Numerical Analysis of Natural Convection in a Concentric Trapezoidal Enclosure Filled with a Porous Medium

Numerical study of natural convection around a heated trapezoidal block of different sizes located centrically in a larger trapezium has been investigated. The annulus between the trapeziums is filled with porous media. The sides of the inner trapezium are heated to a fixed temperature (T_h), and the slanted walls of the outer trapezium are adiabatic while its upper and lower walls are heated to temperatures of 〖T_c+(T_h-T_c)sin〗⁡(πx⁄L) and 〖T_h+(T_h-T_c)sin〗⁡(πx⁄L) respectively. The finite element numerical approach was used to solve the relevant dimensionless equations. Results are gotten for salient parameters including; modified Rayleigh number (10≤Ra_m≤ 1000), Darcy number (10^(-5)≤Da≤ 10^(-2)), and area ratio (1/5≤AR≤ 1/3). The results of this study are shown as isothermal contours, stream functions, and average Nusselt number. The results show that increasing Ra_m improves heat transfer; however, the response of thermal characteristics to AR increment depends on the range of Darcy number considered. Results from this study find application in ingot treatments and microchannel cooling among others.