Effect of a magnetic field on heat transfer rate

Effect of a magnetic field on the heat transfer rate on free convection in a rectangular cavity with high magnetic prandtl

The interaction between magnetic fields and convection is an interesting phenomenon because of its many important engineering applications. Manufacturing processes like a crystal growth involves an electrically conducting fluid subject to a magnetic field. Due to natural convection motion the electric conductive fluid in a magnetic field experiences a Lorenz force and its effect is usually to reduce the flow velocities. A magnetic field can be used to control the flow field and increase or reduce the heat transfer rate. In this paper, the effect of a magnetic field in a natural convection flow of an electrically conducting fluid in a square cavity is studied numerically. The two sides walls of the cavity are maintained at two different constant temperatures while the upper wall and the lower wall are completely insulated. The coupling of the Navier-Stokes equations with the Maxwell equations is discussed with the assumptions and main simplifications assumed in typical problems of magnetohydrodynamics. The Lorenz force generates a rich variety of flow patterns depending on the values of the Rayleigh and Hartmann numbers. The effect of the magnetic field on the Nusselt number as a function of the Rayleigh number and the Hartmann number for different direction of the magnetic field is modeled and solved using  STAR-CCM+®. Numerical implementation using passive scalar is discussed in detail with the main difficulties encountered on convergence of the governing equations. Validation of the numerical results are presented and compared with some results reported on the literature.

University of Puerto Rico
Gustavo Gutierrez