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Heat conduction in a finite medium using the fractional single-phase-lag model

Siedlecka Urszula

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 2

401--407

In the paper, a solution of the time-fractional single-phase-lagging heat conduction problem in finite regions is presented. The heat conduction equation with the Caputo time-derivative is complemented by the Robin boundary conditions. The Laplace transform with respect to the time variable and an expansion in the eigenfunctions series with respect to the space variable was applied. A method for the numerical inversion of the Laplace transforms was used. Formulation and solution of the problem cover the heat conduction in a finite slab, hollow cylinder and hollow sphere. The effect of the fractional order of the Caputo derivative and the phase-lag parameter on the temperature distribution in a slab has been numerically investigated.

Laplace transform solution of the problem of time-fractional heat conduction in a two-layered slab

Kukla S., Siedlecka U.

Journal of Applied Mathematics and Computational Mechanics

2015

Vol. 14, nr 4

105--113

In this paper the Laplace transformation for solving the problem of fractional heat conduction in a two-layered slab has been applied. The different orders of Caputo derivative in the time-fractional equation governed the heat transfer in the layers are assumed. The inverse Laplace transform by using a numerical method is determined. The numerical results obtained by using of the eigenfunctions method and by numerically inverting the Laplace transform are compared.