Variational Approach to Heat Conduction Modeling
Variational Approach to Heat Conduction Modeling作者机构：Faculty of Traffic Engineering University of East Sarajevo Doboj Bosnia and Herzegovina Faculty of Mechanical Engineering University of Belgrade Belgrade Republic of Serbia
出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)
年 卷 期：2024年第12卷第1期
页 面：234-248页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Telegraph Equation Heat Equation Heat Conduction Calculus of Variations
摘 要：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.
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