The Lattice Boltzmann method is actually considered as one of the simplest approach. The flow and heat transfer distribution in a duct containing a backward and an obstacle are studied for different geometric and physical parameters.

The LBM is applied to solve the backward-facing step flow problems for an expansion ratio H/h = 2 in rectangular duct and to determine the effect of the obstacle on flow and heat transfer distribution. The obstacle is situated in the bottom wall of the duct. The effect of various obstacle lengths (0.5<h/S<1.5) will be also considered. All this results were observed for a Prandtl number of 0.71 and different range of Reynolds number (1–200).

This study showed the instabilities of velocity, recirculation length, temperature and Nusselt number with the obstacle downstream the step. These results were compared to with published experimental.

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