PurposeThe purpose of this paper is to apply the lattice Boltzmann method (LBM) to simulate mixed flow, which combines natural convection for temperature difference and forced convection for lid driven, in a two‐dimensional rectangular cavity over a wide range of aspect ratios (A), Rayleigh numbers (Ra) and Reynolds numbers (Re).Design/methodology/approachThe LBM is applied to simulate the mixed flow. A multi‐relaxation technique was used successfully. A scale order analysis helped the understanding and predicting the overall heat transfer.FindingsIn the considered lid driven cavity, the Richardson number emerges as a measure of relative importance of natural and forced convection modes on the heat transfer. An expression of the overall heat transfer depending on the cavity slender (A) is deduced. The validity of the obtained expression was checked in mixed convection under the condition of low Richardson number (Ri) and the limitation condition was deduced.Practical implicationsThis paper has implications for cooling system optimization and LBM technique development.Originality/valueThis paper presents a new cooling configuration, avoiding critical situation where the opposing effect induce weak heat transfer; and a stable and fast LBM approach allowing complex geometry treatment.

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