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In this work, we study numerically a problem of mixed convection in lid driven square cavity, filled with air (Pr = 0.71), whose upper wall is movable and kept at constant cold temperature T C . The cavity contains a porous obstacle of height h and width b, placed on the bottom wall maintained at a constant hot temperature T H . The side walls are adiabatic. Darcy-Brinkmann-forchheimer model is used for modelling the momentum equations in porous medium. This numerical study is based on the multiple relaxation time lattice Boltzmann method (MRT -LBM). The D2Q9 two-dimensional model is adopted to the dynamic part, while the D2Q5 model is applied for the thermal part. The objective of the study is to analyze the effect of Darcy number (10 -1  ≼ Da ≼ 10 -5 ), Richardson number (0.01 ≼ Ri ≼ 100) and the aspect ratio w = b/H (0.2 ≼ w ≼ 1) on the hydrodynamic and thermal characteristics in the cavity through the velocity and temperature as well as the average Nusselt number. The results obtained show a considerable effect of these parameters on the structure of the flow and on the heat exchange in the cavity.

Multiple-relaxation-time Lattice Boltzmann model for flow and convective heat transfer in lid driven cavity with porous obstacle