Dual solutions for fluid flow over a stretching/shrinking rotating disk subject to variable fluid properties

Abstract

The present study is focused towards investigating swirling flow around a disk that undergoes uniform rotation and radial stretching/shrinking simultaneously in its plane. In accordance with the available literature, inversely linear temperature-dependency of fluid viscosity is assumed. Furthermore, the dependence of thermal conductivity on temperature is considered. The solution procedure involves a rather conventional approach of reducing the Navier–Stokes equations into self-similar forms. Finally, a numerical solution is furnished by employing as easy to implement but effective MATLAB’s routine bvp4c. The cases of liquids and gases are separately treated. The solution involves a parameter C that measures the rate of radial stretching/shrinking of the disk. In case of shrinking disk, the problem admits dual solutions under a specific range of values of C. The quantities of practical interest such as the skin friction factor and the Nusselt number change appreciably by varying parameter C. The computations agree very well with the existing literature concerning Von-Kármán flow with constant fluid properties.