Asymptotic solution for the flow due to an infinite rotating disk in the case of large magnetic field

The flow due to a rotating disk of infinite extent is studied in the presence of an axial uniform magnetic field in the case of large magnetic interaction number beta. The solution is given in the form of an asymptotic expansion in powers of beta (-2) whose coefficients are obtained in closed form in terms of a properly scaled von Karman's similarity coordinate that is strained to remove a secular behavior. The process of finding the expansion coefficients is found to be systematic, which makes it possible to produce as many terms of the expansion as may be needed. A comparison between the asymptotic solution and the exact numerical solution which uses finite-differences and linearization is done to check the results of the asymptotic expansion and determine its range of validity.