Passive Laminar Heat Transfer Across Porous Cavities Using the Thermal Non-Equilibrium Model

Abstract

This work presents a study on laminar free convection within a square cavity filled with a fluid saturated porous medium. Macroscopic flow equations are obtained by volume-averaging local instantaneous continuity and momentum equations. The so-called “two-energy equation model” is used, in which distinct macroscopic equations are applied to the working fluid and the solid material. Transport equations are discretized using the control-volume method and the system of algebraic equations is relaxed via the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm. The effect of Ra_m on Nu_w correctly predicted the enhancement of passive heat transfer across the cavity for increasing Ra_m. Increasing k_s/k_f enhances the conduction transport through the solid material and, consequently, dampens the overall Nusselt number, defined here as the ratio between conduction and convection mechanisms over conduction transport only. Further, results indicate that by increasing the void space within the porous material the overall Nusselt number is reduced rather than increased. Individual contributions to the average Nusselt number indicate that, although convection is enhanced with increasing porosity, the reduction of conduction heat transfer through the solid material is the controlling mechanics for Nu_w as porosity increases. The results herein might contribute to design and optimization of passive heat transfer systems.

Notes

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