The problem of Rayleigh–Bénard’s natural convection subjected to a temporally periodic cooling condition is solved numerically by the Lattice Boltzmann method with multiple relaxation time (LBM-MRT). The study finds its interest in the field of thermal comfort where current knowledge has gaps in the fundamental phenomena requiring their exploration. The Boussinesq approximation is considered in the resolution of the physical problem studied for a Rayleigh number taken in the range 103 ≤ Ra ≤ 106 with a Prandtl number equal to 0.71 (air as working fluid). The physical phenomenon is also controlled by the amplitude of periodic cooling where, for small values of the latter, the results obtained follow a periodic evolution around an average corresponding to the formulation at a constant cold temperature. When the heating amplitude increases, the physical phenomenon is disturbed, the stream functions become mainly multicellular and an aperiodic evolution is obtained for the heat transfer illustrated by the average Nusselt number.

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 TC. The cavity contains a porous obstacle of height h and width b, placed on the bottom wall maintained at a constant hot temperature TH. 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.

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Flow and heat transfer analysis in ventilated cavities is one of the most widely studied problems in thermo-fluids area. Two-dimensional mixed convection in a ventilated rectangular cavity with baffles is studied numerically and the fluid considered in this study is hot air (Pr = 0.71). The horizontal walls are maintained at a constant temperature, higher than that imposed on the vertical ones. Two very thin heat-conducting baffles are inserted inside the enclosure, on its horizontal walls, to control the flow of convective fluid. The governing equations are discretized using the finite volume method and the SIMPLER algorithm to treat the coupling velocity–pressure. Line by line method is used to solve iteratively the algebraic equations. The effect of the Richardson number Ri (0.01- 100) and the location of the baffles within the cavity on the isothermal lines, streamlines distributions and the average Nusselt number (Nu) has been investigated. The result shows that the location opposite the baffles, close to the fluid outlet, is the optimal choice to be considered for industrial applications.