A numerical study on the role of dipole interactions on the heat transfer rates in a ferrofluid shear flow

A square partially heated lid-driven cavity filled with ferrofluid subjected to the applied field of a permanent magnet is investigated numerically. These simulations are performed using an in-house code based on the Finite Volume Method. The problem is governed by mass, momentum and energy conservation laws. A phenomenological magnetization equation, which considers the mechanism of long-range dipolar interactions on the scale of the particles, is also used. Laminar steady-state solutions are obtained based on commercial fluids properties and the effects of coupled mechanisms are discussed. A consistent coupling between hydrodynamic, thermal and magnetic effects is observed depending on the particles relaxation time. A high-order model for the equilibrium magnetization, which accounts for the effect of long-range dipolar interactions is considered. The simulations consider particle concentrations of up to 40%. Under such conditions, an enhancement of up to 15% on the average Nusselt number is obtained for R e = 100 due to strong dipolar interaction effects. Different combinations for the thermal boundary conditions and lid velocity orientations are considered. A linear relation between the mean Nusselt number and the dipole coupling parameter is observed and justified in terms of scaling arguments.