Lattice Boltzmann Simulation for Combined Natural and Forced Convection in a Lid-Driven Square Enclosure with an Inner Heat Sink

Abstract

In the present study, we have performed a numerical investigation of the effect of aspect ratio (AR), solid-to-fluid volume fraction (χ) of the heated rectangular block and Richardson number on mixed convection heat transfer in a lid-driven square cavity having centered rectangular heated block inside. The vertical walls of the cavity are exposed to the cold temperature while the horizontal walls are kept at adiabatic, with top wall moving to the right with a constant velocity. The cavity is filled with air (Pr = 0.71) as working fluid. A wide range of Ri (0.01 ≤ Ri ≤ 100) by varying Reynolds number at fixed Rayleigh number Ra = 10 4 , aspect ratio (0.5 ≤ AR ≤ 2) and the solid-fluid volume fraction of the block (20% ≤ χ ≤ 50%) are considered. The obtained results indicate that the total average Nusselt number depends strongly on the Richardson number, the aspect ratio and the solid-to-fluid volume fraction, which reaches its maximum for higher values of χ and for AR = 2 (horizontal rectangular block), at low values of Ri. Additionally, it is observed that more effective cooling of the cavity is generally achieved in the scenario where the aspect ratio is 1 (square heated block) and the solid-fluid volume fraction is 20%. In addition, for Ri = 1, when changing the volume fraction of solid-fluid from 20% to χ = 35% / (χ = 50%), an increase around 37.94% /(90.42%) of Nu is achieved at AR = 1. Nomenclature