Analytic approximate solutions of rotating disk boundary layer flow subject to a uniform vertical magnetic field

The present paper is concerned with the analytical solution of the boundary layer flow of a steady, laminar, incompressible, viscous and electrically conducting fluid due to a rotating disk. Within this purpose, the recently popular homotopy analysis method is employed, making it possible to obtain explicitly analytic expressions for Lighthill's coordinate straining parameter c in terms of the magnetic field parameter m, first used in Ackroyd (J Eng Phys 12:207-220, 1978) for the nonmagnetic case and recently studied to get the small perturbation and large asymptotic representations in Ariel (Z Angew Math Mech 82:235-246, 2001) for the magnetic case. Making use of the outlined approach, the mean velocity profiles corresponding to a wide range of magnetic strength parameters are computed, and also explicit formulas are derived for several quantities of physical significance.