Variational Approach to Heat Conduction Modeling
Апстракт
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
Кључне речи:
Telegraph Equation / Heat Equation / Heat Conduction / Calculus of VariationsИзвор:
Journal of Applied Mathematics and Physics, 2024, 12, 1, 234-248Издавач:
- Scientific Research Publishing
Финансирање / пројекти:
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200105 (Универзитет у Београду, Машински факултет) (RS-MESTD-inst-2020-200105)
Колекције
Институција/група
Mašinski fakultetTY - 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 .