The Non-Monotonic Behavior of Forced Convective Heat Transfer Under the Influence of an External Magnetic Field

Abstract

The heat transfer due to forced convection from an isothermal sphere in a steady stream of viscous, incompressible, and electrically conducting fluid under the influence of an external magnetic field is analyzed. Fourth order compact scheme is combined with the multigrid method to solve the energy equation in spherical polar coordinates. It is known from the literature that in the absence of a magnetic field, the variation of mean Nusselt number N _m with Prandtl number Pr follows a power law which in the present work is modified to include the effect of the magnetic field. For low moderate strength of magnetic field, i.e., 0 < N ≤ 2, a degradation of heat transfer is observed, however for N ≥ 3 the heat transfer is increased leading to a non-monotonic behavior. Further, it is observed that the thermal gradients are found to be non-monotonic with magnetic field. The relation between mean Nusselt number and thermal boundary layer thickness with respect to Prandtl number has also been analyzed.

Acknowledgments

One of the authors, R. Sivakumar, is thankful to U.G.C (F. No. 37-312/2009(SR)) for providing the financial support for this research.

Notes

†for Pr = 0.7.