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Zbl 0753.76194
Garandet, J.P.; Alboussiere, T.; Moreau, R.
Buoyancy driven convection in a rectangular enclosure with a transverse magnetic field. (English)
[J] Int. J. Heat Mass Transfer 35, No.4, 741-748 (1992). ISSN 0017-9310

Summary: We propose an analytical solution to the equations of magnetohydrodynamics that can be used to model the effect of a transverse magnetic field on buoyancy driven convection in a two-dimensional cavity. In the high Hartmann number limit, the velocity gradient in the core is constant outside of the two Hartmann layers at the vicinity of the walls normal to the magnetic field. We show that this core solution is correct everywhere in the cavity except in a boundary layer of extent $Ha\sp{- 1/2}$ at the cold wall. The recirculating part of the flow is studied by means of a series expansion that allows the computation of the stream function. We also present the variation of both components of velocity as a function of $Ha$, along with a discussion of the validity of our assumptions.

MSC 2000:: *76W05 Flows in presence of electromagnetic forces
76R10 Free convection
35C10 Series solutions of PDE

Keywords: Bousinesq approximation; analytical solution; high Hartmann number limit; velocity gradient; core solution; boundary layer; series expansion

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