Boundary Layers and Heat Transfer on a Rotating Rough Disk

Abstract

The study of flow and heat transfer over rotating circular disks is of great practical importance in understanding the cooling of rotatory machinery such as turbines, electric motors and design and manufacturing of computer disk drives. This paper presents an analysis of the flow and heat transfer over a heated infinite permeable rough disk. Boundary-layer approximation reduces the elliptic Navier-Stokes equations to parabolic equations, where the Keller-Cebeci method of finite - difference solution is used to solve the resulting system of partial-differential equations. The surface roughness is assumed to influence the turbulent boundary layer by adding a roughness parameter height K, while a variable surface temperature induces heat transfer into the flow of fluid over the rotating disk. Blowing and suction is also considered as a means of varying the surface shear distribution. The resulting curve-fit equations to the numerically calculated results of the skin-friction coefficient for three regions of laminar, transition and turbulent flow are shown to be consistent to those obtained for flow over a flat plate or a circular cylinder. To study the influence of surface roughness, calculations for various surface roughness parameters are made and results are presented. Velocity and temperature profiles and the shear stress and heat flux at the surface of the rotating disk are presented for a range of the above parameters.