TITLE:
Variational Approach to 2D and 3D Heat Conduction Modeling
AUTHORS:
Slavko Đurić, Ivan Aranđelović, Milan Milotić
KEYWORDS:
Classical Equation of Heat Conduction, Generalized Equation of Heat Conduction, Calculus of Variations, Approximate Solution
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.4,
April
30,
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.