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1 2015

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A solution to the problem of time-fractional heat conduction in a multi-layer slab

Siedlecka U., Kukla S.

Journal of Applied Mathematics and Computational Mechanics

2015

Vol. 14, nr 3

95--102

In this paper a solution of the time-fractional heat conduction problem in a multilayer slab is presented. The boundary conditions of the third kind and the perfect contact at the interfaces are assumed. A space-time dependent volumetric heat source in the slab and time dependent surroundings temperatures are taken into account in the formulation of the problem. The solution is obtained in the form of a series expansion with respect to eigenfunctions of an auxiliary problem. A numerical example shows temperature distribution in the slab for various values of the order of the Caputo fractional derivative in the heat conduction equation.