Solution of an initial-boundary value problem for heat conduction in a parallelepiped by time partitioning

An initial-boundary value problem for transient heat conduction in a rectangular parallelepiped is studied. Solutions for the temperature and heat flux are represented as integrals involving the Greenʹs function (GF), the initial and boundary data, and volumetric energy generation. Use of the usual GF obtained by separation of variables leads to slowly convergent series. To circumvent this difficulty, the dummy time interval of integration is partitioned into a short time and a long time subintervals where the GFs are approximated by their small and large time representations. This paper deals with the analysis and implementation of this time partitioning method.