Flow between two stretchable disks—An exact solution of the Navier–Stokes equations

In this work, an exact solution for the steady state Navier–Stokes equations in cylindrical coordinates is presented by similarity transformation technique. The solution involves the flow between two stretchable infinite disks with accelerated stretching velocity. The similarity equation was solved numerically and the effects of disk stretching parameter and stretching Reynolds number were studied. With the increase of the stretching Reynolds numbers, the fluid begins with a creeping type flow at R = 0 to a typical boundary layer type flow for large Reynolds numbers. The pressure parameter β changes from a positive number to a negative value with the increase of non-zero stretching parameter. The upper wall stretching parameter also greatly affects the velocity distribution between the two disks with a downward net flow for γ ≠ 1. The results are also useful as a benchmark problem for the validation of three-dimensional numerical computation code.