Eyring–Powell fluid flow through a circular pipe and heat transfer: full solutions

Abstract

Purpose The purpose of this study is to examine the non-Newtonian physical model of Eyring–Powell fluid for the rheology inside a long circular pipe. Design/methodology/approach Although many research studies are available now on this topic, none gives full solutions explicitly accessible. Findings It is proven here that the hydrodynamically fully developed fluid flow acknowledges the exact solution, influenced by a non-Newtonian parameter as well as the adverse pressure gradient parameter prevailing the flow domain. These parameters are unified under a new parameter known as the generalized Eyring–Powell parameter. Without the presented analytical data, it is impossible to detect the validity range of such physical non-Newtonian solutions, which is shown to be restricted. Originality/value Full solution of the energy equation for the thermally fully developed laminar regime is also presented under the assumption of uniform wall temperature at the pipe wall. The physical impacts of pertinent parameters on the rheology of the non-Newtonian fluid with regard to the Reynolds number, Darcy friction factor and pressure drop are easy to interpret from the derived formulae. Particularly, a decrease in the centerline velocity and an increase in the rate of heat transfer are clarified for the considered flow configuration.