Influence of Inclined MHD on Unsteady Flow of Generalized Maxwell Fluid with Fractional Derivative between Two Inclined Coaxial Cylinders through a Porous Medium

"This paper presents a study of inclined magnetic field on the unsteady rotating flow of a generalized Maxwell fluid with fractional derivative between two inclined infinite circular cylinders through a porous medium. The analytic solutions for velocity field and shear stress are derived by using the Laplace transform and finite Hankel transform in terms of the generalized G functions. The effect of the physical parameters of the problem on the velocity field is discussed and illustrated graphically.

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The analytic solutions for the unsteady rotating flows of the generalized Maxwell fluid between coaxial cylinders

Thermal Science ◽

10.2298/tsci2006041w ◽

2020 ◽

Vol 24 (6 Part B) ◽

pp. 4041-4048

Author(s):

Fan Wang ◽

Wang-Cheng Shen ◽

Jin-Ling Liu ◽

Ping Wang

Keyword(s):

Shear Stress ◽

Maxwell Fluid ◽

Analytic Solutions ◽

Rotating Flows ◽

Circular Cylinders ◽

Rotating Flow ◽

Coaxial Cylinders ◽

Porous medium on unsteady Helical flows of Generalized Oldroyd-B with two infinite coaxial circular cylinders

Iraqi Journal of Science ◽

10.24996/10.24996/ijs.2021.62.5.31 ◽

2021 ◽

Author(s):

Alaa Waleed

Keyword(s):

Porous Medium ◽

Porous Media ◽

Velocity Field ◽

Fractional Derivative ◽

Kinematic Viscosity ◽

Magnetic Parameter ◽

Velocity Fields ◽

Circular Cylinders ◽

Series Form ◽

Permeability Parameter

This article deals with the influence of porous media on Helical flows of Generalized Oldroyd-B between two infinite coaxial circular cylinders .The fractional derivative are modeled for this problem and studied by using finite Hankel and Laplace transforms .The velocity fields founded by using the fundamentals of the series form in terms of Mittag-leffler equation . The research focused on the parameters like (permeability parameter z ,fractional parameters(ð›¼ , ð›½) , relaxation ðœ†1 , retardation ðœ†2 , kinematic viscosity v , magnetic parameter M and time t) which effected on the velocity field u and w. MATHEMATICA package used to study and analyze the above variables by drawing many graphs .

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Entropy Generation on Maxwell Fluid Flow Past an Inclined Stretching Plate with Slip and Convective Surface Conditon: Darcy-Forchheimer Model

Nano Hybrids and Composites ◽

10.4028/www.scientific.net/nhc.26.62 ◽

2019 ◽

Vol 26 ◽

pp. 62-83

Author(s):

Tunde Abdulkadir Yusuf ◽

Jacob Abiodun Gbadeyan

Keyword(s):

Porous Medium ◽

Differential Equations ◽

Entropy Generation ◽

Mhd Flow ◽

Maxwell Fluid ◽

Entropy Generation Rate ◽

Physical Parameters ◽

Convective Boundary ◽

Linear Ordinary Differential Equations ◽

Non Linear

In this study the effect of entropy generation on two dimensional magnetohydrodynamic (MHD) flow of a Maxwell fluid over an inclined stretching sheet embedded in a non-Darcian porous medium with velocity slip and convective boundary condition is investigated. Darcy-Forchheimer based model was employed to describe the flow in the porous medium. The non-linear thermal radiation is also taken into account. Similarity transformation is used to convert the non-linear partial differential equations to a system of non-linear ordinary differential equations. The resulting transformed equations are then solved using the Homotopy analysis method (HAM). Influence of various physical parameters on the dimensionless velocity profile, temperature profile and entropy generation are shown graphically and discussed in detail while the effects of these physical parameters on velocity gradient and temperature gradient are aided with the help of Table. Furthermore, comparison of some limiting cases of this model was made with existing results. The results obtained are found to be in good agreement with previously published results. Moreover, increase in local inertial coefficient parameter is found to decrease the entropy generation rate.

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Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.2014.m588 ◽

2016 ◽

Vol 8 (5) ◽

pp. 784-794 ◽

Cited By ~ 2

Author(s):

Vatsala Mathur ◽

Kavita Khandelwal

Keyword(s):

Shear Stress ◽

Velocity Field ◽

Newtonian Fluid ◽

Outer Cylinder ◽

Fluid Motion ◽

Maxwell Fluid ◽

Circular Cylinders ◽

Generalized Solutions ◽

Special Cases ◽

Graphical Illustration

AbstractThis paper presents an analysis of unsteady flow of incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal time-dependent shear stress and the outer cylinder that is moving at a constant velocity. The velocity field and shear stress are determined using the Laplace and finite Hankel transforms. Obtained solutions are presented in terms of the generalized G and R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of generalized solutions. The influence of different parameters on the velocity field and shear stress are also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.

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EXACT SOLUTIONS FOR THE POISEUILLE FLOW OF A GENERALIZED MAXWELL FLUID INDUCED BY TIME-DEPENDENT SHEAR STRESS

The ANZIAM Journal ◽

10.1017/s1446181111000514 ◽

2010 ◽

Vol 51 (4) ◽

pp. 416-429 ◽

Cited By ~ 3

Author(s):

W. AKHTAR ◽

CORINA FETECAU ◽

A. U. AWAN

Keyword(s):

Shear Stress ◽

Velocity Field ◽

Circular Cylinder ◽

Poiseuille Flow ◽

Fluid Motion ◽

Maxwell Fluid ◽

Time Dependent ◽

Infinite Cylinder ◽

On analytical study of factional Oldroyd-B flow in annular region of two torsionally oscillating cylinders

Thermal Science ◽

10.2298/tsci110908078m ◽

2012 ◽

Vol 16 (2) ◽

pp. 411-421 ◽

Cited By ~ 1

Author(s):

A. Mahmood

Keyword(s):

Shear Stress ◽

Velocity Field ◽

Analytical Study ◽

Analytic Solutions ◽

Circular Cylinders ◽

Second Grade ◽

General Solutions ◽

Exact Analytic Solutions ◽

Governing Differential Equation ◽

R Functions

The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a fractional Oldroyd-B fluid, also called generalized Oldroyd-B fluid (GOF), between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and after some time both cylinders suddenly begin to oscillate around their common axis with different angular frequencies of their velocities. The exact analytic solutions of the velocity field and associated shear stress, that have been obtained, are presented under integral and series forms in terms of generalized G and R functions. Moreover, these solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of classical Oldroyd-B, generalized Maxwell, classical Maxwell, generalized second grade, classical second grade and Newtonian fluids are also obtained as limiting cases of our general solutions.

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Decay of Potential Vortex and Diffusion of Temperature in a Generalized Oldroyd-B Fluid through a Porous Medium

Mathematical Problems in Engineering ◽

10.1155/2014/719464 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

Xiaoyi Guo

Keyword(s):

Porous Medium ◽

Fractional Derivatives ◽

Maxwell Fluid ◽

Hankel Transform ◽

Temperature Fields ◽

Darcy Law ◽

Porous Space ◽

Maxwell Fluids ◽

Potential Vortex ◽

And Diffusion

Based on a modified Darcy law, the decay of potential vortex and diffusion of temperature in a generalized Oldroyd-B fluid with fractional derivatives through a porous medium is studied. Exact solutions of the velocity and temperature fields are obtained in terms of the generalized Mittag-Leffler function by using the Hankel transform and discrete Laplace transform of the sequential fractional derivatives. One of the solutions is the sum of the Newtonian solutions and the non-Newtonian contributions. As limiting cases of the present solutions, the corresponding solutions of the fractional Maxwell fluid and classical Maxwell fluids are given. The influences of the fractional parameters, material parameters, and the porous space on the decay of the vortex are interpreted by graphical results.

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The First Solution for the Helical Flow of a Generalized Maxwell Fluid within Annulus of Cylinders by New Definition of Transcendental Function BNrrn

Mathematical Problems in Engineering ◽

10.1155/2020/8919817 ◽

2020 ◽

Vol 2020 ◽

pp. 1-15

Author(s):

Fang Wang ◽

Jinling Liu

Keyword(s):

Maxwell Fluid ◽

Hankel Transform ◽

Helical Flow ◽

Transcendental Function ◽

Coaxial Cylinders ◽

Derivative Formulas ◽

Finite Hankel Transform ◽

Axis Of Symmetry ◽

Definition Of ◽

Generalized Maxwell Fluid

Most articles choose the transcendental function B1rrn to define the finite Hankel transform, and very few articles choose B0rrn. The derivations of B0rrn and B1rrn are also considered the same. In this paper, we find that the derivative formulas for the transcend function BNrrn are different and prove the derivative formulas for B0rrn and B1rrn. Based on the exact formulas of B0rrn and B1rrn, we keep on studying the helical flow of a generalized Maxwell fluid between two boundless coaxial cylinders. In this case, the inner and outer cylinders start to rotate around their axis of symmetry at different angular frequencies and slide at different linear velocities at time t=0+. We deduced the velocity field and shear stress via Laplace transform and finite Hankel transform and their inverse transforms. According to generalized G and R functions, the solutions we obtained are given in the form of integrals and series. The solution of ordinary Maxwell fluid has been also obtained by solving the limit of the general solution of fractional Maxwell fluid.

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Multiple Fractional Solutions for Magnetic Bio-Nanofluid Using Oldroyd-B Model in a Porous Medium with Ramped Wall Heating and Variable Velocity

Applied Sciences ◽

10.3390/app10113886 ◽

2020 ◽

Vol 10 (11) ◽

pp. 3886 ◽

Cited By ~ 3

Author(s):

Muhammad Saqib ◽

Ilyas Khan ◽

Yu-Ming Chu ◽

Ahmad Qushairi ◽

Sharidan Shafie ◽

...

Keyword(s):

Porous Medium ◽

Temperature Field ◽

Velocity Field ◽

Fractional Derivatives ◽

Fluid Velocity ◽

Fractional Operators ◽

Caputo Fractional Derivatives ◽

Wall Heating ◽

The Laplace Transform ◽

Fractional Analysis

Three different fractional models of Oldroyd-B fluid are considered in this work. Blood is taken as a special example of Oldroyd-B fluid (base fluid) with the suspension of gold nanoparticles, making the solution a biomagnetic non-Newtonian nanofluid. Based on three different definitions of fractional operators, three different models of the resulting nanofluid are developed. These three operators are based on the definitions of Caputo (C), Caputo–Fabrizio (CF), and Atnagana–Baleanu in the Caputo sense (ABC). Nanofluid is taken over an upright plate with ramped wall heating and time-dependent fluid velocity at the sidewall. The effects of magnetohydrodynamic (MHD) and porous medium are also considered. Triple fractional analysis is performed to solve the resulting three models, based on three different fractional operators. The Laplace transform is applied to each problem separately, and Zakian’s numerical algorithm is used for the Laplace inversion. The solutions are presented in various graphs with physical arguments. Results are computed and shown in various plots. The empirical results indicate that, for ramped temperature, the temperature field is highest for the ABC derivative, followed by the CF and Caputo fractional derivatives. In contrast, for isothermal temperature, the temperature field of C-derivative is higher than the CF and ABC derivatives, respectively. It was noticed that the velocity field for the ABC derivative is higher than the CF and Caputo fractional derivatives for ramped velocity. However, the velocity field for the Caputo fractional derivative is lower than the ABC and CF for isothermal velocity.

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Exact Solutions for the Axial Couette Flow of a Fractional Maxwell Fluid in an Annulus

ISRN Mathematical Physics ◽

10.5402/2012/209678 ◽

2012 ◽

Vol 2012 ◽

pp. 1-15 ◽

Cited By ~ 1

Author(s):

M. Imran ◽

A. U. Awan ◽

Mehwish Rana ◽

M. Athar ◽

M. Kamran

Keyword(s):

Shear Stress ◽

Velocity Field ◽

Differential Equations ◽

Boundary Conditions ◽

Exact Solutions ◽

Couette Flow ◽

Maxwell Fluid ◽

Circular Cylinders ◽

Rotational Flow ◽

Material Parameters

The velocity field and the adequate shear stress corresponding to the rotational flow of a fractional Maxwell fluid, between two infinite coaxial circular cylinders, are determined by applying the Laplace and finite Hankel transforms. The solutions that have been obtained are presented in terms of generalized Ga,b,c(·,t) and Ra,b(·,t) functions. Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions. The corresponding solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting cases of our general solutions. Finally, the influence of the material parameters on the velocity and shear stress of the fluid is analyzed by graphical illustrations.

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