ORIGINAL Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet with prescribed surface heat flux Fazlina Aman • Anuar Ishak Received: 2 December 2009 / Accepted: 22 April 2010 / Published online: 11 May 2010 Ó Springer-Verlag 2010 Abstract The similarity solution for the problem of mixed convection boundary layer flow adjacent to a stretching vertical sheet in an incompressible electrically conducting fluid in the presence of a transverse magnetic field is presented. It is assumed that the sheet is stretched with a power-law velocity and is subjected to a variable surface heat flux. The governing partial differential equa- tions are first transformed into a system of non-linear ordinary differential equations, before being solved numerically by the Keller-box method. The numerical results obtained are then compared with previously repor- ted cases available in the literature as well as the series solution for certain values of parameters, to support their validity. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed. List of symbols a, b Constants B Magnetic field B 0 Uniform magnetic field C f Skin friction coefficient f Dimensionless stream function g Acceleration due to gravity Gr x Local Grashof number k Thermal conductivity M Magnetic parameter Nu x Local Nusselt number Pr Prandtl number q w Wall heat flux Re x Local Reynolds number T Fluid temperature T w Plate temperature T ? Ambient temperature u, v Velocity components along the x and y directions, respectively U w Stretching velocity x, y Cartesian coordinates along the surface and normal to it, respectively Greek symbols a Thermal diffusivity b Thermal expansion coefficient g Similarity variable h Dimensionless temperature k Buoyancy or mixed convection parameter l Dynamic viscosity m Kinematic viscosity q Fluid density r Electrical conductivity s w Wall shear stress w Stream function Subscripts w Condition at the wall ? Ambient condition Superscript 0 Differentiation with respect to g F. Aman Faculty of Science, Art and Heritage, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Johor, Malaysia A. Ishak (&) School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia e-mail: anuarishak@yahoo.com 123 Heat Mass Transfer (2010) 46:615–620 DOI 10.1007/s00231-010-0606-6