Analytical Investigation of Forced Convection Heat Transfer in a Channel Partially Filled with a Porous Material under Local Thermal Non-Equilibrium Condition

Forced convection through a channel partially filled with a porous medium is investigated analytically in the present work. Thermally developed condition is considered and the local thermal non-equilibrium model is utilized to obtain the exact solutions of both fluid and solid temperature fields for flow inside the porous material as well as for flow in the clear region. The ratios of the porous medium thickness to the channel height (S) by which the temperature difference between the two phases approach to zero, for different values of Biot number, the ratio of solid effective thermal conductivity to that of the fluid, and Darcy number are obtained. The results show that, as the porous thickness increases, the error increases, and the validation of thermal equilibrium (LTE) model fails and the fully filled channel, yields the maximum error. Generally, when the channel is partially filled with the porous material for S<0.6, the error is not significant and the LTE model validates, such that for small values of Biot number or thermal conductivity, even at S=1 the LTE model is valid. However, for values of porous thickness larger than 0.6 the LTE condition is not valid. Keywords: Analytical solution, Porous media