Integral transform solution for hyperbolic heat conduction in a finite slab |
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Authors: | Evaldiney R. Monteiro,Emanuel N. Macê do,Joã o N.N. Quaresma,Renato M. Cotta |
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Affiliation: | 1. Mining Engineering Department, CSSPA, Campus de Marabá, Universidade Federal do Pará, UFPA;2. School of Chemical Engineering, FEQ/ITEC/UFPA, Universidade Federal do Pará, 66075-110, Belém, PA, Brazil;3. Mechanical Engineering Department — POLI & COPPE, Universidade Federal do Rio de Janeiro, UFRJ, Cx. Postal 68503 — Cidade Universitária, 21945-970, Rio de Janeiro, RJ, Brazil |
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Abstract: | An analytical integral transformation of the thermal wave propagation problem in a finite slab is obtained through the generalized integral transform technique (GITT). The use of the GITT approach in the analysis of the hyperbolic heat conduction equation leads to a coupled system of second order ordinary differential equations in the time variable. The resulting transformed ODE system is then numerically solved by Gear's method for stiff initial value problems. Numerical results are presented for the local and average temperatures with different Biot numbers and dimensionless thermal relaxation times, permitting a critical evaluation of the technique performance. A comparison is also performed with previously reported results in the literature for special cases and with those produced through the application of the Laplace transform method (LTM), and the finite volume-Gear method (FVGM). |
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Keywords: | Hyperbolic heat conduction Generalized integral transform technique Laplace transform Finite volume-Gear method |
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