Entransy Theory and Its Application to Heat Transfer Analyses in Porous Media

A physical quantity, entransy, is suggested to describe the heat transfer capability of the porous medium in terms of the analogy between heat conduction and electrical conduction. The entransy, which corresponds to the electric potential energy in a capacitor and the fluid potential energy in porous media respectively, is dissipated during heat transfer processes and the entransy dissipation is a measure of the heat transfer irreversibility. Since the existing expression of effective thermal conductivity (ETC) defined by the ratio of the heat flux to the temperature difference is not valid for the porous media with complex thermal and geometric boundary conditions, the entransy dissipation based ETC has been defined to characterize the heat transfer performance of porous media. Another concept of nondimensional particle size (NPS), i.e. the ratio of the element/particle size to the porous media thickness, is introduced to numerically examine the effect of element/particle sizes with the emphasis on the influence of boundary conditions on the new ETC of porous media. The results show that for a two-phase porous media with parallel mode, starting from heat flux boundary there is a thermal entry region of heat conduction, where the temperature distribution is non-uniform. Hence, reducing the NPS will effectively reduce the thermal entry region and the total entransy dissipation rate, and consequently increase the ETC of porous media. Because the temperature profile varies with distance along the heat flow in the entire heat conduction domain for the regular particle distribution mode with a uniform heat flux boundary, decreasing the NPS will heighten the temperature fluctuation frequency in the entire domain, which enlarges the total entransy dissipation rate, and finally leads to the reduction of the ETC of porous media.