Effects of Constant and Space-Dependent Viscosity on Eyring–Powell Fluid in a Pipe: Comparison of the Perturbation and Explicit Finite Difference Methods

Abstract

Abstract The present study explores the effects of constant and space-dependent viscosity on Eyring–Powell fluid inside a circular pipe. The heat transfer analysis is also considered. Using the normalised quantities, the governing equations are transformed into dimensionless form, and then the solution of the constructed nonlinear differential equations is calculated. The perturbation method is used to find the analytical expressions of velocity and temperature profiles as a function of pipe radius. The perturbation solution is validated against explicit finite difference numerical method, and errors of each case are plotted. The accuracy in velocity and temperature of finite difference method relative to the perturbation method is of order 10−2 and 10−4, respectively, in both cases of constant and space-dependent viscosity. The effects of various emerging parameters, namely, modified rheological parameter λ ( = 0.1 ) $\lambda\;\left({=0.1}\right)$ , pressure gradient parameter G ( − 1 ≤ G ≤ − 0.4 ) $G\;\left({-1\leq G\leq-0.4}\right)$ , rheological parameter ξ ( = 0.1 ) $\xi\;\left({=0.1}\right)$ and material parameter E ( 0.1 ≤ E ≤ 1 ) $E\;\left({0.1\leq E\leq 1}\right)$ on temperature and velocity fields, are discussed through plots. The heights of both profiles are maximal for the case of constant model as compared to the variable one. The numerical code is also validated with a previous study of Eyring–Powell fluid in a pipe.