Finite element analysis of MHD free convective flow of nano fluid in a square cavity containing a heated cone of different orientation

Abstract

Free convection of Magnetohydrodynamic (MHD) fluidin a cavity with a heated cone has been investigated in this work. It is carried out in two parts. First, only the MHD fluid is considered. Secondly, nanoparticles are added to the MHD base fluid. The novelty of this work lies in the presence of the heated cone, whose orientation is varied at different angles. The mathematical model is developed by combining the mass, momentum and energy equations. The system of equation is solved by finite element method. Calculations are performed for different values of the dimensionless parameters Prandtl number (Pr), Rayleigh number (Ra), and Hartmann number (Ha). The results are illustrated with streamlines, velocity profiles, isotherms, local and average Nusselt number (Nu), and heat flux. From the first part, it is found thatthe effect of Ha becomes more prominent with higher values of Ra. Magnetic field affects the flow by retarding the fluid movement, and thus affects convective heat transfer. At low Ra, the fluid movement and heat transfer rate are already slow, thus impressing a magnetic field does not produce much effect. It is noted that a combination of low Ra with zero or low Ha produce similar effects with the combination of high Ra and high Ha. Increasing Hanegatively impacts heat transfer. It is also noted that orientation of the cone affects heat transfer. The left and right inclination of the cone results in greater heat transfer but only up to a certain Ha. For the second part, the volume fraction of nanoparticle φ is varied along with Ra and Ha. It is found that,adding nano particles significantly slows down the fluid velocity, but enhances heat transfer. This phenomenon can be explained by the nature of thermal conductivity of the nanofluid. In the nanofluid, the nanoparticles carry heat along with the base fluid. Thus, the overall heat transfer coefficient of the system is increased. The effect of varying φ, surpasses the effects of all other governing parameters with regards to heat transfer.