Anisotropic heat transfer of ferro-nanofluid in partially heated rectangular enclosures under magnetic field

The natural convection and anisotropic heat transfer of ferro-nanofluids in partially heated enclosures is studied for revealing the influence of the anisotropy of thermal conductivity, which is generated by the existence of external magnetic field. The viscosity of the ferro-nanofluid is assumed to vary with the nanoparticle concentration. The constitutive model of the anisotropic thermal conductivity is derived based on the principle of material frame indifference of Continuum Mechanics, and the numerical solver is built based on the library of OpenFOAM. Both problems of pure heat conduction and natural convection are investigated, and a series of numerical simulations are conducted for different relevant parameters such as the types of the magnetic field, nanoparticle concentration, Hartmann number and Rayleigh number. The numerical results show that the heat transfer along the magnetic field direction is apparently enhanced with Hartmann number of 0.1 and nanoparticle concentration of 0.05, which implies the feasibility of controlling the heat transfer of the ferro-nanofluids by adjusting the external magnetic field. Furthermore, for pure heat conduction, the increasing of the Hartmann number and nanoparticle concentration raises the anisotropic thermal conductivity; and in the natural convection case, increasing the intensity of magnetic field could also raises the Lorentz force resistance. In addition, the Nusselt number is larger with higher Rayleigh number and lower Hartmann number, as the Rayleigh number increases from 1 x 10(3) to 1 x 10(5), the average Nusselt number on the heater increases from 0.888 to 3.139, and it decreases from 3.789 to 2.866 when Hartmann number is 0 and 10.