Correlation for Nusselt number in pure magnetic convection ferrofluid flow in a square cavity by a numerical investigation

Magnetic convection heat transfer in a two-dimensional square cavity induced by magnetic field gradient is investigated numerically using a semi-implicit finite volume method. The side walls of the cavity are heated with different temperatures, the top and bottom walls are isolated, and a permanent magnet is located near the bottom wall. Thermal buoyancy-induced flow is neglected due to the nongravity condition on the plane of the cavity. Conditions for the different values of non-dimensional variables in a variety of ferrofluid properties and magnetic field parameters are studied. Based on this numerical analysis, a general correlation for the overall Nusselt number on the side walls is introduced for a wide range of effective parameters. Results showed that maximum error produced by use of this correlation is about 6 percent.