Exact Analysis of the Flow and Heat Transfer of the SA-TiO2 Non-Newtonian Nanofluid Between Two Coaxial Cylinders Through a Porous Medium

In this article, the flow and heat transfer of a non-Newtonian nanofluid between two coaxial cylinders through a porous medium has been investigated. The velocity, temperature, and nanoparticles concentration of the present mathematical model are governed by a system of nonlinear ordinary differential equations. The objective of this article is to obtain new exact solutions for the temperature and the nanoparticles concentration and, therefore, compare them with the previous approximate results in the literature. Moreover, the velocity equation has been numerically solved. The effects of the pressure gradient, thermophoresis, third-grade, Brownian motion, and porosity parameters on the included phenomena have been discussed through several tables and plots. It is found that the velocity profile is increased by increasing the pressure gradient parameter, thermophoresis parameter (slightly), third-grade parameter, and Brownian motion parameter (slightly); however, it decreases with an increase in the porosity parameter and viscosity power index. In addition, the temperature and the nanoparticles concentration reduce with the strengthen of the Brownian motion parameter, while they increase by increasing the thermophoresis parameter. Furthermore, the numerical solution and the physical interpretation in the literature for the same problem have been validated with the current exact analysis, where many remarkable differences and errors have been concluded. Therefore, the suggested analysis may be recommended with high trust for similar problems.