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Two-dimensional steady-state Rayleigh-Bénard convection of thermodependent power-law fluids confined in a square cavity, heated from the bottom and cooled on the top with uniform heat fluxes, has been conducted numerically using a finite difference technique. The effects of the governing parameters, which are the Pearson number (0 ≤ m ≤ 10), the flow behaviour index (0.6 ≤ n ≤ 1.4), and the Rayleigh number (0 < Ra ≤ 10 5 ), on the flow onset, flow structure, and heat transfer have been examined. The heatlines concept has been used to explain the heat transfer deterioration due to temperature-dependent viscosity effect that m expresses.

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The interaction between mixed convection and thermal radiation in ventilated cavities with gray surfaces has been studied numerically using the Navier‐Stokes equations with the Boussinesq approximation. The effect of thermal radiation on streamlines and isotherms is shown for different values of the governing parameters namely, the Rayleigh number (103 ≤ Ra ≤ 106), the Reynolds number (50 ≤ Re ≤ 5000) and the surfaces emissivity (0 ≤ ε≤ 1). The geometrical parameters are the aspect ratio of the cavity A = L’/H’ = 2 and the relative height of the openings B = h’/H’ = 1/4. Results of the study show that thermal radiation alters significantly the temperature distribution, the flow fields and the heat transfer across the active walls of the cavities.

Mixed convection heat transfer in ventilated cavities submitted to a constant heat flux has been numerically studied using the Navier‐Stokes equations with the Boussinesq approximation. Results in terms of streamlines and isotherms are produced for different values of the governing parameters, namely, the Rayleigh number (103 ≤q Ra ≤q 106) and the Reynolds number (5 ≤q Re ≤q 5, 000). The geometrical parameters are the aspect ratio of the cavity A = L’/H’ = 2 and the relative height of the openings B = h’/H’ = 1/4. Results of the simulations show that the maximum interaction between natural and forced convection occurs for couples (Ra, Re) which can be correlated as Re = a Rab.

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