On the Limits of Validity of the Low Magnetic Reynolds Number Approximation in MHD Natural-Convection Heat Transfer

TLDR: In the majority of magnetohydrodynamic (MHD) natural-convection simulations, the Lorentz force due to the magnetic field is suppressed into a damping term resisting the fluid motion as discussed by the authors.

Abstract: In the majority of magnetohydrodynamic (MHD) natural-convection simulations, the Lorentz force due to the magnetic field is suppressed into a damping term resisting the fluid motion. The primary benefit of this hypothesis, commonly called the low-R m approximation, is a considerable reduction of the number of equations required to be solved. The limitations in predicting the flow and heat transfer characteristics and the related errors of this approximation are the subject of the present study. Results corresponding to numerical solutions of the full MHD equations, as the magnetic Reynolds number decreases to a value of 10−3, are compared with those of the low-R m approximation. The influence of the most important parameters of MHD natural-convection problems (such as the Grashof, Hartmann, and Prandtl numbers) are discussed according to the magnetic model used. The natural-convection heat transfer in a square enclosure heated laterally, and subject to a transverse uniform magnetic field, is chosen as a c...