Generalized integral transform solution for hydrodynamically developing non-Newtonian flows in circular tubes

ABSTRACT: The Generalized Integral Transform Technique (GITT) is applied to the solution of the momentum equations in a hydrodynamically developing laminar flow of a non-Newtonian power-law fluid inside a circular duct. A primitive variables formulation is adopted in order to avoid the singularity of the auxiliary eigenvalue problem in terms of Bessel functions at the centerline of the duct when the GITT approach is applied. Results for the velocity field and friction factor-Reynolds number product are computed for different power-law indices, which are tabulated and graphically presented as functions of the dimensionless coordinates. Critical comparisons with previous results in the literature are also performed, in order to validate the numerical codes developed in the present work and to demonstrate the consistency of the final results.

A Law of the Wall Formulation for Recirculating Flows

ABSTRACT: This work presents a new law of the wall formulation for recirculating turbulent flows. An alternative expression for the internal length which can be applied in the separated region is also presented. The formulation is implemented in a numerical code which solves the k-e model through a finite volume method. The theoretical results are compared with the experimental data of Vogel and Eaton (J. of Heat Transfer, Transactions of ASME, vol.107, pp. 922-929, 1985). The paper shows that the present formulation furnishes better results than the standard k-e formulation.