Computational analysis of magneto-hydrodynamic natural convection in partially differentially heated cavity: Effect of cooler size

Abstract

This work presents thermal lattice Boltzmann method simulation of magneto-hydrodynamic, buoyancy-driven convection in a partially differentially heated cavity (aspect ratio = 1) subjected to a magnetic field along the vertical direction, i.e. at 90°. Lattice Boltzmann method simulations are performed for three different cooler lengths (L_c = H/4, H/2, H) placed along the middle of one vertical wall for a wide range of Rayleigh and Hartmann numbers (10³≤ Ra ≤ 10⁵; Ha = 0, 60, 120) at fixed Prandtl number (Pr = 0.71, air). A partial heater is placed at the center of other vertical walls and its size is kept as half of the characteristic length (H/2). The physical insights of the systems are delineated by systematic analysis of stream function and temperature contours. Heat transfer characteristics of the cavity are elucidated by using averaged values of the Nusselt number. It is noted that average Nusselt number has a proportional dependence with cooler length and Rayleigh number, while it varied inversely with Hartmann number. Further, the functional dependence of average Nusselt number with cooler size, Rayleigh number, and Hartmann number is established for possible use in engineering design purpose.