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

摘要

We obtained a new representation of a solution of the heat conductionequation with boundary condition of the third kind for a layer. The result ispresented as a superposition of fundamental solutions for an unbounded systemwith variable coefficients, the explicit form of which is given. We considerthe well-known problem of the evolution of the temperature field initiallyuniformly distributed in a layer. The distribution of the temperature field isrepresented in terms of the obtained functions.