Analytical Solution of Steady Heat Transfer in a Multi-Layer Porous Media under Local Thermal Non-Equilibrium Condition

This paper is concerned with the conduction heat transfer between two parallel plates filled with a multi-layer porous medium under a Local Thermal non - equilibrium condition. Analytical solution is obtained for both fluid and solid temperature fields in the porous channel incorporating the effects of thermal conductivity ratio, porosity, and a non-dimensional heat transfer coefficient at the pore level. The effects of the variable porosity on the temperature distribution are completely shown and compared with the constant porosity model. The presented method for analysis of heat transfer in a multi-layer porous medium is a generalized solution which is valid for arbitrary number of internal porous layers. The local temperature difference between fluid and solid phases is also calculated for a wide range of parameters. The results confirmed that the conductivity ratio and the porosity of the internal layers have significant role in the thermal modeling of the porous channel.