MHD fluid flow and heat transfer due to a shrinking rotating disk

Abstract

The present paper is devoted to the investigation of steady MHD laminar flow of an electrically conducting fluid on a radially shrinking rotating disk in the presence of a uniform vertical magnetic field. The well-known von Karman rotating disk problem is extended here to the situation where a shrinking disk with or without rotation is allowed, whose stretching disk analogy was recently disclosed in Turkyilmazoglu (2012) [1]. With the help of the usual similarity transformations, the equations of motion are simplified to a set of nonlinear ordinary differential equations. Both viscous dissipation and Joule heating effects are incorporated into the energy equation. A Spectral numerical integration scheme of high accuracy is then used to investigate the effects of a rotation parameter, based on the wall shrinking and angular velocity, on the rotating system. The physically paramount properties, including the skin friction, the torque, the suction velocity and the heat transfer rate are evaluated and are compared with those corresponding to stretching disk available in Turkyilmazoglu (2012) [1]. The behavior of the flow and temperature fields is found to be highly influenced by the disk shrinking.