MAGNETIC FIELD EFFECT ON THE HEAT TRANSFER IN A NANOFLUID FILLED LID DRIVEN CAVITY WITH JOULE HEATING

Abstract

In this paper, the effects of magnetic field, Joule heating and volumetric heat generation on the heat transfer and fluid flow in a Cu-Water nanofluid filled lid driven cavity using enhanced streamfunction–velocity method are investigated. The cavity is heated by a uniform volumetric heat density and side walls have constant temperature. The top wall moves with constant velocity in +x direction, while no-slip boundary conditions are imposed on the other walls of the cavity. An inclined fixed magnetic field is applied to the left side wall of the cavity. The dimensionless governing equations are solved numerically for the stream function and temperature using finite difference method for various Richardson(Ri), Reynolds(Re), Hartmann (Ha), Eckert(Ec)numbers, magnetic field angle(α) and solid volume fraction of the nanofluid() in MATLAB software. To discretize the streamfunction-velocity formulation, a five point constant coefficient second-order compact finite difference approximation which avoids difficulties inherent in the conventional streamfunction–vorticity and primitive variable formulations is used. The stream function equation is solved using fast Poisson's equation solver on a rectangular grid (POICALC function in MATLAB) and the temperature equation is solved using Jacobi bi-conjugate gradient stabilized (BiCGSTAB) method. The heat transfer within the cavity is characterized by Nusselt number (Nu1). The results show that Nu1 is significantly increased by increasing Ri and  and increasing the Reynolds number enhances convective cooling. The heat transfer within the cavity is decreased by increasing Hartmann number which improves conduction heat transfer and reduces Nu1. Joule heating has a negative effect on the convection within the cavity and convection is decreased by increasing the value of Ec. It can be investigated that Nu1 is decreased by increasing Ec due to the strong distortion effect of Joule heating on convection current of heat transfer.