Adomian Series Solution to a Rayleigh Power-Law Problem

A Rayleigh power-law problem of a semi-infinite plate moving in an electrically conducting non-Newtonian fluid is investigated. In a special case, exact solutions are established via the use of Crocco variables. Approximate solutions are obtained for the general problem via the Adomian decomposition method where we obtain the first few terms of an infinite power series expansion of the solution. This approximate solution is utilized to estimate a shear stress parameter. (Specifically, we use terms of the infinite series up to the third polynomial, which proves to give high accuracy.) Additionally, a Maclaurin series approach is utilized to approximate solutions as well as estimate the shear stress parameter for different values of the power-law index n. The results of the two methods are compared with results obtained via MATLAB integrators where the efficiency of the Adomian method is established.