Abstract
In this work, fundamental ïŹow problems, namely, Couette flow, fully developed plane Poiseuille flow, and plane CouetteâPoiseuille flow of a third-grade non-Newtonian ïŹuid 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 ïŹow 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 α -cut α â 0,1 and other engineering constants on fuzzy velocity proïŹle are invested in graphically and tabular forms. Also, the variability of the uncertainty is studied through the triangular MF.
Highlights
Introduction e nonNewtonian fluids have gained considerable attention from scientists because of extensive applications in engineering, science, and industry
Paripour et al [19] studied the analytical solution of hybrid fuzzy differential equations (FDEs) by using the fuzzy Adomian decomposition method (ADM) and predictor-corrector method, which shows ADM is better than the predictor-corrector method
We present a numerical solution of Plane Couette flow, fully developed plane Poiseuille flow, and plane CouetteâPoiseuille flow for the third-grade nonNewtonian fluid with fuzzified boundary conditions
Summary
Introduction e nonNewtonian fluids have gained considerable attention from scientists because of extensive applications in engineering, science, and industry. For lower bound of velocity profile, we apply the ADM to equation (31) with the fuzzified boundary conditions (32) as follows: L1v(x; α) dv(x; 6ÎČôŒ dx α) 2 d2v(x; ôŒĄ ôŒ dx2 α) ôŒĄ, (35)
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