Heat transfer through ferrofluids as a function of the magnetic field strength

A theory is presented and is used to estimate weakly supercritical heat transport through a horizontal layer of vertically magnetized ferrofluid over a large range of magnetic field strengths. Finlayson's earlier analysis of the linear thermoconvective stability problem (J. Fluid Mech.40, 753, 1970) contains a parameter (M₃) related to nonlinearity in the magnetization curve of the ferrofluid. This parameter is reinterpreted and we show that for typical models of ferrofluid magnetization it is restricted to a much narrower range of values than the examples of Finlayson suggest. For any fixed value of the ratio of the Rayleigh number to the critical Rayleigh number, the Nusselt number is always larger when the liquid layer is heated from above than when the layer is heated from below.