HEAT TRANSFER OF MAGNETO HYDRODYNAMIC VISCOUS FLUID OVER A LINEAR SHRINKING SHEET PRESCRIBED SECOND ORDER SURFACE TEMPERATURE

A large number of industrial processes especially in the field of metallurgy and chemical engineering process involve a moving surface, stretching or shrinking sheet, with heat transfer which leads to a kind of drying process. Some of these applications are extrusion of polymer plastic sheets, cooling of metallic plates, drawing of paper films, vacuum forming and glass blowing., the final properties of the product depend on the heat transfer rate in the boundary layer during the cooling or heating process on the moving sheet. Therefore, analyze of heat transfer on the shrinking sheet boundary layer is very important because it has a crucial effect on the product quality. In this paper the boundary layer flow and heat and transfer of electrically conducting viscous fluid over a shrinking sheet with wall mass transfer on the sheet is studied. The sheet surface is prescribed to a second order power law temperature and suction. The governing partial differential equations are first reduced into a set of selfsimilar ordinary differential equations by similarity transformations, and they are solved numerically using a finite difference method. The results show that under certain circumstance two distinct solution branches may exist. The behavior of the flow and heat transfer characteristics for different values of the Prandtl number, Eckert number, wall mass transfer parameter and Magnetic parameter are analyzed and discussed. The achieved results for one of the solution branches offer quite interesting nonlinear behaviors. The results show that the Prandtl number signifycantly influenced the wall heat transfer. Both the temperature and thermal boundary layer thickness are decreased by increase of the Prandtl number. The results of the present paper are useful towards the fundamental understanding of the shrinking sheet phenomena in industrial drying process.

Keywords:

Shrinking sheet , Magnetohydrodynamic , Suction