The Effect of Magnetic Field and Nanoparticle Shape on Heat Transfer in an Inclined Cavity with Uniform Heat Generation/Absorption

In the present work, the effect of magnetic field, changes in the angle of inclination of the cavity and the shape of nanoparticles on the flow field and heat transfer of water-alumina with uniform heat generation/absorption is investigated by Lattice Boltzmann method (LBM). The curved wall and the diagonal walls of the cavity are at a constant temperature of hot and cold, respectively. Nanoparticle volume fraction  of 0, 0.02 and 0.04, Hartmann number of 0, 15, 30, 45 and 60, heat generation/absorption coefficient of -5, 0 and +5 and inclination angle of 45, 135 and 225 degrees are studied. The high accuracy of the results compared to previous studies confirmed the correctness of the code written in Fortran language. The results shows that in all cases, increasing the Hartmann number leads to a decrease in the maximum value of the streamlines and the average Nusselt number, with the lowest effect at 225 degrees. Also increasing the strength of the magnetic field leads to an average decrease of 28, 23 and 7% of the average Nusselt number for angles of 45, 135 and 225 degrees, respectively. Increasing the heat generation/absorption coefficient is a determining factor in the effectiveness of the magnetic field and adding nanoparticles, and increasing it reduces the amount of heat transfer. On average, heat generation reduces the average Nusselt number by 71, 98, and 145 percent for the angles of 45, 135, and 225 degrees, respectively. In general, the lowest value of the average Nusselt number is related to the angle of 225 degrees, but the effect of adding nanoparticles in increasing the average Nusselt number is the highest at this angle. Generally, an increase in the percentage of nanoparticles leads to an average increase of 12% in the average Nusselt number. The effect of nanoparticle shape is more apparent with increasing their volume fraction. The highest amount of heat transfer is related to the cylindrical nanoparticles, in which the average Nusselt number is on average about 6% higher than the spherical state.