Effect of alumina nano-powder on the natural convection of water under the influence of a magnetic field in a cavity and optimization using RMS: Using empirical correlations for the thermal conductivity and a sensitivity analysis

In the current research, the free convection and radiation heat transfer of the alumina/water nanofluid in a two-dimensional square cavity at an angle of 45 degrees with the horizontal has been studied numerically. With the aid of the Plackett-Burman method, the orders of the parameters are determined based on the Nusselt number, entropy generation, and irreversibility. After selecting the most important parameters, the relationship between the inputs and outputs is established via central composite design. Hence, the magnetic field, the radiation parameter, the pipes aspect ratio, and the Rayleigh number have the most effect on the flow and heat transfer. With an increase in the Hartmann number, the heat transfer reduces by 30%, and the entropy generation decreases by 25% in the absence of radiation and by 29% in the presence of it. With an increase in radiation, the rate of heat transfer and the generated entropy increase by 98% and 1%, respectively. Adding 6% volume fraction of alumina nanoparticles to water can increase the rate of heat transfer by 3.7%. Sensitivity analysis shows that the heat transfer and the generated entropy are most sensitive to the Rayleigh number and the pipe aspect ratio. Finally, the optimal condition has been presented.