Transient Aspects of Heat Flux Bifurcation in Porous Media: An Exact Solution

The transient thermal response of a packed bed is investigated analytically. A local thermal nonequilibrium model is used to represent the energy transport within the porous medium. The heat flux bifurcation phenomenon in porous media is investigated for temporal conditions and two primary types of heat flux bifurcations in porous media are established. Exact solutions are derived for both the fluid and solid temperature distributions for the constant temperature boundary condition. The fluid, solid, and total Nusselt numbers during transient process are analyzed. A heat exchange ratio is introduced to estimate the influence of interactions between the solid and fluid phases through thermal conduction at the wall within the heat flux bifurcation region. A region where the heat transfer can be described without considering the convection contribution in the fluid phase is found. The two-dimensional thermal behavior for the solid and fluid phases is also analyzed. The temporal temperature differential between the solid and fluid is investigated to determine the domain over which the local thermal equilibrium model is valid. In addition, the characteristic time for reaching steady state conditions is evaluated.