Third Boundary-Value Problem of the Heat Conduction Equation for a System with Plane-Parallel Boundaries

Physics – Mathematical Physics

Scientific paper

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16 pages, 2 figures, RevTeX

Scientific paper

We obtained a new representation of a solution of the heat conduction equation with boundary condition of the third kind for a layer. The result is presented as a superposition of fundamental solutions for an unbounded system with variable coefficients, the explicit form of which is given. We consider the well-known problem of the evolution of the temperature field initially uniformly distributed in a layer. The distribution of the temperature field is represented in terms of the obtained functions.

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