Temperature-dependent conductivity in forced convection of heat exchangers filled with porous media: A perturbation solution

Effects of variation of the thermal conductivity on forced convection in a parallel-plates channel heat exchanger occupied by a fluid saturated porous medium are investigated analytically based on the perturbation methods. Walls of the channel are kept at a constant heat flux. Thermal conductivity of the medium is assumed to be a linear function of temperature (due to moderate radiation heat transfer in cellular foams or temperature dependent conductivity of the material). The Brinkman–Forchheimer–extended Darcy model for the flow field is used. Relations representing the temperature profile and Nusselt number as functions of porous medium shape parameter and thermal conductivity variation parameter are derived. Obtained Nusselt number and temperature profile are studied parametrically. No analytical investigation based on a variable conductivity approach for Brinkman–Forchheimer–extended Darcy model has been previously performed. Results show that a linear increase in the thermal conductivity of the medium results in a semi-linear increase in the Nusselt number.