MHD-mixed convection from a vertical slender cylinder Orhan Aydin a, * , Ahmet Kaya b a Department of Mechanical Engineering, Karadeniz Technical University, 61080 Trabzon, Turkey b Department of Mechanical Engineering, Aksaray University, 68100 Aksaray, Turkey article info Article history: Received 8 May 2010 Received in revised form 3 August 2010 Accepted 3 August 2010 Available online 7 August 2010 Keywords: Vertical slender cylinder Buoyancy effect MHD flow Electric field abstract The problem of steady laminar magnetohydrodynamic (MHD) mixed convection heat transfer about a vertical slender cylinder is studied numerically. A uniform magnetic field is applied perpendicular to the cylinder. The resulting governing equations are transformed into the non-similar boundary layer equations and solved using the Keller box method. The velocity and temperature profiles as well as the local skin friction and the local heat trans- fer parameters are determined for different values of the governing parameters, mainly the transverse curvature parameter, the magnetic parameter, the electric field parameter and the Richardson number. 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, increasing the Richardson number, Ri (i.e. the mixed convection parameter), electric field parameter E 1 and magnetic parameter Mn. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Mixed convection flow along vertical cylinders is important in situations encountered in the areas of geothermal power generation and drilling operation when free stream velocity and induced buoyancy velocity are of comparable order. How- ever it has not drawn much research interest. Free or mixed convection along a vertical slender cylinder is less studied compared to the forced convection along it. Hossain and Alim [1] studied a free convection flow of an optically dense viscous incompressible fluid along a vertical thin circular cylinder with effect of radiation. Chen and Mucoglu [2] analyzed the buoyancy and transverse curvature effects on forced convection of Newtonian fluid flow along an isothermal vertical cylinder using the local non-similarity method. The same problem for a uniform surface heat flux case was conducted by Mucoglu and Chen [3]. Lee et al. [4] studied the problem of mixed convection along a vertical cylinder with uniform surface heat flux for the entire mixed convection regime, ranging from pure forced convection to pure free convection by employing the buoyancy and curvature parameters. Takhar et al. [5] studied the mixed convection flow over a continuous moving vertical slender cylinder under the combined buoyancy effect of thermal and mass diffusion. Kumari and Nath [6] studied the effects of localized cooling/heating and injection/suction on the mixed convection flow on a thin vertical cylinder. Chang [7] numerically investigated of the flow and heat transfer char- acteristics of free convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with conduction effects. Roy et al. [8] developed general analysis for the influence of non-uniform double slot injection (suction) on the steady non-similar incompressible laminar boundary layer flow over a slender cylinder. Singh et al. [9] studied unsteady mixed con- vection flow over a rotating vertical slender cylinder under the combined effects of buoyancy force and thermal diffusion with injection/suction where the slender cylinder is inline with the flow. 1007-5704/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cnsns.2010.08.003 * Corresponding author. Tel.: +90 (462) 377 2974; fax: +90 (462) 325 5526. E-mail address: oaydin@ktu.edu.tr (O. Aydin). Commun Nonlinear Sci Numer Simulat 16 (2011) 1863–1873 Contents lists available at ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns