Experimental and theoretical investigations on thermal conductivity of a ferrofluid under the influence of magnetic field

. The effect of the strength and orientation of magnetic field with respect to the temperature gradient on the effective thermal conductivity λ e f f ( H ) , in a kerosene-based ferrofluid with magnetite particles is reported. A new theoretical model to explain the experimental dependence λ e f f ( H ) , obtained for both the parallel and perpendicular orientation of the magnetic field, relative to the temperature gradient is proposed, based on the Sillars equation (which is applied for the first time to a ferrofluid in this purpose). For computing λ t h e o r , we have considered that the particle agglomerations, arranged in field-induced microstructures, have ellipsoid forms and the ratio a / b between the major axis and the minor axis of the ellipsoid increases with increasing the magnetic field strength. Using the proposed theoretical model, we established for the first time a semi-empirical relationship between the ratio, a / b and the magnetic field, H , both for parallel and perpendicular H relative to the temperature gradient, determining then the dependence on H of λ t h e o r . The theoretical results are in agreement with the experimental measurements. The reported results are of great practical importance and show that ferrofluids may be useful for incorporation in magnetic tuneable heat transfer devices or for other potential thermal applications. Graphical abstract