Natural Convection in a Porous Square Enclosure With Partially Cooled From Vertical Wall

Natural convection flow in a square enclosure filled with a fluid-saturated porous medium is investigated in this paper. The left side wall of the cavity is heated while the right side wall is partially cooled. The cooled portion is located adjacent to the top wall. The remaining walls are adiabatic. The governing equations are solved by using FlexPDE 6.14 Student Version which is based on finite element method. The different parameters in the present study are Darcy number (10-5 ≤ Da ≤ 10-3), Grashof number (103 ≤ Gr ≤ 105), Prandtl number (0.70 ≤ Pr ≤ 10) and Reynolds number (10 ≤ Pr ≤ 100). The results are illustrated in the terms of isotherms, streamlines and heatlines. It is found that the strength of fluid motion and the magnitudes of streamlines increase and temperature distribution decrease as Darcy number and Grashof number increase. In addition, a single circulation cell in clockwise direction is formed in the enclosure. The magnitudes of heatlines become larger at higher Darcy numbers, while the increasing of Grashof number has no effect for the magnitudes of heatlines.

Keywords: Finite element method; Natural convection; Partially cooled; Porous medium.

E-mail: supot_wa@kku.ac.th