Combined effect of radiation and natural convection in a rectangular enclosure discreetly heated from one side

Purpose - The aim of this work consists of studying numerically the coupling between natural convection and radiation in a tall rectangular cavity by examining the effect of the emissivity of the walls, epsilon, the Rayleigh number, Ra, and the inclination of the cavity, theta, on the flow characteristics and the existence ranges of the multiple solutions obtained. Design/methodology/approach - The Navier-Stokes equations were discretized by using a finite difference technique. The vorticity and energy equations were solved by the alternating direction implicit method. Values of the strewn function were obtained by using the point successive over-relaxation method. The calculation of the radiative heat exchange between the walls of the cavity is based on the radiosity method. Findings - For an inclined cavity (theta= 45 degrees), up to four different solutions are obtained and their range of existence is found to be strongly dependent on the Rayleigh number and the emissivity of the cavity walls. In the case of a vertical cavity (theta = 90 degrees), the weak reduction of the convection effect due to radiation is largely compensated for by the contribution of the radiation which enhances the overall heat transfer through the cold surface of the cavity and favours the appearance of secondary cells. Originality/value - The existence of multiple steady-state solutions in an inclined cavity (theta = 45 degrees) and the number of the obtained solutions are affected by the presence of radiation. In face, the increase of the emissivity reduces the number of solutions for weak values of the Rayleigh number. Also, the increase of this parameter favours the multiplicity of solutions for all the considered values of the emissivity. For a vertical cavity (theta = 90 degrees), the effect of radiation generates an oscillatory convection for large values of the Rayleigh number.