Thermo-magneto-convection and mechanism of multiple eddy formation due to applied magnetic field in a lid-driven cavity

Abstract

Abstract Magnetohydrodynamic study of eddy formation and heat transfer in a bottom heated two-dimensional lid-driven cavity with the insulated sidewall is reported in this paper. We consider the classic problem of a two-dimensional lid driven cavity in the presence of an applied external magnetic field. In the standard nonlinear Navier–Stokes equation and the energy equation, appropriate terms are added to model the applied magnetic field and thermo-magnetic convection. And we have derived a higher-order numerical scheme that can provide solutions that are fourth-order accurate. The scheme is implemented with suitable fourth-order accurate boundary conditions. The square LDC enclosure is filled with a fluid of Pr = 6.2. The top lid of the cavity is kept moving with constant velocity. The effect of magnetic field on heat transfer and eddy formation is discussed for 0 ≤ Ha ≤ 250, Re = 10 2 ≤ Re ≤ 10 3 and 103 ≤ Gr ≤ 104 and the results are presented in terms of contour plots of streamlines, isotherms, Lorentz force, and the kinetic energy. The physical mechanism for forming multiple recirculation zones is understood and attributed to two opposite forces acting in the fluid about the center-line of the cavity, which acts like a couple (and hence rotational flow). This is discovered by computing the Lorentz force acting in the entire domain of fluid flow. Similarly, from the computation of kinetic energy of the fluid at all the grid points in the fluid region, it is revealed that conduction is the dominant heat transfer mechanism at higher magnetic fields. At the same time, convection is the prime mode at low magnetic fields. It is ascertained that with an increase in magnetic field intensity, velocity profiles are suppressed, and heat transfer stabilizes, giving rise to the formation of recirculation zones in the cavity.