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In this paper, we explore the von-Kármán infinite disk problem for the situation where ferrofluid resides in the space above the rotating disk. Furthermore, flow field is influenced by axial magnetic field. In this study, we treat water as the base fluid which consists of homogeneous suspensions ofFe3O4${\rm{F}}{{\rm{e}}_{\rm{3}}}{{\rm{O}}_{\rm{4}}}$    ferromagnetic particles. The main motivation here is to resolve heat transfer problem in the existence of non-linear radiative heat transfer. With the aid of von-Kármán relations, the equations of fluid motion and heat transfer are changed into a set of self-similar differential equations. These equations are dealt by an implicit finite-difference method with high precision. The results reveal that wall heat transfer rate can be improved by increasing solid volume fraction of ferromagnetic particles. Drag coefficient at the disk and heat transfer rate are increased as the strength of Lorentz force is enhanced. Viscous dissipation effect has an important part in improving heart transfer process which is vital in some applications. The results demonstrate that cooling capability of magnetite–water nanofluid is much superior to the conventional coolants. An excellent correlation of present results with the previous published articles is found in the all the cases.

Numerical Solutions for Radiative Heat Transfer in Ferrofluid Flow due to a Rotating Disk: Tiwari and Das Model