Natural Convection in a Square Cavity with a Heated Obstacle Using Lattice Boltzmann Method

Natural convection heat transfer in a square cavity induced by heated plate is investigated using the lattice Boltzmann method. A suitable forcing term is represented in the Boltzmann equation. With the representation, the Navier-Stokes equation can be derived from the lattice Boltzmann equation through the Chapman-Enskog expansion. Top and bottom of the cavity are adiabatic; the two vertical walls of the cavity have constant temperatures lower than the plate’s temperature. The flow is assumed to be two-dimensional. Air is chosen as a working fluid (Pr=0.71). The study is performed for different values of Grashof number ranging from 103 to 105 for different aspect ratios and position of heated plate. The effect of the position and aspect ratio of heated plate on heat transfer are discussed. With increase of the Grashof number, heat transfer rate is increased in both vertical and horizontal position of the plate. The obtained results of the lattice Boltzmann method are validated with those presented in the literature.