Natural convection in an enclosure with a pair of cylinders under magnetic field

Abstract

This two-dimensional numerical study investigates magnetohydrodynamic unsteady natural convection heat transfer inside an enclosure with two heated circular cylinders within it in the horizontal mid-plane. The fluid is incompressible and Newtonian. The governing transport equations based on the conservations of mass, momentum and energy are computationally solved using a finite element based numerical solver for the following range of parameters: dimensionless spacing between the cylinders S = 0.1–0.5, Rayleigh number Ra = 103–106 and Hartmann number Ha = 0–120. The results show that for lower values of Ra the heat transfer remains unaltered by the imposed magnetic field for a specific value of S as the transport mechanism is diffusion, while, for higher Ra, there is a complex interaction between the magnetic field and the physico-thermal properties that determines the heat transfer rate. For lower Ra the time-averaged Nusselt number (Nut) remains almost unaltered with Ha. However, at higher Ra, Nut initially decreases with Ha and then remains approximately constant and the transition between conductive and convective heat transfer occurs at higher Ra values. Moreover, for higher Ra, Nut decreases somewhat initially with the increase of S from 0.1 to 0.2 and thereafter, Nut slightly increases with S.

Keywords

• Enclosure
• Magnetic field
• Natural convection
• Nusselt number