### Numerical Study of Two-Dimensional Transient Natural Convection in an Inclined Shallow Porous Cavity Exposed to a Constant Heat Flux

*Engineering and Technology Journal*

2012, Volume 30, Issue 15, Pages 2577-2596

2012, Volume 30, Issue 15, Pages 2577-2596

#### Abstract

Numerical method is used to solve the two-dimensional transient natural convection heat transfer problem in an inclined shallow porous cavity. A constant heat flux is applied for heating and cooling all opposing walls. Solutions for laminar case are obtained within Rayleigh number varied from 20 to 500 and aspect ratio for porous cavity varied from 2 to 4. A finite difference method is used to obtain numerical solutions of full governing equations. Energy equation is solved using alternating direct implicit (ADI) method and stream function equation by successive over relaxation (SOR) method. The results are presented for the flow filed, temperature distributions, and average Nusselt number in terms of the Rayleigh number, aspect ratio, and the inclination angle of cavity. the convection becomes more and more vigorous as the orientation angle of the cavity is increased and for high Rayligh number no steady unicellular flow could be maintained inside the cavity. The effect of inclination angle on Nasselt number is more pronounced as the Rayleigh number is increased. When the inclination angle increased the Nusselt number increased and sudden transition appears and flow becomes unicellular and Nusselt number increased clearly. The value of mean Nusselt number strong function with the value of Rayleigh number, aspect ratio and the orientation of porous cavity.

#### Keywords

Numerical Study, Transient, Natural Convection, Inclined, Shallow Porous Cavity, Constant Heat Flux#### Metrics