Effect of two isothermal obstacles on the natural convection of nanofluid in the presence of magnetic field inside an enclosure with sinusoidal wall temperature distribution

In this study, the effect of magnetic field on the natural convection of Al2O3-water nanofluid inside a square enclosure with isothermal obstacles and sinusoidal wall temperature distribution has been numerically studied. The sidewalls were subject to sinusoidal boundary conditions, while the top and bottom walls were insulated. Two isothermal heat sources were implemented within the enclosure at the same distance from the center. The governing equations were transformed into the algebraic form using finite volume method and were then simultaneously solved using the SIMPLE algorithm. The proposed model by Vajjha was used to calculate the coefficient of thermal conductivity by taking Brownian motion of particles into account. In this study, the effect of Rayleigh number, aspect ratio, Hartmann number, direction change of applied magnetic field, and the volumetric percentage of nanoparticles was investigated. The results indicated that by increasing the Hartmann number, the fluid velocity as well as the Nusselt number decreased at all volumetric fractions of nanoparticles. An increase in the volumetric fraction of nanoparticles increased the Nusselt number, so that at a nanoparticle concentration of 6%, the mean Nusselt number increased by 9.04% compared to that of the base fluid. Moreover, the Nusselt number increased by increasing the magnetic field angle and the Rayleigh number, while it decreased as the aspect ratio was increased.