The homotopy perturbation method and analytical solution of the problem of flow past a rotating disk

Analytical solutions have been obtained for the problem of steady, laminar flow of a viscous, incompressible fluid past a rotating disk using the homotopy perturbation method (HPM). The single-parameter HPM is attempted first. Since it does not give adequately accurate results, the extended HPM is invoked next, in which the independent variable is scaled, and the scale factor is expanded in a power series in p, the homotopy parameter. The coefficients in this power series are calculated by ensuring that the resulting solution is free of secular terms. It is shown that the extended HPM solution converges to the true solution and that just eight terms in the perturbation expansion are sufficient to produce a highly accurate, yet fully analytical, solution.