Natural convection and flow simulation in differentially heated isosceles triangular enclosures filled with porous medium

Abstract

A finite element analysis is performed to investigate the effects of uniform and non-uniform heating of bottom wall on natural convection flows within isosceles triangular enclosures filled with porous medium. The detailed analysis is carried out in two cases depending on various thermal boundary conditions: (I) two inclined walls are maintained at constant cold temperature while the bottom wall is uniformly heated; (II) two inclined walls are maintained at constant cold temperature while the bottom wall is non-uniformly heated. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters of Darcy number, Da ( 10 - 5 ⩽ Da ⩽ 10 - 3 ), Rayleigh number, Ra ( 10 3 ⩽ Ra ⩽ 10 6 ) and Prandtl number, Pr ( 0.026 ⩽ Pr ⩽ 1000 ) in all the cases mentioned above. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. It is observed that at small Darcy numbers, the heat transfer is primarily due to conduction irrespective of Pr. As the Darcy number increases, there is a change from conduction dominant regime to convection dominant regime. Flow circulations are also found to be strong functions of Pr at large Da ( Da = 10 - 3 ) and multiple circulation cells occur at small Pr with Ra = 10 6 . Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case, but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. As average Nusselt number is same on both the inclined walls, the average Nusselt number for bottom wall is 2 times that of the inclined wall which is well matched in two cases considered for verifying the thermal equilibrium of the system. The correlations are proposed for average Nusselt number as functions of Ra for various Darcy and Prandtl numbers.