In this paper, the 2D fluid flow pass a heated/cooled square cylinder exposed to a constant free-stream upward velocity is simulated via a multiple relaxation time (MRT) lattice-Boltzmann (LB) method. The buoyancy effect on the drag and lift coefficients as well as Nusselt number related is compared with the results in the existing literatures to validate the code used. The effect of temperature-viscosity dependence is then investigated to test whether the effect can be neglected or not for the mixed convection case. It is shown that the effect cannot be ignored when |Ri| > 0.15. Fortunately, the effect can be captured by using an effective temperature formula [J. M. Shi, D. Ferlach, M. Breuer, G. Biswas and F. Durst, Phys. Fluids16, 4331 (2004)] in a rather large range of Ri. All the numerical results, from another angle, also demonstrate that the MRT method is an efficient tool in simulating the problems such as the present one.
