Purely analytic solutions of the compressible boundary layer flow due to a porous rotating disk with heat transfer

The motivation of the present study is to obtain exact analytical solution of the steady laminar flow of a compressible viscous fluid over a rotating disk subjected to a uniformly applied suction or blowing. Classical Von Karman problem of a rotating disk is extended to account for the compressibility effects with insulated and isothermal wall conditions. Using Von Karman similarity transformation the compressible nonlinear equations of motion are reduced to a boundary value problem whose solution was first obtained by Ackroyd [J. A. D. Ackroyd, “On the steady flow produced by a rotating disc with either surface suction of injection,” J. Eng. Phys. 12, 207 (1978)] for the velocity field in terms of a series of exponentially decaying functions. This kind of an approach, however, besides being incapable of resolving the velocity field for higher values of injection (see the conclusion of Ackroyd) is also shown not to be suitable for the temperature distribution of the compressible flow, necessitating the us...