Lattice Boltzmann Simulation of Magnetic Field Effect on Electrically Conducting Fluid at Inclined Angles in Rayleigh-B閚ard Convection

Abstract

The magneto-hydrodynamics (MHD) effect is studied at different inclined angles in Rayleigh-Bénard (RB) convection inside a rectangular enclosure using the lattice Boltzmann method (LBM). The enclosure is filled with electrically conducting fluids of different characteristics. These characteristics are defined by Prandtl number, Pr. The considered Pr values for this study are 10 and 70. The influence of other dimensionless parameters Rayleigh numbers Ra = 103; 104; 105; 106 and Hartmann numbers Ha = 0, 10, 25, 50, 100, on fluid flow and heat transfer, are also investigated considering different inclined angles φ of magnetic field by analyzing computed local Nusselt numbers and average Nusselt numbers. The results of the study show the undoubted prediction capability of LBM for the current problem. The simulated results demonstrate that the augmentation in heat transfer is directly related to Ra values, but it is opposite while observing the characteristics of Ha values. However, it is also found that φ has a significant impact on heat transfer for different fluids. Besides, isotherms are found to be always parallel to the horizontal axis at Ra = 103 as conduction overcomes the convection in the heat transfer, but this behaviour is not seen at Ra = 104 when Ha ≥ 25. Furthermore, at Ra = 106, oscillatory instability appears but LBM is still able to provide a complete map of this predicted behavior. An appropriate validation with previous numerical studies demonstrates the accuracy of the present approach.