Study of Third-Grade Fluid under the Fuzzy Environment with Couette and Poiseuille Flows

Abstract

In this work, fundamental flow problems, namely, Couette flow, fully developed plane Poiseuille flow, and plane Couette–Poiseuille flow of a third-grade non-Newtonian fluid between two horizontal parallel plates separated by a finite distance in a fuzzy environment are considered. The governing nonlinear differential equations (DEs) are converted into fuzzy differential equations (FDEs) and explain our approach with the help of the membership function (MF) of triangular fuzzy numbers (TFNs). Adomian decomposition method (ADM) is used to solve fundamental flow problems based on FDEs. In a crisp environment, the current findings are in good accord with their previous numerical and analytical results. Finally, the effect of the $\alpha$ -cut $\left(\alpha \in \left[\mathrm{0,1}\right]\right)$ and other engineering constants on fuzzy velocity profile are invested in graphically and tabular forms. Also, the variability of the uncertainty is studied through the triangular MF.