Finite element simulations of natural convection flow in an isosceles triangular enclosure filled with a porous medium: Effects of various thermal boundary conditions

Abstract

The phenomena of natural convection in an isosceles triangular enclosure filled with a porous matrix has been studied numerically. A penalty finite element analysis with bi-quadratic elements is used for solving the Navier–Stokes and energy balance equations. The detailed study is carried out in two cases depending on various thermal boundary conditions; case I: two inclined walls are uniformly heated while the bottom wall is isothermally cooled and case II: two inclined walls are non-uniformly heated while the bottom wall is isothermally cooled. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters, Darcy number, Da ( 10 - 5 ⩽ Da ⩽ 10 - 3 ) , Rayleigh number, Ra ( 10 3 ⩽ Ra ⩽ 10 6 ) and Prandtl number, Pr ( 0.026 ⩽ Pr ⩽ 10 ) for all the cases mentioned above. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. It has been found that at low Darcy numbers ( Da ⩽ 10 - 5 ) the heat transfer is primarily due to conduction irrespective of the Ra and Pr . In this regime, the isotherms are almost parallel near the bottom portion of the triangular enclosure whereas at Da = 10 - 3 , the isotherms are more distorted. As Rayleigh number increases, there is a change from conduction dominant region to convection dominant region for Da = 10 - 3 , and the critical Rayleigh number corresponding to on-set of convection is obtained. Some interesting features of stream function and isotherm contours are discussed especially for low and high Prandtl number limits. Complete heat transfer analysis is performed in terms of local and average Nusselt numbers.