Modeling and optimization of MHD mixed convection in a lid-driven trapezoidal cavity filled with alumina–water nanofluid: Effects of electrical conductivity models

Abstract

In this study, mixed convection in a lid driven trapezoidal cavity filled with Al2O3–water nanofluid under the effect of an inclined magnetic field was numerically investigated for various electrical conductivity models. The top and bottom wall of the trapezoidal cavity were maintained at constant cold and hot temperatures and the top wall is moving at a constant speed in positive x direction. The governing equations are solved with finite element method. Numerical simulations were performed for different values of Richardson numbers (between 0.01 and 25), strength and orientation of the uniform magnetic field (Hartmann number (between 0 and 40), magnetic inclination angle (between 0o and 90o)) and solid volume fraction of the nanofluid (between 0 and 0.03) for different electrical conductivity models. It was observed that as the value of the Richardson number, strength of the magnetic field and solid particle volume fractions enhance, discrepancy between the average Nusselt number increases for systems with different electrical conductivity models. Magnetic inclination angle for which the difference between average heat transfer rate is minimized for different electrical conductivity models depends on the side wall inclination angle of the trapezoidal cavity. After performing an optimization study, it was found that the optimum value of magnetic inclination angle is dependent on the electrical conductivity model.