Authors: A Barletta M Celli E Magyari E Zanchini
Publish Date: 2007/09/14
Volume: 44, Issue: 8, Pages: 1005-1013
Abstract
Buoyant magnetohydrodynamic MHD flows with Joulean and viscous heating effects are considered in a vertical parallel plate channel The applied magnetic field is uniform and perpendicular to the plates which are subject to adiabatic and isothermal boundary conditions respectively The main issue of the paper is the levitation regime ie the fully developed flow regime for large values of the Hartmann number M when the hydrodynamic pressure gradient evaluated at the temperature of the adiabatic wall is vanishing The problem is solved analytically by Taylor series method and the solution is validated numerically It is found that the fluid velocity points everywhere and for all values of M downward For small M’s the velocity field extends nearly symmetrically with respect to the midplane over the whole section of the channel between the adiabatic and the isothermal walls For large values of M by contrast the fluid levitates over a broad transversal range of the channel while the motion becomes concentrated in a narrow boundary layer in the neighborhood of the isothermal wall Accordingly the fluid temperature is nearly uniform in the levitation range and decreases rapidly within the boundary layer in front of the isothermal wall It also turns out that not only the volumetric heat generation by the Joule effect but also that by viscous friction increases rapidly with increasing values of M the latter effect being even larger than the former one for all M
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