TWO-DIMENSIONAL LATTICE BOLTZMANN SIMULATION OF NATURAL CONVECTION IN DIFFERENTIALLY HEATED SQUARE CAVITY: EFFECT OF PRANDTL AND RAYLEIGH NUMBERS

A thermal lattice Boltzmann method is utilized for the numerical simulation of the natural convection heat transfer phenomena inside a differentially heated square cavity. Numerical simulations are performed to elucidate the combined effects of Prandtl number (0.71 Pr 100) and Rayleigh number (10(4) Ra 10(6)) on heat transfer and fluid flow characteristics inside the cavity. Detailed insights are gained by the evaluation of isotherms, stream functions and vorticity profiles. For higher Prandtl and Rayleigh numbers, streamlines become more confined to hot wall with the loss of symmetry. Similarly, isotherms patterns become more stratified towards the hot wall. The centre-line velocity and temperature profiles are also analyzed. Further, the heat transfer rate is estimated in terms of average Nusselt number. It suggests a proportional increase in the average Nusselt number with the increasing values of Prandtl number for considered range of Rayleigh numbers. Finally, the numerical data for the average Nusselt number are presented in the form of a correlation for their best utilization in design and engineering practices.