Kambiz Vafai
University of California Riverside, USA
Abstract: The phenomenon of heat flux bifurcation in porous medium is presented for the first time in this work. To this end, convective heat transfer within a channel filled with a porous medium subject to a constant wall heat flux boundary condition, with internal heat generation in both the fluid and solid phases, is investigated analytically. A local thermal non-equilibrium (LTNE) model is used to represent the energy transport within the porous medium. Exact solutions are derived for both the fluid and solid temperature distributions for two primary approaches (Models A and B) for the constant wall heat flux boundary condition. It is shown that the internal heat generation in the solid phase is significant for the heat transfer characteristics. The phenomenon of temperature gradient bifurcation for the fluid and solid phases at the wall for Model A is established and demonstrated. When the phenomenon of heat flux bifurcation occurs, the direction of the temperature gradient for the fluid and solid phases are different at the wall, and part of the internal heat generation in the solid phase will transfer to fluid phase through the thermal conduction at the wall, instead of through the internal heat transfer exchange between the fluid and solid phase. It was also established that the phenomenon of heat flux bifurcation for the constant temperature boundary condition can occur over a given axial region. The heat flux bifurcation phenomenon in porous media is also investigated analytically for temporal conditions and two primary types of heat flux bifurcations in porous media are established. The phenomenon of heat flux bifurcation for the solid and fluid phases at the wall is found to occur over a given axial region at a given time frame. Heat flux bifurcation is also found to occur along the channel. The heat flux bifurcation region moves downstream with time, and thermal conduction at the wall is found to play an important role on the total exchange between the solid and fluid phases within the bifurcation region. A characteristic time is introduced to evaluate the time that it takes for either the solid or fluid to reach steady state. Furthermore, two practical applications for heat flux bifurcation are investigated analytically, Case (a): Porous heat sink for electric cooling; Case (b): Heat exchange between fluid and solid phases in fixed-bed with internal heat generation. And two different primary approaches (Models A and B) are adopted for the constant wall heat flux boundary condition, especially for the adiabatic boundary condition. The results showed that, when Model A is used, heat flux bifurcation can occur at the wall. It is also found that the total heat transfer heat exchange between solid and fluid phases for Model A is stronger than that for Model B, and the Nusselt number for Model A is larger than that for Model B.
Keywords: Transport in Porous Media, Heat Flux Bifurcation, Local Thermal Non-Equilibrium