In the present paper a numerical simulation is performed to study the laminar flow and the heat transfer characteristics in a two-dimensional horizontal channel containing three heated square obstacles (blocks) placed side-by-side unequally or equally spaced. The numerical scheme is based on a Double Multiple Relaxation Time Lattice Boltzmann Method (MRT-LBM). The flow and the temperature fields are treated using the MRT-D2Q9 model and the MRT-D2Q5 model, respectively. The Lattice Boltzmann method (LBM) is an accurate and efficient method for direct numerical simulations of hydrodynamics phenomena in complex geometries.

The problem considered here is a laminar, incompressible, and two-dimensional flow. The fluid circulating in the channel is the air (Pr = 0.71) and its physical properties, except its density, are supposed to be constant. The cylinders are placed at a distance Xin downstream from the inlet section of the channel. The two channel walls are assumed to be adiabatic, the temperature of the incoming air flow is fixed to θc =-0.5 (cold temperature), and the temperature of each cylinder is constant and equal to θh= 0.5 (hot temperature). At the inlet, the flow is fully developed with a parabolic velocity profile and at the outlet, the temperature and velocity gradients are assumed to be zero. The effect of the Reynolds number and the dimensionless separation distances a1 and a2 on the fluid flow and the heat transfer is examined. The simulation results are presented in terms of streamline contours, isotherms, local and average Nusselt numbers.