Analytical Solution of the Problem on the Three-Dimensional Transient Heat Conduction in a Multilayer Rectangular Region

Abstract

An exact analytical solution of the problem on the three-dimensional transient heat conduction in a Rectangular with multiple layers, in which time-dependent, spatially non-uniform internal volume heat sources are installed, is presented. The transient temperature distribution in this rectangle was determined with the use of the eigenfunction expansion method. The solution obtained is valid for any combination of homogenous first- and second-kind boundary conditions in the Y and Z directions of the rectangle and for the nonhomogeneous third-kind boundary conditions in the X direction. As a partial case, the problem on the heat conduction in a three-layer rectangle region was solved.