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Effects of magnetic field and nonlinear temperature profile on Marangoni convection in micropolar fluid. (English) Zbl 1186.80008
Summary: The combined effects of a uniform vertical magnetic field and a nonuniform basic temperature profile on the onset of steady Marangoni convection in a horizontal layer of micropolar fluid are studied. The closed-form expression for the Marangoni number \(M\) for the onset of convection, valid for polynomial-type basic temperature profiles upto a third order, is obtained by the use of the single-term Galerkin technique. The critical conditions for the onset of convection have been presented graphically.

MSC:
80A20 Heat and mass transfer, heat flow (MSC2010)
76R10 Free convection
76W05 Magnetohydrodynamics and electrohydrodynamics
76A05 Non-Newtonian fluids
35Q35 PDEs in connection with fluid mechanics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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