Convective flow and heat transfer in a tall porous cavity side-cooled with temperature profile

Natural convection in an air-filled (Prandtl number = 0.7) porous cavity with profiled side cooling and constant bottom heating is investigated over the Rayleigh number range of 1×10⁴ to 1×10⁸ at two Darcy numbers: 1×10^-4 and 1×10^-6. The aspect ratio based on cavity height was varied from 0.5 to 0.1 to investigate penetration length according to linear or sinusoidal temperature profile. The general non-Darcy model adopted in this work was validated against experimental and theoretical results in the literature and Nusselt number was predicted within less than 3% in the worst case. The effect of left wall imposed temperature profile was investigated in detail. Different convective regimes were observed depending on the imposed profile. An active region was found to take place with the linear temperature profile and with extent proportional to Rayleigh number as predicted by scale analysis.