MHD mixed convection in an inclined cavity containing adiabatic obstacle and filled with Cu-water nanofluid in the presence of the heat generation and partial slip

A steady laminar two-dimensional magneto-hydrodynamics mixed convection flow in a square inclined cavity filled with Cu-water nanofluid is investigated numerically by using the finite difference method. The left and right vertical sidewalls of the cavity are considered adiabatic and move upward, while a partial slip flow condition is imposed on these walls. The horizontal top wall is considered cold and stationary, while a part of the stationary bottom wall is subjected to a uniform heat source and the remaining parts of it are considered adiabatic. An adiabatic obstacle is located in the center of the cavity and an external magnetic field is applied parallel to the horizontal x-axis. Parametric studies of the influence of various parameters such as Hartmann number, inclination angle of the cavity, dimensionless heat generation/absorption coefficient, obstacle aspect ratio, dimensionless length and location of the heat source, and solid volume fraction on the fluid flow and heat transfer have been performed. Comparisons with previously published numerical work are performed, and good agreements between the results are observed. It is found that the nanofluid was better than water to enhance the heat transfer when the effect of the magnetic field is weak, while the water is better than the nanofluid when its effect is strong. Moreover, the results indicated that the partial slip has a significant effect on the above-mentioned parameters.