The role of magnetic Reynolds number in MHD forced convection heat transfer

Higher Order Compact (HOC) Scheme combined with multigrid method is developed to investigate the role of magnetic Reynolds number in MHD heat transfer from a circular cylinder which is under the influence of an external magnetic field. The governing equations are coupled nonlinear Navier-Stokes and nonlinear Maxwell's equations which are expressed in stream function, vorticity and magnetic stream function (ψ-ω-A) formulation and decoupled energy equation. Apart from the usual kinetic Reynolds number Re, the parameters that governs the flow are magnetic Reynolds number Rm, Alfvén number β and Prandtl number Pr. The velocities of the flow are calculated with second order accurate based finite difference scheme and heat transfer equation is solved with fourth order accurate HOC scheme. The influence of the magnetic field and magnetic Reynolds number on velocity gradients is presented. It is found that the mean Nusselt number decreases until N ≤ 1 and then increases with further increase in the interaction parameter. It is also found that fluids having higher electrical conductivity can be effectively controlled with relatively low magnetic fields. The decrease in mean Nusselt number with β and Rm is in agreement with experimental findings.