The effect of magnetic field on instabilities of heat transfer from an obstacle in a channel

This paper presents forced convective heat transfer in a channel with a built-in square obstacle. The governing equations with the boundary conditions are solved using a finite volume method. The computations were done for a fixed blockage ratio (S=1/8) at Pr=0.71, and Reynolds (Re) and Stuart (N) numbers ranging from 1 to 250 and 0 to 10, respectively. The results are presented to show the effect of the channel walls and streamwise magnetic field at different Reynolds numbers on forced convection heat transfer from a square cylinder. A correlation is obtained for Nusselt number, in which the effect of a magnetic field is taken into account. The obtained results revealed that the existence of channel walls decreases the effects of magnetic field on Nusselt number. It also showed that by increasing Stuart number the thickness of thermal boundary layer increases and the convective heat transfer decreases. •The magnetic field is used to control the instabilities of heat transfer.•The thickness of thermal boundary layer increases by increasing Stuart number.•Unsteadiness in temperature field increases with increase in Reynolds number.•Time-averaged Nusselt number decreases with increase in Stuart number.•The Lorentz forces are much denser near the surface of the obstacle.