Optimization of Heat Transfer in a Square Cavity With Nonuniform Wall Cooling and Thermal Radiation Using MRT-LBM

The current study investigates the coupling of radiation and natural convection heat transfer in a two-dimensional square cavity using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Particular emphasis is placed on comparing uniform and sinusoidal cooling on one vertical wall. The key parameters explored are the Rayleigh number (103 ≤ Ra ≤ 107), heater position (0.2 ≤ b ≤ 0.8), phase shift (0 ≤ φ ≤ π), and wall emissivity (0 ≤ ε ≤ 1). The findings are presented in the form of comprehensive streamline graphs, isotherms, and heat transfer plots. Results show that an increase in the Rayleigh number and wall emissivity considerably augments the flow complexity as well as the heat transfer. Sinusoidal cooling is discovered to be much more effective than uniform cooling, especially for high Rayleigh numbers in the presence of radiation. In all the configurations that have been explored, the mid-height heater position (b = 0.5) has shown the best performance. The study concludes by declaring that the most efficient way to enhance combined surface radiation and natural convection heat transfer inside enclosures is sinusoidal cooling at a π/3 - π/2 phase shift in combination with central heating (b = 0.5).