A fully analytical solution of convection in ferrofluids during Couette-Poiseuille flow subjected to an orthogonal magnetic field

Abstract

We report the transport of thermal energy during a hydrodynamically as well as thermally developed Couette-Poiseuille flow of ferrofluid (FF) through parallel-plate channels subjected to a constant magnetic field, orthogonal to the channel axis. The fluid motion is imparted by a combination of tangential stress, attributable to the motion of one of the plates, and a constant pressure gradient present in the direction of the channel axis. Apart from imparting a body force and torque, the application of an external magnetic field increases both the dynamic viscosity and effective thermal conductivity of the FF. As a result, thermal energy transport is uniquely affected. The complex coupling of magnetics with hydrodynamics results in implicit governing equations, which cannot be solved analytically in their full form. On the basis of logical reasoning, the governing equations are simplified to generate closed-form solutions of temperature profiles and Nusselt numbers. For a comprehensive study, we consider three different sets of thermal boundary conditions amenable to analytical solutions. Till the saturation of magnetization, we observe an increase in the local temperature as the strength of the applied magnetic field increases. The effects of particle loading in FF, Brinkman number, and heat flux ratio on the temperature field are also discussed.