Publicado 18 números por año
ISSN Imprimir: 1064-2285
ISSN En Línea: 2162-6561
Indexed in
ANALYTICAL SOLUTION OF THE PROBLEM OF NON-FOURIER HEAT CONDUCTION IN A SLAB USING THE SOLUTION STRUCTURE THEOREMS
SINOPSIS
This paper studies an analytical method which combines the superposition technique along with the solution structure theorem such that a closed-form solution of the hyperbolic heat conduction equation can be obtained by using the fundamental mathematics. In this paper, the non-Fourier heat conduction in a slab at whose a left boundary there is a constant heat flux and at the right boundary, a constant temperature Ts = 15, has been investigated. The complicated problem is split into multiple simpler problems that in turn can be combined to obtain a solution to the original problem. The original problem is divided into five subproblems by setting the heat generation term, the initial conditions, and the boundary conditions for different values in each subproblem. All the solutions given in this paper can be easily proven by substituting them into the governing equation. The results show that the temperature will start retreating at approximately t = 2 and for t = 2 the temperature at the left boundary decreases leading to a decrease in the temperature in the domain. Also, the shape of the profiles remains nearly the same after t = 4. The solution presented in this study can be used as benchmark problems for validation of future numerical methods.
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Yang Wanyou, Zhou Qinghua, Zhai Yu, Lyu Ding, Huang Yanyan, Wang Jiaxu, Jin Xiaoqing, Keer Leon M., Wang Q. Jane, Semi-analytical solution for steady state heat conduction in a heterogeneous half space with embedded cuboidal inhomogeneity, International Journal of Thermal Sciences, 139, 2019. Crossref
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Mozafarifard Milad, Toghraie Davood, Numerical analysis of time-fractional non-Fourier heat conduction in porous media based on Caputo fractional derivative under short heating pulses, Heat and Mass Transfer, 56, 11, 2020. Crossref
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Ymeli Guillaume Lambou, Kamdem Hervé Thierry Tagne, Tchinda Réné, Lazard Myriam, Analytical layered solution of radiation and non–Fourier conduction problems in optically complex media, International Journal of Heat and Mass Transfer, 145, 2019. Crossref
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Tribess Richard, Bertoli Sávio L., K. de Souza Carolina, Reiter Mercedes Gabriela Ratto, Krautler Maria I. L., Gonçalves Marcel J., Analytical solution of a heat transfer model for a tubular co-current diluted moving bed heat exchanger with indirect heating and thermal losses to the environment, Chemical Engineering Communications, 209, 6, 2022. Crossref