Numerical analysis of local thermal non-equilibrium free convection in a porous enclosure with a wavy cold side wall

Abstract

In this piece of communication, numerical heat transfer and fluid flow in a Darcy porous enclosure are investigated. The right wavy wall is maintained at a constant low temperature, with the top and bottom preserved thermally insulated, while the left vertical wall is uniformly heated. The governing equations for non-dimensional systems are solved using the Galerkin finite element method; a local thermal non-equilibrium appears between the base fluid and porous matrix. The effects of interface heat transfer parameter $(0 \leq N h s \leq 10^{3})$ along with porosity of porous media $(0.1 \leq ϵ \leq 0.9)$ , Rayleigh-Darcy number $(10 \leq R a \leq 10^{3})$ , and parameters involving waviness of cavities, such as the number of undulations in a unit length $(1 \leq N \leq 5)$ and amplitude of the wave $(0.05 \leq a \leq 0.25)$ are investigated. The results show that increment waviness augments heat transfer enhancement for fluid and solid phases. The local thermal equilibrium cases for various parameters are pointed out at a 5% significance level of the average temperature difference between the two phases.

Keywords

Finite element method local thermal non-equilibrium natural convection wavy cavity porous media

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