TY  - JOUR
AU  - Đurić, Slavko
AU  - Aranđelović, Ivan
AU  - Milotić, Milan
PY  - 2024
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7799
AB  - The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximate solution of the generalized (hyperbolic) 2D and 3D equation for the considered plate and cube is also proposed. Approximate solutions were obtained by applying calculus of variations and Euler-Lagrange equations. In order to verify the correctness of the proposed approximate solutions, they were compared with the exact solutions of parabolic and hyperbolic equations. The paper also presents the research on the influence of time parameters τ as well as the relaxation times τ∗ to the variation of the profile of the temperature field for the considered aluminum plate and cube.
PB  - Scientific Research Publishing
T2  - Journal of Applied Mathematics and Physics, 2024, 12, 1383-1400
T1  - Variational Approach to 2D and 3D Heat Conduction Modeling
EP  - 1400
IS  - 4
SP  - 1383
VL  - 12
DO  - 10.4236/jamp.2024.124085
ER  - 

@article{
author = "Đurić, Slavko and Aranđelović, Ivan and Milotić, Milan",
year = "2024",
abstract = "The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximate solution of the generalized (hyperbolic) 2D and 3D equation for the considered plate and cube is also proposed. Approximate solutions were obtained by applying calculus of variations and Euler-Lagrange equations. In order to verify the correctness of the proposed approximate solutions, they were compared with the exact solutions of parabolic and hyperbolic equations. The paper also presents the research on the influence of time parameters τ as well as the relaxation times τ∗ to the variation of the profile of the temperature field for the considered aluminum plate and cube.",
publisher = "Scientific Research Publishing",
journal = "Journal of Applied Mathematics and Physics, 2024, 12, 1383-1400",
title = "Variational Approach to 2D and 3D Heat Conduction Modeling",
pages = "1400-1383",
number = "4",
volume = "12",
doi = "10.4236/jamp.2024.124085"
}

Đurić, S., Aranđelović, I.,& Milotić, M.. (2024). Variational Approach to 2D and 3D Heat Conduction Modeling. in Journal of Applied Mathematics and Physics, 2024, 12, 1383-1400
Scientific Research Publishing., 12(4), 1383-1400.
https://doi.org/10.4236/jamp.2024.124085

Đurić S, Aranđelović I, Milotić M. Variational Approach to 2D and 3D Heat Conduction Modeling. in Journal of Applied Mathematics and Physics, 2024, 12, 1383-1400. 2024;12(4):1383-1400.
doi:10.4236/jamp.2024.124085 .

Đurić, Slavko, Aranđelović, Ivan, Milotić, Milan, "Variational Approach to 2D and 3D Heat Conduction Modeling" in Journal of Applied Mathematics and Physics, 2024, 12, 1383-1400, 12, no. 4 (2024):1383-1400,
https://doi.org/10.4236/jamp.2024.124085 . .

TY  - JOUR
AU  - Đurić, Slavko
AU  - Aranđelović, Ivan
AU  - Milotić, Milan
PY  - 2024
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7744
AB  - It is known that Fourier’s heat equation, which is parabolic, implies an infinite
velocity propagation, or, in other words, that the mechanism of heat
conduction is established instantaneously under all conditions. This is unacceptable
on physical grounds in spite of the fact that Fourier’s law agrees well
with experiment. However, discrepancies are likely to occur when extremely
short distances or extremely short time intervals are considered, as they must
in some modern problems of aero-thermodynamics. Cattaneo and independently
Vernotte proved that such process can be described by Heaviside’s telegraph
equation. This paper shows that this fact can be derived using calculus of
variations, by application of the Euler-Lagrange equation. So, we proved that
the equation of heat conduction with finite velocity propagation of the thermal
disturbance can be obtained as a solution to one variational problem
PB  - Scientific Research Publishing
T2  - Journal of Applied Mathematics and Physics
T1  - Variational Approach to Heat Conduction Modeling
EP  - 248
IS  - 1
SP  - 234
VL  - 12
UR  - https://hdl.handle.net/21.15107/rcub_machinery_7744
ER  - 

@article{
author = "Đurić, Slavko and Aranđelović, Ivan and Milotić, Milan",
year = "2024",
abstract = "It is known that Fourier’s heat equation, which is parabolic, implies an infinite
velocity propagation, or, in other words, that the mechanism of heat
conduction is established instantaneously under all conditions. This is unacceptable
on physical grounds in spite of the fact that Fourier’s law agrees well
with experiment. However, discrepancies are likely to occur when extremely
short distances or extremely short time intervals are considered, as they must
in some modern problems of aero-thermodynamics. Cattaneo and independently
Vernotte proved that such process can be described by Heaviside’s telegraph
equation. This paper shows that this fact can be derived using calculus of
variations, by application of the Euler-Lagrange equation. So, we proved that
the equation of heat conduction with finite velocity propagation of the thermal
disturbance can be obtained as a solution to one variational problem",
publisher = "Scientific Research Publishing",
journal = "Journal of Applied Mathematics and Physics",
title = "Variational Approach to Heat Conduction Modeling",
pages = "248-234",
number = "1",
volume = "12",
url = "https://hdl.handle.net/21.15107/rcub_machinery_7744"
}

Đurić, S., Aranđelović, I.,& Milotić, M.. (2024). Variational Approach to Heat Conduction Modeling. in Journal of Applied Mathematics and Physics
Scientific Research Publishing., 12(1), 234-248.
https://hdl.handle.net/21.15107/rcub_machinery_7744

Đurić S, Aranđelović I, Milotić M. Variational Approach to Heat Conduction Modeling. in Journal of Applied Mathematics and Physics. 2024;12(1):234-248.
https://hdl.handle.net/21.15107/rcub_machinery_7744 .

Đurić, Slavko, Aranđelović, Ivan, Milotić, Milan, "Variational Approach to Heat Conduction Modeling" in Journal of Applied Mathematics and Physics, 12, no. 1 (2024):234-248,
https://hdl.handle.net/21.15107/rcub_machinery_7744 .