Analytic approximate solutions of rotating disk boundary layer flow subject to a uniform suction or injection

The present paper is devoted to the study of derivation of analytical expressions for the solution of steady, laminar, incompressible, viscous fluid of the boundary layer flow due to a rotating disk in the presence of a uniform suction or injection. Within this aim, the recently popular homotopy analysis method is employed to obtain the exact solutions, in contrast to the full numerically or perturbative/asymptotically evaluated ones in the literature. It is shown here that such a technique is extremely powerful in gaining solutions in terms of the purely exponential and decaying functions if the proposed approach introduced here is carefully pursued. The homotopy technique makes it possible to obtain explicitly analytic expressions for Lighthillʹs coordinate straining parameter c in terms of the suction/blowing parameter s, first used in [1]. Using the outlined approach, not only the mean velocity profiles corresponding to a wide range suction/blowing parameter are computed non-iteratively and analytically, but also explicit formulas are derived for some quantities of physical significance. The notion of optimal convergence control parameter is made use to accelerate the rate of convergence of the homotopy series, whose convergence is later proven via a convergence theorem.