Effects of magnetic field and nonlinear temperature profile on Marangoni convection in micropolar fluid.

*(English)*Zbl 1186.80008Summary: 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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\textit{M. N. Mahmud} et al., Differ. Equ. Nonlinear Mech. 2009, Article ID 748794, 11 p. (2009; Zbl 1186.80008)

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