Analytical solution of the problem of heat conduction in a bounded multilayer region containing a local volume source in a layer

In the present paper, a solution to the heat conduction problem is obtained for a finite multilayer region containing a heat source in one of the layers. For the parameters defining the solution, recurrent relations are derived, which can be used to unify both the computer program and the form of the solution, regardless of the number of layers. A solution for the structure of an integrated circuit is analyzed numerically.