Dual solutions of fluid flow and heat transfer over a spinning and vertically moving disk

The present study concerns how fluid flow and heat transfer are affected when a spinning disk moves vertically up or down due to an unsteady flow motion. The disk is assumed to be porous and subject to a variable wall temperature. The governing equations are reduced to ordinary differential equations using similarity transformations to those reported in von Karman’s classic viscous pumping study for a vertically stationary but still spinning disk. The resulting equations are solved numerically by employing MATLAB’s bvp4c routine, which is a finite-difference code that implements the three-stage Lobatto IIIa formula. It has been discovered that despite observable differences, the disk’s upward and downward motion similarly impacts the injection and suction through the wall. It is shown that the temperature field largely depends on the shape of the wall temperature controlled by a time-varying function. In addition, the effect of vertical wall movement is found to be overloading at high disk speeds. The outcomes show that dual solutions are verifiable in certain operating parameters.