Analytical Solution of Fractional Oldroyd-B Fluid via Fluctuating Duct

Ying Qing Song,Muhammad Tamoor,Rewayat Khan,Muhammad Kamran,Aamir Farooq,Asfand Fahad,Muhammad Imran Qureshi,Sadique Rehman,Muhammad Imran Asjad

doi:10.1155/2021/9576873

Abstract

This investigation focuses on the mixed initial boundary value problem with Caputo fractional derivatives. The studied pour an incompressible fractionalized Oldroyd-B fluid prompted by fluctuating rectangular tube. The explicit expression of the velocity field and shear stresses for the fractional model are obtained by utilizing the integral transforms, i.e., double finite Fourier sine transform and Laplace transform. Furthermore, the confirmation of the analytical solutions is also analyzed by utilizing the Tzou’s and Stehfest’s algorithms in the tabular form. In limited cases, ordinary Oldroyd-B fluid similar solutions and classical Maxwell and fractional Maxwell fluid are derived. The flow field’s graphs with the influences of relevant parameters are also mentioned.

Highlights

Ying Qing Song,1 Aamir Farooq,2 Muhammad Kamran,3 Sadique Rehman,4 Muhammad Tamoor,5,6 Rewayat Khan,2 Asfand Fahad,7 and Muhammad Imran Qureshi 7
Academic Editor: Muhammad Imran Asjad is investigation focuses on the mixed initial boundary value problem with Caputo fractional derivatives. e studied pour an incompressible fractionalized Oldroyd-B fluid prompted by fluctuating rectangular tube. e explicit expression of the velocity field and shear stresses for the fractional model are obtained by utilizing the integral transforms, i.e., double finite Fourier sine transform and Laplace transform
Introduction e liquids which change their viscosity under force to either more liquid or solid are famous. ese liquids are known as non-Newtonian fluids. e understanding can be improved by studying such types of fluids

Summary

Introduction

Ying Qing Song,1 Aamir Farooq,2 Muhammad Kamran ,3 Sadique Rehman,4 Muhammad Tamoor,5,6 Rewayat Khan,2 Asfand Fahad ,7 and Muhammad Imran Qureshi 7. The researchers want to know the relation of the vibratory motion of the fractionalized Oldroyd-B fluid by discovering the shear stress and velocity motion, and the first “time” derivative of the velocity is taken “zero” as its extra condition to simplify the model at time t 0.

Results

Conclusion