Natural Convection of an Electrically Conducting Fluid from a Vertical Plate in the Presence of a Magnetic Field

The natural convection of an electrically conducting fluid on a vertical plate in the presence of a transverse magnetic field is analysed for the magnetic field depending on the λ th power of the vertical distance. The effect of the magnetic field on the heat transfer may be uniformlly described by the magnetic parameter Z=Z0 (x/L)2λ+1/2, where Z0=2M^-2/GrL1/2 (M^- : Hartmann number, GrL : Grashof number, L : plate length). The local Nusselt number is reduced as the magnetic parameter is increased, for example, 14% at Z=1, 45% at Z=5 for Prandtl number Pr∼0.01, while 11% at Z=1, 36% at Z=5 for Pr∼1. Also, if the total magnetic field intensity is equal, the larger effect for the mean Nusselt number is expected in the case λ>0.