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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
##### Keywords:
Marangoni convection; Galerkin technique
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