Validation of the Thermal Equilibrium Assumption in Periodic Natural Convection in Porous Domains

Abstract

The validity of the local thermal equilibrium assumption in the periodic free convection channel flow is investigated analytically. Two cases are considered where in the first case transverse conduction in the solid domain is included while in the second case transverse conduction in the fluid domain is included. The periodic disturbance in the free convection flow is due to a periodic thermal disturbance imposed on the channel walls. The DarcyBrinkman model is used to model the flow inside the porous domain. It is found that four dimensionless parameters control the local thermal equilibrium assumption in the first case and five parameters control the local equilibrium assumption in the second case. The criteria that secure the validity of the local thermal equilibrium assumption are derived.

Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review

“…They concluded that the LTE assumption is valid and can be considered in such application with enough precision for higher values of Biot number, Darcy number, and the viscosity, and for lower values of Rayleigh number. Khadrawi et al [57] examined analytically the validity of LTE assumption inside a porous channel under a periodic free convection by imposing a thermal sinusoidal disturbance on the channel surfaces, as shown in Figure 33. They considered two cases: The first case is by ignoring the conductive term in the fluid and including only the transverse conductive term in the solid, and inversely for the second case.…”

“…In contrast, it was revealed that higher values of modified Biot number or the fluid/solid thermal conductivity ratio depreciate the LTNE and improve the LTE condition, as shown in Figure 37. Tahat et al [59] analysed numerically the same physical problem studied by Khadrawi et al [57] to examine the possibility of adaption the LTE model in a porous channel, but this time under periodic magneto-hydrodynamic (MHD) free convection flow. They found that the LTE assumption can be adapted for large values of magnetic field parameter (M), see Figure 38, or for higher values of interphase convective heat transfer parameter, called in their paper as volumetric Nusselt number Nu = h s f L 2 /(1 − ε)k s as shown in Figure 39, and/or for higher values of solid/fluid thermal conductivity ratio (1 − ε)k s /εk f .…”

Free convection of composite porous medium in a vertical channel

“…Extensive work has been done by Al-Nimr et al [12,[14][15][16][17] with his coworkers in porous media. Beavers and Joseph [18] first investigated the fluid mechanics at the interface between fluid layer and a porous medium over a flat plate.…”

Transient Response in a Micropolar Mixture of Porous Media During Thermal Shock

“…There are two main topics in heat transfer studies of porous media; these are the assumptions of local thermal equilibrium (LTE) and the uniformity of the temperature in both the fluid and the solid. Al-Nimr et al [7][8][9][10][11][12] have investigated the problems of heat transfer in porous media for different flow conditions and geometries in the context of the LTE assumption. On the other hand, several studies [13][14][15][16] adopted the two-phase model where there are two energy equations for the solid and fluid domains.…”