Approximate analytical solution for the heat transfer in packed beds for solar thermal storage in building simulators

Schumann solution for the heating (cooling) of onedimensional packed beds by the passage of a hot (cool) fluid is extended by the incorporation of a small solid thermal conductivity by means of using  perturbation methods based on the Laplace transform and a Picard iteration for the Green’s functions for the heat transfer of both phases. The new solution shows smooth heat front propagation through the medium during either the heating or the cooling (depending on its initial temperature) and can be easily incorporated into solar thermal storage simulators currently using Schumann solution, but with increased thermal accuracy.