Investigations on the effect of non-uniform temperature on fluid flow and heat transfer in a trapezoidal cavity filled with porous media

Simulations were carried out for natural convection in a trapezoidal cavity filled with porous media to investigate the effect of uniformly and non-uniformly heated bottom wall using finite element computational procedure. The enclosure used for flow and heat transfer analysis has hot bottom wall, constant temperature cold top wall and adiabatic side walls. The bottom wall is subjected to uniform/linear/sinusoidally varying temperatures. Results are presented in the form of stream lines, isotherms, heatline plots, local and average Nusselt numbers. Heatline visualization technique is a useful method that gives information on heat transport from the heated to cold region inside the porous trapezoidal enclosure with varying temperature boundary conditions. Nusselt numbers are computed for Darcy-modified Rayleigh numbers or Rayleigh number (Ra) ranging from 100 to 2000 for an aspect ratio (H/L) of 0.5. It is observed from this study that the uniform temperature at the bottom wall of the enclosure gives higher Nusselt number as compared to the linear and sinusoidally varying temperature cases. The average Nusselt numbers increases monotonically with Rayleigh number for bottom wall and top walls. The power law correlations between average Nusselt number and Rayleigh numbers are presented for convection dominated regions.