Mixed convection in a driven cavity with an internal obstacle using the lattice Boltzmann method

Abstract

The flow and heat transport of a viscous fluid contained in a square cavity have been extensively studied using parametric analysis. Lattice Boltzmann method is used to simulate fluid-flow in a square lid-driven cavity with a square-shaped obstacle in the cavity?s centre. The cavity?s top wall generates flow that moves at a constant speed in its own plane and is maintained at a higher temperature than the bottom wall. Reynolds number, Rayleigh number, Prandtl number, Grashof number, and Richardson number are the primary parameters used in this study. The relevance of natural and forced convection, contributions of conduction, and convection to total heat transfer are estimated. The influence of the temperature of the obstacle on the velocity and temperature of the fluid is also being investigated. When, Ri ? 1, the temperature of the obstacle has almost negligible influence on fluid velocity, the fluids are well mixed, and temperature fluctuations are minor in the bulk of the cavity interior. When, Ri ? 1, the obstacle?s temperature, has a considerable impact on fluid velocity, much of the fluid in the cavity?s middle and bottom regions remains stationary. These regions have a vertically linear temperature distribution. Further studies were carried out to investigate how the Prandtl number influenced the fluid?s temperature. The findings are presented as contour plots of velocity and temperature, streamlines, horizontal and vertical velocity profiles, and vertical temperature profiles.