Analysis of thermal convection in a fluid-saturated porous cavity with internal heat generation

Abstract

In this paper, the thermal convection flow in a fluid-saturated porous cavity with external sidewall heating and internal heat generation is studied by a semi-implicit projection finite element method. Concerned physical phenomena are constructed by impulsively switching on a uniform internal heat generation at t = 0 in a steady state flow field established by two different sidewall temperatures. Flows in the range 103 ≤ Ra I ≤ 108 and Ra E = 105 are mainly investigated for porous media ɛ = 0.4 and 10–10 < Da < 10–1. The results include the steady state flow field and heat transfer phenomena, as well as the evolution of heat transfer. According to the results, porosity demonstrates obvious influence in heat transfer as Da ≥ 10–2, and permeability significantly affects the flow field and heat transfer rate for Da < 10–2. The decrease in permeability diminishes the strength of external heating driven circulation and provides a chance for the cell driven by internal heat generation to develop. In addition, the flow in a porous medium with smaller flow restriction more quickly reaches the steady state from the instantaneously started internal heat generation.