Numerical simulation of turbulent natural convection combined with surface thermal radiation in a square cavity

Purpose – The purpose of this paper is to present transient turbulent natural convection with surface thermal radiation in a square differentially heated enclosure using non-primitive variables like stream function and vorticity. Design/methodology/approach – The governing equations formulated in dimensionless variables “stream function, vorticity and temperature,” within the Boussinesq approach taking into account the standard two equation k-ε turbulence model with physical boundary conditions have been solved using an iterative implicit finite-difference method. Findings – It has been found that using of the presented algebraic transformation of the mesh allows to effectively conduct numerical analysis of turbulent natural convection with thermal surface radiation. It has been shown that the average convective Nusselt number increases with the Rayleigh number and decreases with the surface emissivity, while the average radiative Nusselt number is an increasing function of these key parameters. It has been shown that a presence of surface thermal radiation effect leads to an expansion of the eddy viscosity zones close to the walls. Originality/value – It should be noted that for the first time in this paper we used stream function and vorticity variables with very effective algebraic transformation of the mesh in order to create a non-uniform mesh for an analysis of turbulent flow. Such method allows to reduce the computational time essentially in comparison with using of the primitive variables. The considered method has been successfully validated on the basis of the experimental and numerical data of other authors in case of turbulent natural convection without thermal radiation. The used numerical method would benefit scientists and engineers to become familiar with the analysis of turbulent convective heat and mass transfer, and the way to predict the properties of the turbulent flow in advanced nuclear systems, in industrial sectors including transportation, power generation, chemical sectors, ventilation, air-conditioning, etc.