Exact Solutions for the Poiseuille Flow of a Generalized Maxwell Fluid Induced by Time-Dependent Shear Stress

Akhtar, Waseem; Fetecău, Constantin; Awan, Aziz Ullah

doi:10.1017/s1446181111000514

Cited by 5 publications

(2 citation statements)

References 17 publications

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“…Eqs. (10) and (11) can be written in suitable form as By using variable transformation m = r √ a(s) in Eq. (12), we get…”

Section: Calculation Of the Velocity Fieldmentioning

confidence: 99%

“…The books written by Chandrasehkar [1], Drazin and Reid [2] are considered standard for the exact solutions of non-Newtonian fluids in cylindrical domains. After the publication of these books, many papers associated to non-Newtonian fluids in cylindrical geometry have been proclaimed [3][4][5][6][7][8][9][10]. To study the rheological flow assumptions of differential type fluids by Rajagopal [11] and rate type fluids by Dunn and Rajagopal [12] have acquired acceptance of both experimentalists and theoreticians.…”

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confidence: 99%

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Semi-analytical technique for the solution of fractional Maxwell fluid

et al. 2017

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In this work, the flow of a fractional Maxwell fluid is discussed. The velocity function and time-dependent shear stress of a Maxwell fluid with fractional derivatives are calculated. It is considered that the fluid in the infinitely long circular cylinder is moving with a velocity ft. The fluid in the infinitely long circular cylinder of radius R is initially at rest and at t = 0+, because of shear, it instantly starts to move longitudinally. To obtain the solutions, we have employed Laplace transformation and modified Bessel equation. The solutions are in series form, which are expressed in terms of modified Bessel functions [Formula: see text] and [Formula: see text], and satisfy all given conditions. In this paper, Laplace inverse transformation has been calculated numerically by using MATLAB. The behavior of the following physical parameters on the flow are investigated: relaxation time, dynamic viscosity, kinematics viscosity, similarity parameters of fractional derivatives and radius of the circular cylinder. Finally, the impact of the fractional parameter and material elements is shown by graphical demonstration.

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“…Eqs. (10) and (11) can be written in suitable form as By using variable transformation m = r √ a(s) in Eq. (12), we get…”

Section: Calculation Of the Velocity Fieldmentioning

confidence: 99%

mentioning

confidence: 99%

Semi-analytical technique for the solution of fractional Maxwell fluid

et al. 2017

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A hybrid technique for the solution of unsteady Maxwell fluid with fractional derivatives due to tangential shear stress

2017

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The role of relaxation and retardation phenomenon of Oldroyd-B fluid flow through Stehfest’s and Tzou’s algorithms

Awan

Riaz

Abro

et al. 2022

Nonlinear Engineering

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Delayed response (delay of the elasticity) and time needed for initial stress can lead to relaxation and retardation phenomenon; this is because of the consistent behavior of viscoelastic fluid on thermodynamic principles. In this context, the aim of this article is to investigate the unsteady, incompressible, and Oldroyd-B viscoelastic fluid under wall slip conditions to know the hidden aspects of relaxation and retardation. The motion of the liquid is assumed over a flat vertical plate which moves through an oscillating velocity. A fractional model is developed by using the modern definition of the non-singular kernel proposed by Caputo and Fabrizio. We have obtained a semi-analytical solution of the non-dimensional model by using the Laplace transformation that satisfies our imposed suitable boundary conditions. We have tackled the Laplace inverse by employing Stehfest’s and Tzou’s algorithms. The velocity is enhanced by decreasing the estimations of relaxation time λ as well as slip parameter, and the temperature is also increasing for a considerable measure of the fractional factor. The effects of different fractional and physical parameters are plotted using Mathcad software based on the relaxation and retardation phenomenon of Oldroyd-B viscoelastic fluid.

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Exact Solutions for the Poiseuille Flow of a Generalized Maxwell Fluid Induced by Time-Dependent Shear Stress

Cited by 5 publications

References 17 publications

Semi-analytical technique for the solution of fractional Maxwell fluid

Semi-analytical technique for the solution of fractional Maxwell fluid

A hybrid technique for the solution of unsteady Maxwell fluid with fractional derivatives due to tangential shear stress

The role of relaxation and retardation phenomenon of Oldroyd-B fluid flow through Stehfest’s and Tzou’s algorithms

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