Existence and nonexistence of solutions for unsteady shrinking disk flow

We analyze a mathematical model recently proposed by Mehmood et al. [J. Appl. Mech. Tech. Phys. 63(2022), 782–789] of unsteady fluid flow over a shrinking porous disk. Mehmood et al. conjectured that solutions to the model exist only for suf-ficiently strong suction of fluid through the disk surface. Here we prove that solutions in fact exist for both suction and injection. However, with injection, the solutions are very difficult to determine numerically. In this case, we derive precise bounds on the skin friction coefficient as a function of injection velocity. These bounds are then used to pinpoint the solutions computationally.