Heatline analysis of thermal mixing due to natural convection in discretely heated porous cavities filled with various fluids

Abstract

Applications involving porous media occur widely in chemical engineering processes, e.g., oil and gas production, groundwater pollution, food processing, nuclear waste repository etc. The present study focuses on enhancing thermal processing of materials via distributed heating. Thermal mixing during laminar natural convection is analyzed in four different discretely heated porous square cavities. Heatline approach of visualizing heat flow is implemented to gain in-depth understanding of complex heat flow patterns for wide range of parameters ( Pr = 0.015 – 1000 , Da = 10 − 6 – 10 − 3 , Ra = 10 3 – 10 6 ). Results indicate that at lower Da ( = 10 − 6 ) heat flow is weak and transport is conduction dominant. At Da = 10 − 3 , the smaller hydraulic resistance of porous medium results in enhanced convection. The role of hot regime at bottom wall or hot regime at side walls to efficiently heat the cavity has been depicted via heatlines. It is illustrated by heatlines that when the heat sources are centrally located on the wall of the cavity, thermal mixing is significantly increased with subsequent rise in maximum temperature in the cavity. Effect of Da on local and average Nusselt numbers in different cases of porous cavities are adequately explained based on heatlines for the first time in this work. Average Nusselt number distributions show that hot regime of bottom wall transfers larger amount of heat whereas cold regimes of side wall receive larger amount of heat, especially at higher Da for all cases (cases 1–4). Further, cup-mixing temperature is evaluated for various cases to establish optimal thermal mixing by distributed heating in comparison to conventional bottom wall heating.