Natural convection in nanofluid-filled quadrantal cavities under magnetic field: Application of the SUPS formulation

A computational investigation of magnetohydrodynamic natural convection heat transfer phenomena, which find applications from energy conversation systems to lab-on-a-chip technologies, in nanofluid-filled quarter-circle-shaped (quadrantal) cavities with various temperature boundary conditions is presented. Toward that end, using the Boussinesq approximation for density, the Navier-Stokes equations of incompressible flows are coupled with the heat equation, and magnetic source terms are also incorporated into the governing equations. In computations, pure water serves as the base fluid; Cu (copper) or Al2O3 (alumina) serve as the nanoparticles, and it is assumed that the nanofluids are homogeneous. It is well known that when simulating incompressible flows within the classical framework of the Galerkin finite element method (GFEM), inappropriate choice of interpolation functions leads to nonphysical oscillations in the flow field, particularly for high Rayleigh numbers. In order to get around such numerical instabilities, the streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) stabilization terms are incorporated into the GFEM formulation. Numerical simulations are performed for various values of Rayleigh (Ra) and Hartman (Ha) numbers, ranging between 103 <= Ra <= 106 and 0 <= Ha <= 100. The proposed formulation and techniques work quite well even at high Rayleigh numbers, according to numerical simulations and comparisons with reported findings. Furthermore, it is demonstrated that the proposed formulation yields no significant numerical instabilities either locally or globally and that this is achieved only by using linear and equal-order interpolation functions, hence eliminating the requirement for adaptive mesh strategies and saving computing time considerably.