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

• Unlike the stretching disk, a continuous inflow occurs in the radial direction.
• High rotations yield the same phenomenon for both stretching and shrinking disks.
• Low rotations cause considerable increases in the axial and tangential velocities.
• Dissimilar to the stretching disk, the heat transfer is reduced for low rotations.
• Radial shrinking of the disk can overcome the wall heating, similar to radial stretching.

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.