Semi-analytical solution of thermal energy storage system with conjugate laminar forced convection

A thermal energy storage system with a hollow cylinder of Phase Change Material (PCM) was studied semi-analytically. The melting of the PCM was solved by using an integral approximate method, and heat transfer in the container wall was treated as a radial one dimensional conduction problem. The forced convective heat transfer inside the tube was solved by an analytical method, which was coupled with the heat conduction in the PCM and the container wall. The results show that the laminar forced convective heat transfer inside the tube never reached the fully developed state, even for a very long tube. For a transfer fluid of moderate Prandtl number, the laminar forced convective transfer inside the tube must be solved simultaneously with the phase change of the PCM.