Steady natural convection in a horizontal channel containing heated rectangular blocks periodically mounted on its lower wall

In this paper, we perform a numerical investigation of laminar steady natural convection flows in a two-dimensional horizontal channel containing heating rectangular blocks, periodically mounted on its lower wall. The blocks are heated at a constant temperature, TH′ and connected with adiabatic surfaces. The upper wall of the channel is maintained at a cold temperature TC′. The parameters governing the problem are the Rayleigh number (102 ⩽ Ra ⩽ 2 × 106), the geometric parameter C (0.25 ⩽ C = l′/H′ ⩽ 0.75) and the relative height of the blocks (1/8 ⩽ B = h′/H′ ⩽ 1/2). The effect of the computational domain choice on the multiplicity of solutions is also investigated. The results obtained using air (Pr = 0.72) as the working fluid show that the parameters B and C have a significant effect on the fluid flow and temperature fields. The symmetry of the flow is not always maintained although the boundary conditions for this problem are symmetrical, and the difference between two multiple solutions in terms of heat transfer may reach 34% for a given set of the governing parameters.