Flow in a channel of porous parallel and inclined walls: Carreau fluid of variable density

Abstract

An exact similarity solution of Carreau fluid flow has been attempted in this paper. Whereas, the flow is maintained inside a channel of both parallel and inclined walls. The previous issues of pseudo-similarity solutions for such problems have been resolved here. Moreover, a single model is devised for the flow of Carreau fluid in both Poiseuille and Jeffery-Hammel type structures. Furthermore, the problem has exactly described the two previous (classical) simulations for flow of Carreau fluid. The present investigations have been carried out without incorporating the boundary layer approximation and stream function assumptions and we utilized the full form of constitutive equations. The system of PDEs is exactly converted into and exact system of ODEs and later the final equation are solved by a powerful and well established numerical tool. The analysis has been independently carried out for straight and inclined walls channels, whereas, the classical results of both types have been retrieved in special circumstances. It is observed that parabolic profiles for velocity spread over the width of the channel large value of Weissenberg number ${\sigma }_1<0$ and an increase in the velocity is noted for large ${\sigma }_1<0$. It demonstrates the nozzle flow of Carreau fluid inside a converging channel of inclined walls.