Time-dependent double phase dusty fluid flow over an oscillatory rotating disk

The dispersion of solid particles in a viscous fluid leads to a two-phase flow nature. The present study incorporates the time-dependent three-dimensional dusty fluid flow generated by a periodically oscillatory rotating disk. The disk is stretchable along the radial axis with time-based sinusoidal fluctuations. The governing incompressible flow equations for two-phase equilibrium are normalized in the form of similarity systems consisting of the fluid stage and dust phase. The whole normalized system reduces to the familiar Von Karman similarity system for the flow configuration of rotating disk by removing the dust phase and periodic oscillations of the disk. The two-phase flow model is then numerically solved by a built-in method namely "pdsolve" in Maple built program. The graphical aspects of the obtained physical parameters on velocity and thermal fields of the dust particle stage are investigated to show how the oscillatory disk contributes to the dusty flow features. The wall shears and thermal rates of the fluid and dust particles are also calculated in limiting case of disk rotation. It is observed that in time-based flow, the oscillatory profiles preserve a phase shifting phenomenon. For centrifugal forces, the particle cloud moves away from the surface along a tangential direction. The thermal field is reduced by the dust particle stages.