Finite element simulation of natural convection flow in a trapezoidal enclosure filled with porous medium due to uniform and non-uniform heating

Abstract

The phenomena of natural convection in a trapezoidal enclosure filled with porous matrix has been studied numerically. A penalty finite element analysis with bi-quadratic elements is performed to investigate the influence of uniform and non-uniform heating of bottom wall while two vertical walls are maintained at constant cold temperature and the top wall is well insulated. Parametric study for the wide range of Rayleigh number Ra ( 10 3 ⩽ Ra ⩽ 10 5 ) , Prandtl number Pr ( 0.015 ⩽ Pr ⩽ 1000 ) and Darcy number ( 10 - 3 ⩽ Da ⩽ 10 - 5 ) shows consistent performance of the present numerical approach to obtain the solutions in terms of stream function and isotherm contours. For parameters studied in the above range, a symmetry is observed for temperature and flow simulations. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh and Darcy numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. It is observed that the conduction is dominant irrespective of Ra for Da = 10 - 5 . As Rayleigh number increases, there is a change from conduction dominant region to convection dominant region for Da = 10 - 3 . The correlations between average Nusselt number and three parameters (Rayleigh number ( Ra), Prandtl number ( Pr) and Darcy number ( Da)) are also obtained.