Modeling and simulations of the Marangoni effect in phase change materials embedded in metallic foams

Abstract

We investigate for the first time the heat transfer, thermal energy storage, and flow dynamic generated by Marangoni flows in a phase change material embedded in a porous media. We present a full hydrodynamics model and perform detailed simulations based on the Darcy–Brinkman–Forchheimer bulk equations and a linear shear stress boundary condition on the porosity. We study a set of four porosities, from ϵ=0.85 to 0.95 , four Darcy numbers, from Da=10−4 to Da=10−2, two Stefan numbers Ste=0.33 and Ste=0.67, and rectangular geometries with three different aspect ratios (AR) between the horizontal free surface length and thickness. The porous matrix weakens the Marangoni effect by decreasing the surface shear stress. Reduction of the porosity leads to shorter melting times and more efficiency in thermal energy storage due to the higher effective conductivity at AR=1. However, increasing the aspect ratio, these enhancements decay, and for high aspect ratios, AR=16, the Marangoni flows are strong enough to offset the advantage of high thermal effective conductivity at high volumes of the metallic foam. The non-Darcy effects are strong for high aspect ratios, and the optimum configurations correspond to high porosities and permeabilities to suppress less the thermocapillary flows. The position of the surface melting front follows a power law for square geometries.