673
UR - https://machinery.mas.bg.ac.rs/handle/123456789/6032
AB - A non-isothermal pressure-driven compressible subsonic slip gas flow in microchannels with variable cross section (convergent, divergent and constant high channel) is analyzed in this paper analytically. Since the flows correspond to microspaces, the rarefaction effect must be taken into account. Solutions are obtained for gas flow with equal temperatures of the walls. The slip gas flow is defined by macroscopic approach, using the continuity, Navier-Stokes and energy continuum equations, along with the velocity slip and temperature jump Maxwell-Smoluchowski first order boundary conditions. The Knudsen number is supposed for the slip gas flow, and Mach number for the subsonic flow. Fully developed flow is considered, which assumes a slow variation of all physical quantities in the streamwise direction. These assumptions, along with the known relationship between the Mach, Reynolds and Knudsen numbers, are used to derive a precise estimation of each term's contribution in the non-dimensional governing equations, as well as in the boundary conditions. This evaluation also makes a distinction between low and moderately high Reynolds numbers flows, which are solved separately. The solutions correspond to the slip and continuum flows. Finally, the analytical solutions for the pressure, velocity , and temperature are obtained. The results are in a good agreement with those obtained by some experiments found in the open literature.
PB - Gesellschaft für Angewandte Mathematik und Mechanik, Republika Srbija
C3 - 84th Annual Meeting of the International Association of Applied Mathematics and Mechanics
T1 - Non-isothermal gas flow in microchannel with equal wall temperatures
EP - 304
SP - 304
UR - https://hdl.handle.net/21.15107/rcub_machinery_6032
ER -

@conference{
author = "Milićev, Snežana and Stevanović, Nevena",
year = "2013",
abstract = "A non-isothermal pressure-driven compressible subsonic slip gas flow in microchannels with variable cross section (convergent, divergent and constant high channel) is analyzed in this paper analytically. Since the flows correspond to microspaces, the rarefaction effect must be taken into account. Solutions are obtained for gas flow with equal temperatures of the walls. The slip gas flow is defined by macroscopic approach, using the continuity, Navier-Stokes and energy continuum equations, along with the velocity slip and temperature jump Maxwell-Smoluchowski first order boundary conditions. The Knudsen number is supposed for the slip gas flow, and Mach number for the subsonic flow. Fully developed flow is considered, which assumes a slow variation of all physical quantities in the streamwise direction. These assumptions, along with the known relationship between the Mach, Reynolds and Knudsen numbers, are used to derive a precise estimation of each term's contribution in the non-dimensional governing equations, as well as in the boundary conditions. This evaluation also makes a distinction between low and moderately high Reynolds numbers flows, which are solved separately. The solutions correspond to the slip and continuum flows. Finally, the analytical solutions for the pressure, velocity , and temperature are obtained. The results are in a good agreement with those obtained by some experiments found in the open literature.",
publisher = "Gesellschaft für Angewandte Mathematik und Mechanik, Republika Srbija",
journal = "84th Annual Meeting of the International Association of Applied Mathematics and Mechanics",
title = "Non-isothermal gas flow in microchannel with equal wall temperatures",
pages = "304-304",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6032"
}

Milićev, S.,& Stevanović, N.. (2013). Non-isothermal gas flow in microchannel with equal wall temperatures. in 84th Annual Meeting of the International Association of Applied Mathematics and Mechanics
Gesellschaft für Angewandte Mathematik und Mechanik, Republika Srbija., 304-304.
https://hdl.handle.net/21.15107/rcub_machinery_6032

Milićev S, Stevanović N. Non-isothermal gas flow in microchannel with equal wall temperatures. in 84th Annual Meeting of the International Association of Applied Mathematics and Mechanics. 2013;:304-304.
https://hdl.handle.net/21.15107/rcub_machinery_6032 .

Milićev, Snežana, Stevanović, Nevena, "Non-isothermal gas flow in microchannel with equal wall temperatures" in 84th Annual Meeting of the International Association of Applied Mathematics and Mechanics (2013):304-304,
https://hdl.handle.net/21.15107/rcub_machinery_6032 .

Non-isothermal gas flow in microchannel with equal wall temperatures

(Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2013)

TY  - JOUR
AU  - Milićev, Snežana
AU  - Stevanović, Nevena
PY  - 2013
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6009
AB  - A non-isothermal two-dimensional compressible subsonic slip gas flows is analyzed in this paper. It is pressure-driven steady flow in microchannels with variable cross section (convergent, divergent, and constant height channel). Since the flows correspond to microspaces, the rarefaction effect is taken in account. The obtained gas temperature profiles are non-uniform.
PB  - Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
T2  - PAMM
T1  - Non-isothermal gas flow in microchannel with equal wall temperatures
EP  - 284
IS  - 1
SP  - 283
VL  - 13
DO  - 10.1002/pamm.201310137
ER  -

@article{
author = "Milićev, Snežana and Stevanović, Nevena",
year = "2013",
abstract = "A non-isothermal two-dimensional compressible subsonic slip gas flows is analyzed in this paper. It is pressure-driven steady flow in microchannels with variable cross section (convergent, divergent, and constant height channel). Since the flows correspond to microspaces, the rarefaction effect is taken in account. The obtained gas temperature profiles are non-uniform.",
publisher = "Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim",
journal = "PAMM",
title = "Non-isothermal gas flow in microchannel with equal wall temperatures",
pages = "284-283",
number = "1",
volume = "13",
doi = "10.1002/pamm.201310137"
}

Milićev, S.,& Stevanović, N.. (2013). Non-isothermal gas flow in microchannel with equal wall temperatures. in PAMM
Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim., 13(1), 283-284.
https://doi.org/10.1002/pamm.201310137

Milićev S, Stevanović N. Non-isothermal gas flow in microchannel with equal wall temperatures. in PAMM. 2013;13(1):283-284.
doi:10.1002/pamm.201310137 .

Milićev, Snežana, Stevanović, Nevena, "Non-isothermal gas flow in microchannel with equal wall temperatures" in PAMM, 13, no. 1 (2013):283-284,
https://doi.org/10.1002/pamm.201310137 . .

A non-isothermal Couette slip gas flow

Stevanović, Nevena; Milićev, Snežana; Đorđević, Vladan

(Science Press, Beijing, 2013)

TY - JOUR
AU - Milićev, Snežana
AU - Stevanović, Nevena
PY - 2013
UR - https://machinery.mas.bg.ac.rs/handle/123456789/1695
AB - A steady plane subsonic compressible non-isothermal Couette gas flow is analyzed for moderately high and low Reynolds numbers. The flow channel is formed by two plates in relative motion. Two cases are considered: (a) isothermal walls where the temperatures of the plates are equal and constant and (b) with constant but different plate temperatures. The Knudsen number is Kn a (c) 1/2 0.1, which corresponds to the slip and continuum flow. The flow is defined by continuity, Navier-Stokes and energy continuum equations, along with the velocity slip and the temperature jump first order boundary conditions. An analytical solution for velocity and temperature is obtained by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the others represent the contribution of the rarefaction effect. In addition, a numerical solution of the problems is given to confirm the accuracy of the analytical results. The exact analytical solution, for constant viscosity and conductivity is found for the isothermal walls case as well. It is shown that it is entirely a substitution to the exact numerical solution for the isothermal walls case.
PB - Science Press, Beijing
T2 - Science China-Physics Mechanics & Astronomy
T1 - A non-isothermal Couette slip gas flow
EP - 1797
IS - 9
SP - 1782
VL - 56
DO - 10.1007/s11433-013-5120-7
ER -

@article{
author = "Milićev, Snežana and Stevanović, Nevena",
year = "2013",
abstract = "A steady plane subsonic compressible non-isothermal Couette gas flow is analyzed for moderately high and low Reynolds numbers. The flow channel is formed by two plates in relative motion. Two cases are considered: (a) isothermal walls where the temperatures of the plates are equal and constant and (b) with constant but different plate temperatures. The Knudsen number is Kn a (c) 1/2 0.1, which corresponds to the slip and continuum flow. The flow is defined by continuity, Navier-Stokes and energy continuum equations, along with the velocity slip and the temperature jump first order boundary conditions. An analytical solution for velocity and temperature is obtained by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the others represent the contribution of the rarefaction effect. In addition, a numerical solution of the problems is given to confirm the accuracy of the analytical results. The exact analytical solution, for constant viscosity and conductivity is found for the isothermal walls case as well. It is shown that it is entirely a substitution to the exact numerical solution for the isothermal walls case.",
publisher = "Science Press, Beijing",
journal = "Science China-Physics Mechanics & Astronomy",
title = "A non-isothermal Couette slip gas flow",
pages = "1797-1782",
number = "9",
volume = "56",
doi = "10.1007/s11433-013-5120-7"
}

Milićev, S.,& Stevanović, N.. (2013). A non-isothermal Couette slip gas flow. in Science China-Physics Mechanics & Astronomy
Science Press, Beijing., 56(9), 1782-1797.
https://doi.org/10.1007/s11433-013-5120-7

Milićev S, Stevanović N. A non-isothermal Couette slip gas flow. in Science China-Physics Mechanics & Astronomy. 2013;56(9):1782-1797.
doi:10.1007/s11433-013-5120-7 .

Milićev, Snežana, Stevanović, Nevena, "A non-isothermal Couette slip gas flow" in Science China-Physics Mechanics & Astronomy, 56, no. 9 (2013):1782-1797,
https://doi.org/10.1007/s11433-013-5120-7 . .

	2
	3
	4

Microbearing gas flow modeling by fractional derivative for entire Knudsen number range

(Department of Mechanics, University of Novi Sad, 2012)

TY - CONF
AU - Stevanović, Nevena
AU - Milićev, Snežana
AU - Đorđević, Vladan
PY - 2012
UR - https://machinery.mas.bg.ac.rs/handle/123456789/6112
AB - Rarefied gas flow is encountered in many technical applications as well as in scientific inquiry. It may appear in low-pressure or vacuum environmental conditions and, on the other hand at standard atmospheric conditions. First category include gas flow in the devices used in hypersonic space vehicles and in several types of vacuum instruments, while the second category relates to the gas flow in micro/nano-electro-mechanical-systems (MEMS, NEMS) with characteristic dimension of the order of and . In these systems the ratio between the mean free path of the molecules and the characteristic length, which is defined as the Knudsen number (Kn), is not negligible and continuum approach breaks down. As a consequence gas slips along the wall and classical no-slip boundary conditions are no more valid. In the range , known as the slip flow regime, gas flow still obeys continuum i.e. Navier-Stokes equations, but now with slip boundary conditions at the walls. In the range (transitional flow regime) more complex Burnett equations have to be applied. The accuracy of the Burnett equations is of the order and they are solved under the boundary conditions of the same second order accuracy. Besides, the individual particle-based direct simulation Monte Carlo (DSMC) approach might be employed. Finally, for the gas flow is considered as a free molecular flow amenable to the methods of kinetic theory of gases.
In this paper rarefied compressible two-dimensional gas flows in microbearings that are often part of MEMS and NEMS are treated. Instead of different approaches for slip velocity for the three rarefied gas flow regimes, slip at the boundaries is modeled by fractional derivative for the whole Knudsen number range. For this purpose a version of Caputo derivative is defined, with the order α defined as a function of the local value of the Knudsen number in the microbearing. For no-slip boundary conditions i.e. for continuum flow regime , while for free molecular flow when the Knudsen number approaches infinity . The correlation between and Kn is derived in the following way. The flow rate coefficient of Poiseuille flow is calculated for various Knudsen numbers by utilizing the numerical solution of the Boltzmann equation obtained by Fukui and Kaneko (1988). The obtained values of for specified Kn numbers are used for the derivation of the analytical relation between and Kn. Such a universal boundary condition that defines velocity at the wall for an arbitrary Knudsen number value is incorporated in the system of continuity and momentum equation, which leads to the general slip-corrected Reynolds lubrication equation. It is shown that it possesses the analytical solution which is obtained by a suitable transformation of the independent variable (Stevanovic and Djordjevic, 2012). It provides the mass flow rate as well as the pressure distribution in the microbearing for a specified bearing number , the reference Knudsen number at the exit cross section and the ratio of the inlet and exit microbearing height.
The results for a wide range of the Knudsen number and the continuum flow conditions, obtained by the general analytical solution from this paper, are in excellent agreement with Fukui and Kaneko’s (1988) numerical solution of the Boltzmann equation.
PB - Department of Mechanics, University of Novi Sad
C3 - International Conference Contemporary Problems of Mechanics and Applied Mathematics, Novi Sad
T1 - Microbearing gas flow modeling by fractional derivative for entire Knudsen number range
EP - 52
SP - 51
UR - https://hdl.handle.net/21.15107/rcub_machinery_6112
ER -

@conference{
author = "Stevanović, Nevena and Milićev, Snežana and Đorđević, Vladan",
year = "2012",
abstract = "Rarefied gas flow is encountered in many technical applications as well as in scientific inquiry. It may appear in low-pressure or vacuum environmental conditions and, on the other hand at standard atmospheric conditions. First category include gas flow in the devices used in hypersonic space vehicles and in several types of vacuum instruments, while the second category relates to the gas flow in micro/nano-electro-mechanical-systems (MEMS, NEMS) with characteristic dimension of the order of and . In these systems the ratio between the mean free path of the molecules and the characteristic length, which is defined as the Knudsen number (Kn), is not negligible and continuum approach breaks down. As a consequence gas slips along the wall and classical no-slip boundary conditions are no more valid. In the range , known as the slip flow regime, gas flow still obeys continuum i.e. Navier-Stokes equations, but now with slip boundary conditions at the walls. In the range (transitional flow regime) more complex Burnett equations have to be applied. The accuracy of the Burnett equations is of the order and they are solved under the boundary conditions of the same second order accuracy. Besides, the individual particle-based direct simulation Monte Carlo (DSMC) approach might be employed. Finally, for the gas flow is considered as a free molecular flow amenable to the methods of kinetic theory of gases.
In this paper rarefied compressible two-dimensional gas flows in microbearings that are often part of MEMS and NEMS are treated. Instead of different approaches for slip velocity for the three rarefied gas flow regimes, slip at the boundaries is modeled by fractional derivative for the whole Knudsen number range. For this purpose a version of Caputo derivative is defined, with the order α defined as a function of the local value of the Knudsen number in the microbearing. For no-slip boundary conditions i.e. for continuum flow regime , while for free molecular flow when the Knudsen number approaches infinity . The correlation between and Kn is derived in the following way. The flow rate coefficient of Poiseuille flow is calculated for various Knudsen numbers by utilizing the numerical solution of the Boltzmann equation obtained by Fukui and Kaneko (1988). The obtained values of for specified Kn numbers are used for the derivation of the analytical relation between and Kn. Such a universal boundary condition that defines velocity at the wall for an arbitrary Knudsen number value is incorporated in the system of continuity and momentum equation, which leads to the general slip-corrected Reynolds lubrication equation. It is shown that it possesses the analytical solution which is obtained by a suitable transformation of the independent variable (Stevanovic and Djordjevic, 2012). It provides the mass flow rate as well as the pressure distribution in the microbearing for a specified bearing number , the reference Knudsen number at the exit cross section and the ratio of the inlet and exit microbearing height.
The results for a wide range of the Knudsen number and the continuum flow conditions, obtained by the general analytical solution from this paper, are in excellent agreement with Fukui and Kaneko’s (1988) numerical solution of the Boltzmann equation.",
publisher = "Department of Mechanics, University of Novi Sad",
journal = "International Conference Contemporary Problems of Mechanics and Applied Mathematics, Novi Sad",
title = "Microbearing gas flow modeling by fractional derivative for entire Knudsen number range",
pages = "52-51",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6112"
}

Stevanović, N., Milićev, S.,& Đorđević, V.. (2012). Microbearing gas flow modeling by fractional derivative for entire Knudsen number range. in International Conference Contemporary Problems of Mechanics and Applied Mathematics, Novi Sad
Department of Mechanics, University of Novi Sad., 51-52.
https://hdl.handle.net/21.15107/rcub_machinery_6112

Stevanović N, Milićev S, Đorđević V. Microbearing gas flow modeling by fractional derivative for entire Knudsen number range. in International Conference Contemporary Problems of Mechanics and Applied Mathematics, Novi Sad. 2012;:51-52.
https://hdl.handle.net/21.15107/rcub_machinery_6112 .

Stevanović, Nevena, Milićev, Snežana, Đorđević, Vladan, "Microbearing gas flow modeling by fractional derivative for entire Knudsen number range" in International Conference Contemporary Problems of Mechanics and Applied Mathematics, Novi Sad (2012):51-52,
https://hdl.handle.net/21.15107/rcub_machinery_6112 .

The exact analytical solution for the gas lubricated bearing in the slip and continuum flow regime

Stevanović, Nevena; Đorđević, Vladan D.

(Srpska akademija nauka i umetnosti SANU - Matematički institut, Beograd, 2012)

TY  - JOUR
AU  - Stevanović, Nevena
AU  - Đorđević, Vladan D.
PY  - 2012
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1442
AB  - The exact analytical solution for the compressible two-dimensional gas flow in the microbearing is presented. The general slip-corrected Reynolds lubrication equation is derived and it is shown that it possesses an exact analytical solution. It is obtained by a suitable transformation of the independent variable, and it provides the pressure distribution in the bearing as well as the mass flow rate through it. By neglecting the rarefaction effect, this solution is also applicable to the continuum gas flow in the bearing, which also does not exist in the open literature. The obtained analytical solution can be usefully applied for testing the other, experimental or numerical results.
PB  - Srpska akademija nauka i umetnosti SANU - Matematički institut, Beograd
T2  - Publications De L Institut Mathematique-Beograd
T1  - The exact analytical solution for the gas lubricated bearing in the slip and continuum flow regime
EP  - 93
IS  - 105
SP  - 83
VL  - 91
DO  - 10.2298/PIM1205083S
ER  -

@article{
author = "Stevanović, Nevena and Đorđević, Vladan D.",
year = "2012",
abstract = "The exact analytical solution for the compressible two-dimensional gas flow in the microbearing is presented. The general slip-corrected Reynolds lubrication equation is derived and it is shown that it possesses an exact analytical solution. It is obtained by a suitable transformation of the independent variable, and it provides the pressure distribution in the bearing as well as the mass flow rate through it. By neglecting the rarefaction effect, this solution is also applicable to the continuum gas flow in the bearing, which also does not exist in the open literature. The obtained analytical solution can be usefully applied for testing the other, experimental or numerical results.",
publisher = "Srpska akademija nauka i umetnosti SANU - Matematički institut, Beograd",
journal = "Publications De L Institut Mathematique-Beograd",
title = "The exact analytical solution for the gas lubricated bearing in the slip and continuum flow regime",
pages = "93-83",
number = "105",
volume = "91",
doi = "10.2298/PIM1205083S"
}

Stevanović, N.,& Đorđević, V. D.. (2012). The exact analytical solution for the gas lubricated bearing in the slip and continuum flow regime. in Publications De L Institut Mathematique-Beograd
Srpska akademija nauka i umetnosti SANU - Matematički institut, Beograd., 91(105), 83-93.
https://doi.org/10.2298/PIM1205083S

Stevanović N, Đorđević VD. The exact analytical solution for the gas lubricated bearing in the slip and continuum flow regime. in Publications De L Institut Mathematique-Beograd. 2012;91(105):83-93.
doi:10.2298/PIM1205083S .

Stevanović, Nevena, Đorđević, Vladan D., "The exact analytical solution for the gas lubricated bearing in the slip and continuum flow regime" in Publications De L Institut Mathematique-Beograd, 91, no. 105 (2012):83-93,
https://doi.org/10.2298/PIM1205083S . .

	8
	8
	10

A microbearing gas flow with different walls' temperatures

Stevanović, Nevena; Milićev, Snežana

(Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd, 2012)

TY - JOUR
AU - Milićev, Snežana
AU - Stevanović, Nevena
PY - 2012
UR - https://machinery.mas.bg.ac.rs/handle/123456789/1375
AB - An analytical solution for the non-isothermal 2-D compressible gas flow in a slider microbearing with different temperatures of walls is presented in this paper. The slip flow is defined by the continuity, Navier-Stokes and energy continuum equations, along with the velocity slip and the temperature jump first order boundary conditions. Knudsen number is in the range of 10-3-10-1, which corresponds to the slip flow. The ratio between the exit microbearing height and the microbearing length is taken to be a small parameter. Moreover, it is assumed that the microbearing cross-section varies slowly, which implies that all physical quantities vary slowly in x-direction. The model solution is treated by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the second one involves the influence of rarefaction effect. The analytical solutions of the pressure, velocity, and temperature for moderately high Reynolds numbers are presented here. For these flow conditions the inertia, convection, dissipation, and rate at which work is done in compressing the element of fluid are presented in the second approximation, also.
PB - Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd
T2 - Thermal Science
T1 - A microbearing gas flow with different walls' temperatures
EP - 132
IS - 1
SP - 119
VL - 16
DO - 10.2298/TSCI110804086M
ER -

@article{
author = "Milićev, Snežana and Stevanović, Nevena",
year = "2012",
abstract = "An analytical solution for the non-isothermal 2-D compressible gas flow in a slider microbearing with different temperatures of walls is presented in this paper. The slip flow is defined by the continuity, Navier-Stokes and energy continuum equations, along with the velocity slip and the temperature jump first order boundary conditions. Knudsen number is in the range of 10-3-10-1, which corresponds to the slip flow. The ratio between the exit microbearing height and the microbearing length is taken to be a small parameter. Moreover, it is assumed that the microbearing cross-section varies slowly, which implies that all physical quantities vary slowly in x-direction. The model solution is treated by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the second one involves the influence of rarefaction effect. The analytical solutions of the pressure, velocity, and temperature for moderately high Reynolds numbers are presented here. For these flow conditions the inertia, convection, dissipation, and rate at which work is done in compressing the element of fluid are presented in the second approximation, also.",
publisher = "Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd",
journal = "Thermal Science",
title = "A microbearing gas flow with different walls' temperatures",
pages = "132-119",
number = "1",
volume = "16",
doi = "10.2298/TSCI110804086M"
}

Milićev, S.,& Stevanović, N.. (2012). A microbearing gas flow with different walls' temperatures. in Thermal Science
Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd., 16(1), 119-132.
https://doi.org/10.2298/TSCI110804086M

Milićev S, Stevanović N. A microbearing gas flow with different walls' temperatures. in Thermal Science. 2012;16(1):119-132.
doi:10.2298/TSCI110804086M .

Milićev, Snežana, Stevanović, Nevena, "A microbearing gas flow with different walls' temperatures" in Thermal Science, 16, no. 1 (2012):119-132,
https://doi.org/10.2298/TSCI110804086M . .

	5
	1
	5

Strujanje gasa u mikroležajima sa zidovima konstantnih temperatura

(Univerzitet u Beogradu - Mašinski fakultet, Beograd, 2010)

TY - JOUR
AU - Stevanović, Nevena
AU - Milićev, Snežana
PY - 2010
UR - https://machinery.mas.bg.ac.rs/handle/123456789/1027
AB - U radu je analizirano neizotermsko dvodimenzijsko stišljivo strujanje gasa u mikroležaju konstantnih i jednakih temperatura zida. Vrednost Knudsenovog broja je između 10-3 i 10-1, što odgovara režimu strujanja sa klizanjem. Ovaj režim strujanja definiše se jednačinama kontinuuma: Navije-Stoksovom i jednačinom energije i graničnim uslovom klizanja i temperaturskog skoka na zidu. Strujanje gasa je dozvučno, pa se mali parametar definiše kao ε = κM2/Re. Osim toga pretpostavljeno je se poprečni presek mikrokanala menja sporo, što dovodi do spore promene svih veličina u pravcu strujanja. Rešenje je dobijeno perturbacionom metodom. Prva aproksimacija predstavlja rešenje za slučaj strujanja gasa bez klizanja, dok se u drugoj aproksimaciji javlja uticaj klizanja i inercije. Dobijena su analitička rešenja za raspodelu pritiska, brzine i temperature u mikroležaju pri umereno velikim vrednostima Rejnoldsovog broja.
AB - A non-isothermal two-dimensional compressible gas flow in a slider microbearing with constant and equal wall temperature is investigated in this paper analytically. The slip flow is defined by the Navier-Stokes and energy continuum equations along with the velocity slip and the temperature jump first order boundary conditions. Knudsen number is in the range of 10-3 to 10-1, which corresponds to the slip flow. The gas flow is subsonic and the ratio κM2/Re is taken to be a small parameter. Moreover, it is assumed that the microbearing cross-section varies slowly, which implies that all physical quantities vary slowly in x-direction. The model solution is treated by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the second one involves the influence of inertia as well as rarefaction effect. The analytical solutions of the pressure, velocity and temperature for moderately high Reynolds numbers are obtained.
PB - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2 - FME Transactions
T1 - Strujanje gasa u mikroležajima sa zidovima konstantnih temperatura
T1 - A constant wall temperature microbearing gas flow
EP - 77
IS - 2
SP - 71
VL - 38
UR - https://hdl.handle.net/21.15107/rcub_machinery_1027
ER -

@article{
author = "Stevanović, Nevena and Milićev, Snežana",
year = "2010",
abstract = "U radu je analizirano neizotermsko dvodimenzijsko stišljivo strujanje gasa u mikroležaju konstantnih i jednakih temperatura zida. Vrednost Knudsenovog broja je između 10-3 i 10-1, što odgovara režimu strujanja sa klizanjem. Ovaj režim strujanja definiše se jednačinama kontinuuma: Navije-Stoksovom i jednačinom energije i graničnim uslovom klizanja i temperaturskog skoka na zidu. Strujanje gasa je dozvučno, pa se mali parametar definiše kao ε = κM2/Re. Osim toga pretpostavljeno je se poprečni presek mikrokanala menja sporo, što dovodi do spore promene svih veličina u pravcu strujanja. Rešenje je dobijeno perturbacionom metodom. Prva aproksimacija predstavlja rešenje za slučaj strujanja gasa bez klizanja, dok se u drugoj aproksimaciji javlja uticaj klizanja i inercije. Dobijena su analitička rešenja za raspodelu pritiska, brzine i temperature u mikroležaju pri umereno velikim vrednostima Rejnoldsovog broja., A non-isothermal two-dimensional compressible gas flow in a slider microbearing with constant and equal wall temperature is investigated in this paper analytically. The slip flow is defined by the Navier-Stokes and energy continuum equations along with the velocity slip and the temperature jump first order boundary conditions. Knudsen number is in the range of 10-3 to 10-1, which corresponds to the slip flow. The gas flow is subsonic and the ratio κM2/Re is taken to be a small parameter. Moreover, it is assumed that the microbearing cross-section varies slowly, which implies that all physical quantities vary slowly in x-direction. The model solution is treated by developing a perturbation scheme. The first approximation corresponds to the continuum flow conditions, while the second one involves the influence of inertia as well as rarefaction effect. The analytical solutions of the pressure, velocity and temperature for moderately high Reynolds numbers are obtained.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Strujanje gasa u mikroležajima sa zidovima konstantnih temperatura, A constant wall temperature microbearing gas flow",
pages = "77-71",
number = "2",
volume = "38",
url = "https://hdl.handle.net/21.15107/rcub_machinery_1027"
}

Stevanović, N.,& Milićev, S.. (2010). Strujanje gasa u mikroležajima sa zidovima konstantnih temperatura. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 38(2), 71-77.
https://hdl.handle.net/21.15107/rcub_machinery_1027

Stevanović N, Milićev S. Strujanje gasa u mikroležajima sa zidovima konstantnih temperatura. in FME Transactions. 2010;38(2):71-77.
https://hdl.handle.net/21.15107/rcub_machinery_1027 .

Stevanović, Nevena, Milićev, Snežana, "Strujanje gasa u mikroležajima sa zidovima konstantnih temperatura" in FME Transactions, 38, no. 2 (2010):71-77,
https://hdl.handle.net/21.15107/rcub_machinery_1027 .

Analytical solution of gas lubricated slider microbearing

(Springer Heidelberg, Heidelberg, 2009)

TY - JOUR
AU - Stevanović, Nevena
PY - 2009
UR - https://machinery.mas.bg.ac.rs/handle/123456789/981
AB - The analytical solution of a two-dimensional, isothermal, compressible gas flow in a slider microbearing is presented. A higher order accuracy of the solution is achieved by applying the boundary condition of Kn (2) order for the velocity slip on the wall, together with the momentum equation of the same order (known as the Burnett equation). The analytical solution is obtained by the perturbation analysis. The order of all terms in continuum and momentum equations and in boundary conditions is evaluated by incorporating the exact relation between the Mach, Reynolds and Knudsen numbers in the modelling procedure. Low Mach number flows in microbearing with slowly varying cross-sections are considered, and it is shown that under these conditions the Burnett equation has the same form as the Navier-Stokes equation. Obtained analytical results for pressure distribution, load capacity and velocity field are compared with numerical solutions of the Boltzmann equation and some semi-analytical results, and excellent agreement is achieved. The model presented in this paper is a useful tool for the prediction of flow conditions in the microbearings. Also, its results are the benchmark test for the verifications of various numerical procedures.
PB - Springer Heidelberg, Heidelberg
T2 - Microfluidics and Nanofluidics
T1 - Analytical solution of gas lubricated slider microbearing
EP - 105
IS - 1
SP - 97
VL - 7
DO - 10.1007/s10404-008-0367-4
ER -

@article{
author = "Stevanović, Nevena",
year = "2009",
abstract = "The analytical solution of a two-dimensional, isothermal, compressible gas flow in a slider microbearing is presented. A higher order accuracy of the solution is achieved by applying the boundary condition of Kn (2) order for the velocity slip on the wall, together with the momentum equation of the same order (known as the Burnett equation). The analytical solution is obtained by the perturbation analysis. The order of all terms in continuum and momentum equations and in boundary conditions is evaluated by incorporating the exact relation between the Mach, Reynolds and Knudsen numbers in the modelling procedure. Low Mach number flows in microbearing with slowly varying cross-sections are considered, and it is shown that under these conditions the Burnett equation has the same form as the Navier-Stokes equation. Obtained analytical results for pressure distribution, load capacity and velocity field are compared with numerical solutions of the Boltzmann equation and some semi-analytical results, and excellent agreement is achieved. The model presented in this paper is a useful tool for the prediction of flow conditions in the microbearings. Also, its results are the benchmark test for the verifications of various numerical procedures.",
publisher = "Springer Heidelberg, Heidelberg",
journal = "Microfluidics and Nanofluidics",
title = "Analytical solution of gas lubricated slider microbearing",
pages = "105-97",
number = "1",
volume = "7",
doi = "10.1007/s10404-008-0367-4"
}

Stevanović, N.. (2009). Analytical solution of gas lubricated slider microbearing. in Microfluidics and Nanofluidics
Springer Heidelberg, Heidelberg., 7(1), 97-105.
https://doi.org/10.1007/s10404-008-0367-4

Stevanović N. Analytical solution of gas lubricated slider microbearing. in Microfluidics and Nanofluidics. 2009;7(1):97-105.
doi:10.1007/s10404-008-0367-4 .

Stevanović, Nevena, "Analytical solution of gas lubricated slider microbearing" in Microfluidics and Nanofluidics, 7, no. 1 (2009):97-105,
https://doi.org/10.1007/s10404-008-0367-4 . .

	7
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	9

A new analytical solution of microchannel gas flow

(IOP Publishing Ltd, Bristol, 2007)

TY - JOUR
AU - Stevanović, Nevena
PY - 2007
UR - https://machinery.mas.bg.ac.rs/handle/123456789/696
AB - A two-dimensional, isothermal, compressible and subsonic gas flow in a microchannel with slowly varying cross-section is analytically investigated. The microchannel gas flow is described by the Burnett momentum equation that comprises the shear stress tensor of the second order. The application of the Burnett equation allows the introduction of the second-order boundary condition for the gas velocity slip on microchannel walls. The model solution is based on perturbation analysis. The analytical solution procedure incorporates the exact physical relation between Mach, Reynolds and Knudsen numbers, which enables the evaluation of the order of all terms within the balance equations and the boundary conditions and provides high accuracy of the model. It is shown that the Burnet equation has the same form as the Navier-Stokes equation for low Mach number flows in channels with slowly varying cross sections. The obtained analytical results are in excellent agreement with available measured data and numerical solutions of the Boltzmann equation. The presented analytical model is new since previous solutions are limited to microchannels with uniform cross sections, while here the presented solution is obtained for microchannels with varying cross sections. The presented model is a useful tool for the design and analysis of gas flows in microchannels, and it provides accurate benchmark results for the validation of the numerically obtained results.
PB - IOP Publishing Ltd, Bristol
T2 - Journal of Micromechanics and Microengineering
T1 - A new analytical solution of microchannel gas flow
EP - 1702
IS - 8
SP - 1695
VL - 17
DO - 10.1088/0960-1317/17/8/036
ER -

@article{
author = "Stevanović, Nevena",
year = "2007",
abstract = "A two-dimensional, isothermal, compressible and subsonic gas flow in a microchannel with slowly varying cross-section is analytically investigated. The microchannel gas flow is described by the Burnett momentum equation that comprises the shear stress tensor of the second order. The application of the Burnett equation allows the introduction of the second-order boundary condition for the gas velocity slip on microchannel walls. The model solution is based on perturbation analysis. The analytical solution procedure incorporates the exact physical relation between Mach, Reynolds and Knudsen numbers, which enables the evaluation of the order of all terms within the balance equations and the boundary conditions and provides high accuracy of the model. It is shown that the Burnet equation has the same form as the Navier-Stokes equation for low Mach number flows in channels with slowly varying cross sections. The obtained analytical results are in excellent agreement with available measured data and numerical solutions of the Boltzmann equation. The presented analytical model is new since previous solutions are limited to microchannels with uniform cross sections, while here the presented solution is obtained for microchannels with varying cross sections. The presented model is a useful tool for the design and analysis of gas flows in microchannels, and it provides accurate benchmark results for the validation of the numerically obtained results.",
publisher = "IOP Publishing Ltd, Bristol",
journal = "Journal of Micromechanics and Microengineering",
title = "A new analytical solution of microchannel gas flow",
pages = "1702-1695",
number = "8",
volume = "17",
doi = "10.1088/0960-1317/17/8/036"
}

Stevanović, N.. (2007). A new analytical solution of microchannel gas flow. in Journal of Micromechanics and Microengineering
IOP Publishing Ltd, Bristol., 17(8), 1695-1702.
https://doi.org/10.1088/0960-1317/17/8/036

Stevanović N. A new analytical solution of microchannel gas flow. in Journal of Micromechanics and Microengineering. 2007;17(8):1695-1702.
doi:10.1088/0960-1317/17/8/036 .

Stevanović, Nevena, "A new analytical solution of microchannel gas flow" in Journal of Micromechanics and Microengineering, 17, no. 8 (2007):1695-1702,
https://doi.org/10.1088/0960-1317/17/8/036 . .

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	35

Pad pritiska usled trenja pri strujanju razređenog gasa u mikrokanalima

Stevanović, Nevena; Đorđević, Vladan D.

(Univerzitet u Beogradu - Mašinski fakultet, Beograd, 2005)

TY - JOUR
AU - Stevanović, Nevena
PY - 2005
UR - https://machinery.mas.bg.ac.rs/handle/123456789/538
AB - Strujanje gasa kroz mikrokanale prisutno je u mikro elektro mehaničkim sistemima (MEMS). Dimenzije mikrokanala su reda veličine µm, pa dužina slobodnog puta molekula nije zanemarljivo mala. Efekat razređenosti dolazi do izražaja, pa je potrebno uzeti u obzir granične uslove klizanja na zidu. U ovom radu dobijena su rešenja za dvodimenzijsko, izotermsko, stišljivo strujanje gasa kroz mikrokanale sporo promenljivog poprečnog preseka, pri veoma malim vrednostima Mach-ovog broja. Korišćeni su granični uslovi klizanja drugog reda, što je uslovilo korišćenje i jednačina količine kretanja drugog reda, tj. Burnettovih jednačina. Pokazalo se da se za pomenute uslove strujanja one svode na Navier-Stokes-ove. U radu je prikazano analitičko rešenje za slučajeve strujanja gasa kada je vrednost Reynolds-ovog broja veća, pa osim razređenosti do izražaja dolazi i uticaj inercije. Za takve uslove strujanja dobijena su rešenja za polje pritiska i brzine, kao i analitički izrazi za određivanje faktora trenja duž kanala i njegove srednje vrednosti. Iz njih se vidi da pri strujanju razređenog gasa faktor trenja zavisi i od Reynolds-ovog i od Knudsen-ovog broja.
AB - Gas flows through micro-channels are encountered in many applications of Micro-Electro-Mechanical Systems (MEMS) Dimensions of the MEMS are within µm range, which means that rarefaction must be considered. It is common to use slip conditions at the wall and continuum equations for solving these problems. In this paper isothermal, compressible and subsonic gas flows through micro channels with slowly varying cross sections are analyzed. In order to provide a higher accuracy, the second order boundary conditions are used. This approach requires the higher order momentum equation, i.e. the Burnett equation. Solutions are obtained for higher Reynolds number values when the inertia effect is important together with the rarefaction effect. For such flow conditions analytical relations for pressure and velocity fields are presented. Also, analytical expressions for the friction factor change along a micro channel with constant cross section and for the average friction factor are obtained. The derived relations show that the friction factor depends not only on the Reynolds number, but also on the Knudsen number.
PB - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2 - FME Transactions
T1 - Pad pritiska usled trenja pri strujanju razređenog gasa u mikrokanalima
T1 - Friction pressure loss in micro channel rarefied gas flows
EP - 72
IS - 2
SP - 65
VL - 33
UR - https://hdl.handle.net/21.15107/rcub_machinery_538
ER -

@article{
author = "Stevanović, Nevena",
year = "2005",
abstract = "Strujanje gasa kroz mikrokanale prisutno je u mikro elektro mehaničkim sistemima (MEMS). Dimenzije mikrokanala su reda veličine µm, pa dužina slobodnog puta molekula nije zanemarljivo mala. Efekat razređenosti dolazi do izražaja, pa je potrebno uzeti u obzir granične uslove klizanja na zidu. U ovom radu dobijena su rešenja za dvodimenzijsko, izotermsko, stišljivo strujanje gasa kroz mikrokanale sporo promenljivog poprečnog preseka, pri veoma malim vrednostima Mach-ovog broja. Korišćeni su granični uslovi klizanja drugog reda, što je uslovilo korišćenje i jednačina količine kretanja drugog reda, tj. Burnettovih jednačina. Pokazalo se da se za pomenute uslove strujanja one svode na Navier-Stokes-ove. U radu je prikazano analitičko rešenje za slučajeve strujanja gasa kada je vrednost Reynolds-ovog broja veća, pa osim razređenosti do izražaja dolazi i uticaj inercije. Za takve uslove strujanja dobijena su rešenja za polje pritiska i brzine, kao i analitički izrazi za određivanje faktora trenja duž kanala i njegove srednje vrednosti. Iz njih se vidi da pri strujanju razređenog gasa faktor trenja zavisi i od Reynolds-ovog i od Knudsen-ovog broja., Gas flows through micro-channels are encountered in many applications of Micro-Electro-Mechanical Systems (MEMS) Dimensions of the MEMS are within µm range, which means that rarefaction must be considered. It is common to use slip conditions at the wall and continuum equations for solving these problems. In this paper isothermal, compressible and subsonic gas flows through micro channels with slowly varying cross sections are analyzed. In order to provide a higher accuracy, the second order boundary conditions are used. This approach requires the higher order momentum equation, i.e. the Burnett equation. Solutions are obtained for higher Reynolds number values when the inertia effect is important together with the rarefaction effect. For such flow conditions analytical relations for pressure and velocity fields are presented. Also, analytical expressions for the friction factor change along a micro channel with constant cross section and for the average friction factor are obtained. The derived relations show that the friction factor depends not only on the Reynolds number, but also on the Knudsen number.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Pad pritiska usled trenja pri strujanju razređenog gasa u mikrokanalima, Friction pressure loss in micro channel rarefied gas flows",
pages = "72-65",
number = "2",
volume = "33",
url = "https://hdl.handle.net/21.15107/rcub_machinery_538"
}

Stevanović, N.. (2005). Pad pritiska usled trenja pri strujanju razređenog gasa u mikrokanalima. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 33(2), 65-72.
https://hdl.handle.net/21.15107/rcub_machinery_538

Stevanović N. Pad pritiska usled trenja pri strujanju razređenog gasa u mikrokanalima. in FME Transactions. 2005;33(2):65-72.
https://hdl.handle.net/21.15107/rcub_machinery_538 .

Stevanović, Nevena, "Pad pritiska usled trenja pri strujanju razređenog gasa u mikrokanalima" in FME Transactions, 33, no. 2 (2005):65-72,
https://hdl.handle.net/21.15107/rcub_machinery_538 .

On the simultaneous effects of gas rarefaction, wall porosity, and inertia in microchannel flows

(Wiley-V C H Verlag Gmbh, Weinheim, 2005)

TY  - JOUR
AU  - Stevanović, Nevena
AU  - Đorđević, Vladan D.
PY  - 2005
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/491
AB  - The superposition of two effects that cause the flow to slip over the walls of a microchannel: Gas rarefaction and wall porosity, is treated in the paper. At that, in order to account for moderately high values of the Reynolds number, observed in some experiments, the effect of inertia is included into the analysis as a second order effect. The approach is fully analytic and consists in the development of a simple perturbation scheme in which the Knudsen number plays the role of a unique small parameter. The obtained results are in qualitative agreement with experiments, and may be usefully applied for the design of aerostatic bearings in which a porous material is used as the flow restrictor.
PB  - Wiley-V C H Verlag Gmbh, Weinheim
T2  - Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik
T1  - On the simultaneous effects of gas rarefaction, wall porosity, and inertia in microchannel flows
EP  - 522
IS  - 7
SP  - 516
VL  - 85
DO  - 10.1002/zamm.200310199
ER  -

@article{
author = "Stevanović, Nevena and Đorđević, Vladan D.",
year = "2005",
abstract = "The superposition of two effects that cause the flow to slip over the walls of a microchannel: Gas rarefaction and wall porosity, is treated in the paper. At that, in order to account for moderately high values of the Reynolds number, observed in some experiments, the effect of inertia is included into the analysis as a second order effect. The approach is fully analytic and consists in the development of a simple perturbation scheme in which the Knudsen number plays the role of a unique small parameter. The obtained results are in qualitative agreement with experiments, and may be usefully applied for the design of aerostatic bearings in which a porous material is used as the flow restrictor.",
publisher = "Wiley-V C H Verlag Gmbh, Weinheim",
journal = "Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik",
title = "On the simultaneous effects of gas rarefaction, wall porosity, and inertia in microchannel flows",
pages = "522-516",
number = "7",
volume = "85",
doi = "10.1002/zamm.200310199"
}

Stevanović, N.,& Đorđević, V. D.. (2005). On the simultaneous effects of gas rarefaction, wall porosity, and inertia in microchannel flows. in Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik
Wiley-V C H Verlag Gmbh, Weinheim., 85(7), 516-522.
https://doi.org/10.1002/zamm.200310199

Stevanović N, Đorđević VD. On the simultaneous effects of gas rarefaction, wall porosity, and inertia in microchannel flows. in Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik. 2005;85(7):516-522.
doi:10.1002/zamm.200310199 .

Stevanović, Nevena, Đorđević, Vladan D., "On the simultaneous effects of gas rarefaction, wall porosity, and inertia in microchannel flows" in Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik, 85, no. 7 (2005):516-522,
https://doi.org/10.1002/zamm.200310199 . .

A high order theory for an isothermal rarefied gas flow in micro channels