Three-dimensional simulation of full conduction-convection-radiation coupling with high Rayleigh numbers

The present research is focused on numerical analysis of heat transfer and fluid flow patterns when taking into account conduction, natural convection and surface thermal radiation under three-dimensional problem formulation. A hybrid mathematical model coupling the mesoscopic lattice Boltzmann equations with the macroscopic energy equation is built. The governing equations are solved in MATLAB. An in-house code developed in this work can be both run on central processing units and graphics processing units with almost no changes. Multiparameter analysis was performed when varying the Rayleigh number (Ra), surface emissivity, Biot number, conduction-radiation number, thermophysical properties and thickness of the solid walls. During numerical simulation, it was found that the vertical walls emissivity can be used as a tool to control thermal and flow behavior. In fact, three modes of heat transfer such as thermal stratification, thermal fluctuations and thermal plume were revealed when Ra = 108. With further increase of the Rayleigh number thermal and flow fluctuations were observed at the bottom half of the cavity. A significant discrepancy in results was observed between the 2D and 3D models when taking into account surface radiation. Finally, correlations for mean convective, radiative and effective Nusselt numbers were proposed.