MHD mixed convection of a viscous dissipating fluid about a permeable vertical flat plate.

*(English)*Zbl 1205.76292Summary: The problem of steady laminar magnetohydrodynamic (MHD) mixed convection heat transfer about a vertical plate is studied numerically, taking into account the effects of Ohmic heating and viscous dissipation. A uniform magnetic field is applied perpendicular to the plate. The resulting governing equations are transformed into the non-similar boundary layer equations and solved using the Keller box method. Both the aiding-buoyancy mode and the opposing-buoyancy mode of the mixed convection are examined. The velocity and temperature profiles as well as the local skin friction and local heat transfer parameters are determined for different values of the governing parameters, mainly the magnetic parameter, the Richardson number, the Eckert number and the suction/injection parameter, \(f_{w}\). For some specific values of the governing parameters, the results agree very well with those available in the literature. Generally, it is determined that the local skin friction coefficient and the local heat transfer coefficient increase owing to suction of fluid, increasing the Richardson number, \(R_i\) (i.e. the mixed convection parameter) or decreasing the Eckert number. This trend reverses for blowing of fluid and decreasing the Richardson number or decreasing the Eckert number. It is disclosed that the value of \(Ri\) determines the effect of the magnetic parameter on the momentum and heat transfer.

##### MSC:

76W05 | Magnetohydrodynamics and electrohydrodynamics |

76E06 | Convection in hydrodynamic stability |

74K20 | Plates |

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\textit{O. Aydın} and \textit{A. Kaya}, Appl. Math. Modelling 33, No. 11, 4086--4096 (2009; Zbl 1205.76292)

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