Unsteady flow over a rotating and vertically moving disk with variable fluid properties

Abstract

A numerical solution is worked out for unsteady flow around a revolving disk exhibiting upward/downward motion. A temperature-dependent viscosity model is introduced that yields a system in which momentum and energy equations are coupled in terms of a parameter ${\theta }_e$ . The disk revolves with the time-dependent angular velocity $\mathrm{\Omega }(t)$ and vertically moves with the axial velocity $\dot{a}(t)$ , where $a(t)$ denotes the location of disk at any time t. The considered expressions of $a(t)$ and $\mathrm{\Omega }(t)$ suggest that upward/downward motion of the rotating disk leads to the case of accelerated/decelerated disk. Solutions are worked out by a widely employed routine bvp4c of MATLAB. The vertical motion of the disk leads to a two-dimensional flow problem when the disk is nonrotating. However, simultaneous vertical movement and rotation of the disk impart a three-dimensional motion. A marked variation in solution profiles is detected whenever temperature dependency in fluid viscosity is retained. In addition, the deceleration phenomenon of the disk declines heat transfer rate from the surface.