Heat transfer due to natural convection in an inclined square cavity using the lattice Boltzmann equation method

The heat transfer due to natural convection of air in a square cavity with two differentially heated opposite walls and the other two adiabatic is numerically studied in the laminar regime as both the Rayleigh number and the inclination angle of the cavity change. The range of the inclination angle covers a whole revolution. The lattice Boltzmann method with two distribution functions, one for particles and the other for temperature is used. The method is validated with a benchmark result for a vertical cavity. A general power law dependence of the Nusselt number with respect to the Rayleigh number with the coefficient and exponent as functions of the inclination angle is presented. For a fixed Rayleigh number, hysteresis as the inclination angle increases or decreases is found. The range of inclination angles for hysteresis depends on the Rayleigh number. (C) 2012 Elsevier Masson SAS. All rights reserved.