Purely analytic solutions of magnetohydrodynamic swirling boundary layer flow over a porous rotating disk

The prime objective of the present study is to derive analytical expressions for the solution of steady, laminar, incompressible, viscous and electrically conducting fluid of the boundary layer flow due to a rotating disk subjected to a uniform suction and injection through the wall in the presence of a uniform transverse magnetic field. To serve this purpose, the recently popular homotopy analysis method is employed to obtain the exact solutions, in contrast to the numerically evaluated ones in the literature. It is shown here that such a technique is extremely powerful in gaining magnetohydrodynamic solutions in terms of the purely exponential and decaying functions if a special care is taken into account. This makes it possible to obtain explicitly analytic solutions particularly in coincident with the Ackroyd's solutions in (Ackroyd, 1978) [1] and with the solutions in (Ariel, 2001) [2]. The method is further shown to be capable of overcoming the difficulties existed in calculating Ackroyd's solutions for high values of injection. Using the homotopy analysis method, electrically conducting mean velocity profiles corresponding to a wide range of suction and injection velocities can be readily computed non-iteratively and analytically. Explicit formulas are also derived for some parameters of physical significance.