Analysis of non-Newtonian power-law fluids flow over a rotating body

Abstract

The present analysis considers the momentum transfer within a laminar boundary layer of non-Newtonian power-law fluids flow over a rotating axisymmetrical body. The work is an extension of a previous analysis of power-law fluid flow over a non-rotating axisymmetrical body. Newtonian fluids, as well, are evaluated within the scope of this paper. A generalized coordinate transformation is utilized with a Merk-Meksyn series expansion to transform the nonlinear governing momentum equations into a set of coupled ordinary differential equations. The first three terms of the set are derived for general evaluation. The first term equations are numerically integrated for a non-rotating and rotating sphere to obtain the axial and tangential velocity gradients. The Runge-Kutta method for numerical integration is used with the control of integrating step size. The iteration procedure is the Newton-Raphson technique. The friction coefficient is then determined using the velocity gradients and presented in the form of 1/2CfRe1/(n+1). The initial velocity gradients and friction coefficients for Newtonian fluids are tabulated and compared to the results from Lee, Jeng, and DeWitt for equivalent values on n. Likewise, the initial axial velocity or non-rotating bodies is compared to the results of Kim. The non-Newtonian portion of this analysis compares the friction coefficient for three values of n to the published results of Kleinstreuer and Wang. Axial and tangential velocities through the boundary layer for Newtonian and non-Newtonian fluids are also graphically shown.