Heat flow visualization during mixed convection within entrapped porous triangular cavities with moving horizontal walls via heatline analysis

This paper analyzes the fluid and heat flow within entrapped porous triangular cavities involving various thermal boundary conditions (case 1: hot horizontal walls and cold inclined walls; case 2: cold horizontal walls and hot inclined walls). Finite element based numerical study has been performed for various values of Prandtl number (Prm=0.026 and 7.2), Darcy number (Dam=10-4-10-2), Reynolds number (Re=1-1000) at a high value of Grashof number (Gr=105). The upper cavity for the case 1 and the lower cavity for the case 2 show almost similar trends and vice versa based on the exact opposite thermal boundary conditions. Heat transfer is conduction dominant at Dam=10-4 involving both Prm whereas, convection heat transfer dominates at Dam=10-2 especially for Prm=7.2. Although the motion of the horizontal walls significantly influences the fluid flow field within the cavities, due to the decoupling between the fluid and thermal fields at the low Pem (Pem=0.026,0.26 and 2.6), conduction dominant heat transfer occurs. At the high Dam and Prm=7.2, a pair of symmetric streamline or heatline cells are seen for Re≤1 whereas, a bigger primary streamline or heatline cell is accompanied by a secondary streamline or heatline cell for 1⩽Re≤100. At 500⩽Re⩽1000, the single larger streamlines or heatline cells are seen especially for Prm=7.2 involving Dam=10-2. At Prm=0.026, the average heat transfer rates (Nut‾,Nub‾, Nul‾ and Nur‾) are almost constant with Re and Dam. At Prm=7.2, the larger magnitudes ofNut‾ and Nul‾ are observed for Re≤10 compared to those for Re=100 involving Dam⩾10-3 whereas, the magnitudes of Nur‾ are almost similar for all Re involving all Dam in the upper cavity (case 1) within Re⩽100. In the lower cavity (case 1), the magnitudes of Nub‾ and Nur‾ are larger for Re=100 whereas, the magnitudes of Nul‾ are larger for Re≤1 for almost entire range of Dam within Re≤100 involving Prm=7.2. The average Nusselt numbers are significantly larger at the high Re (Re=500 and 1000) involving all Dam (except for the horizontal walls involving Dam⩽8×10-4) in the cases 1 and 2 at Prm=7.2.