Thermal Behavior of Newtonian and Non-Newtonian Fluid Flows in Ring-Shaped Pipe

Abstract

TO IMPLEMENT non-Newtonian properties of fluids, the power-law model is used in the evaluation of the heat transfer process in industrial and technological applications. Several recent studies have been conducted, dealing with heat transfer of nonNewtonian fluids [1–3]. Ostrach [4] and Khalifa [5] presented a review of heat transfer due to natural convection. Rashad et al. performed an analysis to study the effect of uniform transpiration velocity on free convection boundary-layer flow of a non-Newtonian fluid over a permeable vertical cone embedded in a porous medium saturatedwith a nanofluid [6].A numerical analysiswas performed to examine the heat transfer of colloidal dispersions of Au nanoparticles in water by Ternik et al. [7]. They reported highly exact numerical results, showing clearly that the averageNusselt number is a growing function of both the volume fraction of Au nanoparticles and Rayleigh number. Niu et al. studied the slip flow and heat transfer of a non-Newtonian nanofluid in a microtube by means of a theoretical method [8]. In their research, the velocity profile, volumetric flow rate, and local Nusselt number were calculated for different values of nanoparticle volume fraction and slip length. Despite the fact that most thermal and fluid phenomenona are expressed by nonlinear equations, only a few methods are able to solve them. One of these methods is the homotopy perturbation method (HPM), which was introduced by He [9].