Nusselt–Rayleigh correlations for design of industrial elements: Experimental and numerical investigation of natural convection in tilted square air filled enclosures

Abstract

Natural convection in air filled 2D tilted square cavities is experimentally and numerically studied. The hot and cold walls of the cavity are maintained isothermal at temperatures T h and T c, respectively, and the channel of the cavity is adiabatic. Measurements and simulations are performed for various geometrical and thermal configurations. Different values of the Rayleigh number Ra and the tilt angle α of the cavity are considered. The range of Ra covered in our work extends from 10 to 10 10 while α varies from 0 to 360°. This permits the analysis of several significant situations corresponding to vertical active walls ( α = 0°), hot wall at the bottom ( α = 90°; Rayleigh–Bénard convection) and hot wall at the top, pure conductive mode ( α = 270°). A computational 2D model based on the finite volume method is used for solving the mass, momentum and energy transfer governing equations. The simulation provides thermal and dynamic maps of the fluid for all configurations treated. The influence of Ra and α on the flow pattern and on the convective heat transfer are analysed and discussed. The thermal boundary distribution and the convective heat transfer calculated are, for most treated cases, close to those obtained experimentally by means of a simple bench specifically designed for this purpose. The maximum discrepancy between the simulations and measurements is relatively small, corresponding to the expected uncertainty of the model and measurements. The convective heat transfer is determined while calculating the radiative and conductive contributions to the global exchange. Radiation is determined by the radiosity method associated with the measured field of temperatures as well as to the global IR emissivities of all the internal elements of the cavity. The average Nusselt number Nu ¯ is used to quantify the calculated convective contribution of the heat exchange within the cavity, and is compared with the measured value Nu ¯ m . We propose Nu ¯ – Ra type correlations that are useful for sizing structures based on this type of cavities. In those aspects that are comparable, the results presented here are congruent with the numerous analyses found in the literature on this matter. The experimental results of this work complement the relatively small amount of values available in the literature since most of the studies are numerical. Covering a wide range of Rayleigh numbers, the good correlation between the experimental and computational results constitute an interesting tool for sizing systems in several industrial sectors.