Abstract
We examine the transition region between two solids which state differs from the state of contacting media. Small thickness of the intermediate region allows us to reduce a three-dimensional problem to a two-dimensional one for a median surface endowed with equivalent physical properties. In the present paper, we consider the generalized boundary conditions of nonperfect thermal contact for the time-fractional heat conduction equation with the Caputo derivative and solve the problem for a composite medium consisting of two semi-infinite regions. Numerical results are illustrated graphically.
Highlights
Near the interface between two solids, there arises a transition region which state differs from the state of contacting media owing to different conditions of material–particle interaction
For the classical heat conduction equation, which is based on the conventional Fourier law, the reduction of the three-dimensional problem to the simplified two-dimensional one was proposed by Marguerre [16,17] and later on developed by many authors
We consider the generalized boundary conditions of nonperfect thermal contact for the time-fractional heat conduction equation with the Caputo derivative and solve the problem for a composite medium consisting of two semi-infinite regions
Summary
Near the interface between two solids, there arises a transition region which state differs from the state of contacting media owing to different conditions of material–particle interaction. For the classical heat conduction equation, which is based on the conventional Fourier law, the reduction of the three-dimensional problem to the simplified two-dimensional one was proposed by Marguerre [16,17] and later on developed by many authors (see [18,19,20,21,22,23,24,25], among others). In this case, the assumption on linear or polynomial dependence of temperature on the normal coordinate or more general operator method was used.
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