Analysis of local thermal non-equilibrium condition for unsteady heat transfer in porous media with closed cells: Sparrow number

Abstract

The local thermal non-equilibrium condition for a porous medium with closed cells under unsteady state heat transfer is analyzed. Although the fluid circulates in the closed pores due to the buoyancy effect, the volume averaged velocity for a closed pore is zero causing excluding of the continuity and momentum equations from the volume averaged governing equations. The volume averaged governing equations are non-dimensionalized by using the equilibrium thermal diffusivity and Sparrow number appears in the dimensionless governing equations automatically. The Sparrow number is interpreted as the equilibrium conduction thermal resistance to the convection thermal resistance for the entire domain. For the high values of Sparrow number (such as 1000), the convection heat transfer resistance is considerably smaller than the heat conduction resistance resulting in high possibility of the local thermal equilibrium. Dimensionless governing equations show that four dimensionless parameters as porosity, Sparrow number, solid (or fluid) dimensionless thermal capacitance and thermal conductivity play important roles on the prediction of the local thermal non-equilibrium state in a closed cell porous medium. A chart for the prediction of local thermal non-equilibrium is presented for Sparrow number of 1, 50, 100 and 500. Furthermore, a pore scale study for a closed cell porous medium with working fluids as water and air is performed. A good agreement between the pore scale and volume averaged results is observed. The obtained pore scale results support the results of the volume averaged parametric study and also the suggested chart for the prediction of local thermal non-equilibrium state.