Numerical Investigation of Optimized Cooling of Square Obstacle

In this paper, natural convection heat transfer in a cavity induced by an isothermal obstacle is investigated. This paper is an extension of our previous paper [1] so that the effects of geometrical parameters and position of the obstacle are considered precisely. Air is chosen as a working fluid and the flow is assumed to be two-dimensional, steady and incompressible. Lattice Boltzmann method is employed for numerical analysis and the results are compared with finite volume results. A scale analysis is also performed for both numerical methods which have not been presented in the literature. With the representation, the Navier-Stokes equation can be derived from the lattice Boltzmann equation through the Chapman-Enskog expansion. The study is performed for different aspect ratios and different values of Rayleigh number. Heat transfer rate increases by either way of increasing the Ra number from 103 to 105 and increasing the aspect ratio from 0.1 to 0.4. At last, the Nusselt number versus the obstacle’s position, for different aspect ratios and Rayleigh numbers is shown and the position of the obstacle in which heat transfer rate is maximum is investigated.