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

Integral transform solution for heat transfer in parallel-plates micro-channels: Combined electroosmotic and pressure driven flows with isothermal walls

“…An alternative to traditional numerical methods, is the hybrid analytical-numerical method known as the Generalized Integral Transform Technique (GITT) [14], which is based on seeking solutions in terms of orthogonal eigenfunction expansions. Among the recent advancements of GITT solution in internal forced convection problems, one should mention [15], which investigates the effect of periodically varying inlet temperature, [16], which deals with non-Newtonian flows in circular shaped ducts, [17], which presents a solution for non-Newtonian flows in elliptical cross-section ducts, and [18], which investigates the MHD flow and heat transfer within parallel-plates channels. Other recent applications of the GITT include a variety of problems, such as the intensification of thermophysical properties [19] and conjugated convection-conduction problems [20].…”