Study of Jeffery-Hamel flow problem for nanofluid with fuzzy volume fraction using double parametric based Adomian decomposition method

This paper aims to study the flow of water-Copper nanofluid in a channel formed by two inclined planes, with imprecise nanoparticle volume fraction. In this study, the impreciseness of the volume fraction has been considered as a triangular fuzzy number [0%, 0.1%, 0.2%]. Double parametric concept has been used to handle the fuzziness of the involved fuzzy parameters. As such, double parametric-based Adomian Decomposition Method (ADM) is developed to solve the governing nonlinear fuzzy differential equation. Convergence of the obtained results shows the efficiency of the present method. For validation, the present solution has been compared with the previously published results in special cases of crisp environment. Further, the nature of dimensionless velocity has been studied by varying values of involved parameters. The value of nanoparticle volume fraction has been taken between 0% - 0.2% to see the effect of volume fraction on the velocity profile. Here, the null value of volume fraction indicates the use of traditional fluid without any nanoparticle. Different values of Reynolds number viz. Re = 25, 50, and 75 and different angles such as 3 degrees, 5 degrees, and 7 degrees have been taken to understand their effects on the velocity profile. Finally, fuzzy plots of velocities at different positions of the channel are shown, and velocity bounds at different locations of the channel are presented digitally.

Automated summary

This paper investigates the flow of water-Copper nanofluid in a channel with imprecise nanoparticle volume fraction, using a double parametric concept to handle fuzzy parameters. A double parametric-based Adomian Decomposition Method is developed to solve the nonlinear fuzzy differential equation, showing efficient convergence. The study compares the present solution with previously published results in crisp environments and examines the effects of parameters such as nanoparticle volume fraction and Reynolds number on velocity profiles.