FORCED FLOW NEAR A HEATED ROTATING DISK: A SIMILARITY SOLUTION

Abstract

This paper presents an analysis of the flow and heat transfer between two parallel infinite disks that are separated by a distance L. One of the disks is solid, heated, and rotated; the other disk is porous, unheated, and stationary. Fluid is injected through the porous disk normal to its surface and toward the rotating disk. The three-dimensional Navier-Stokes and energy equations have been reduced to a system of ordinary differential equations by means of a similarity transformation and have been solved over a range of values of the two Reynolds numbers Re_ωequals; L²ω/ν_L and Re_ν = LU/ν_L, for two values of the temperature ratio Tr = (T_s - T_L)/T_L, of 0.001 (constant property flow) and 2.33. For Tr = 0.001 the velocity profiles are independent of the temperature profile which is determined for Pr = 0.67; for Tr = 2.33, the velocity and temperature profiles are determined for helium. The assumptions made in the analysis are shown to be valid provided that the mixed convection parameter , is small. Velocity and temperature profiles and the shear stress and the heat flux at the surface of the rotating disk are persented for a range of the above parameters.