Heat transfer analysis of rectangular porous fins in local thermal non-equilibrium model

In this study, an analytical solution of a porous fin with natural convection and radiation heat transfer is carried out. For the first time, the analysis is accomplished in Local Thermal Non-Equilibrium (LTNE) model. The investigation is carried out on a porous fin with finite length and adiabatic tip. The Darcy model and Boussinesq approximation for buoyancy effects are used to evaluate the infiltration velocity in the porous medium. Two energy equations are solved using the Adomian Decomposition Method (ADM). The solution is validated with the numerical solution of the finite difference method, and with the asymptotic solution for the Local Thermal Equilibrium (LTE) model. The results are presented in terms of temperature profiles and total average Nusselt numbers. They pointed out the effects of internal and external radiation and convection heat transfer, as well as thermal conductivity ratio and dimensionless thickness. It was found that solid phase temperature profiles decrease as the Biot, Bi, and Rayleigh, Ra*, numbers decrease, whereas the difference between the solid phase and fluid phase temperatures, for assigned Bi, decreases for lower Ra. Thermal conductivity ratio and dimensionless thickness increase engender higher solid phase temperature for assigned Bi and Ra*. The total Nusselt number increases as Ra*, Bi and external radiation increase, whereas it decreases with the thermal conductivity ratio. Criteria to compare LTNE and LTE assumptions are proposed, and they highlight the fact that the minimum Biot number to accept the LTE assumption becomes lower as the Rayleigh number decreases.