Local thermal non-equilibrium (LTNE) model for developed flow in porous media with spatially-varying Biot number

Abstract

The local thermal non-equilibrium (LTNE) model has been extensively used to model convective heat transfer in porous media. Most of the past LTNE-based models account for thermal interactions between fluid and solid phases in the form of a constant Biot number (Bi). This work presents a local thermal non-equilibrium model for fully developed flow in a channel filled with a porous medium where Bi itself varies across the channel. A set of differential equations for fluid and solid phase temperature fields are derived under this condition, which are shown to be generalizations of previously presented results for constant Bi. Results from the present analysis are shown to reduce to and agree with past work for the special case of constant Bi. The variable Bi model is used to investigate the effect of thermal properties such as thermal conductivity on the fluid and solid temperature profiles. The nature of temperature distributions are correlated with the spatial variation in Bi, including for parabolic and sinusoidal variation. Specifically, for periodic Bi, the locations of maxima and minima in temperature fields are found to be well correlated with corresponding maxima and minima in Bi. Nusselt number (Nu) for different values of thermal conductivities and heat generation rates are determined for variable Bi. This work accounts for an important physical consideration in porous media and generalizes previously-presented LTNE models for porous media in a channel.