Integral transform solution for hyperbolic heat conduction in a finite slab

• Published in: International communications in heat and mass transfer 2009-04, Vol.36 (4), p.297-303
• Main Authors: Monteiro, Evaldiney R., Macêdo, Emanuel N., Quaresma, João N.N., Cotta, Renato M.
• Format: Article
• Language: English
• Subjects: Analytical and numerical techniques; Conduction; Exact sciences and technology; Finite volume-Gear method; Fundamental areas of phenomenology (including applications); Generalized integral transform technique; Heat conduction; Heat transfer; Hyperbolic heat conduction; Integrals; Laplace transform; Mathematical analysis; Mathematical models; Physics; Slabs; Transforms
• ISSN: 0735-1933; 1879-0178
• DOI: 10.1016/j.icheatmasstransfer.2009.01.002

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).