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

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

NUMERICAL STUDY OF TWO-DIMENSIONAL TRANSIENT NATURAL CONVECTION IN AN INCLINED SHALLOW POROUS CAVITY EXPOSED TO A CONSTANT HEAT FLUX

Numerical models are 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. Both vorticity and energy equation are 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 thr orientation angle of the cavity is increased and for high Rayligh number no steady unicellular flow could be maintained in side 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

NUMERICAL SIMULATION OF TWO DIMENSIONAL TRANSIENT NATURAL CONVECTION HEAT TRANSFER FROM ISOTHERMAL HORIZONTAL CYLINDRICAL ANNULI

Numerical solutions are presented for the transient natural convection heat transfer problem in horizontal isothermal cylindrical annuli, enclosed in heated inner and cooled outer cylinders. Solutions for laminar case were obtained within Grashof number based on the inner diameter which varied from 1x102 to 1x105 in air. Both vorticity and energy equations were solved using alternating direction implicit (ADI) method and stream function equation by successive over relaxation (SOR) method. The structure of fluid flow such as a velocity vector and temperature distribution as well as Nusselt number were obtained and the effect of diameter ratio on them is examined. In addition, the Grashof number was changed with the influence of variation Prandtle number and diameter ratio. Our numerical calculation are summarized by Nussult number vs. Grashof number curves with diameter ratios and prandtl as a parameter, which serves as a guide to natural convection heat transfer calculated from annulus. Good agreement with previous data were obtained.