Helices of fractionalized Maxwell fluid

2015 ◽  
Vol 4 (4) ◽  
Author(s):  
Muhammad Jamil ◽  
Kashif Ali Abro ◽  
Najeeb Alam Khan
Keyword(s):  
Angular Velocity ◽  
General Solution ◽  
Circular Cylinder ◽  
Special Function ◽  
Fluid Model ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Initial Moment ◽  
Special Cases ◽  
In Series

AbstractIn this paper the helical flows of fractionalized Maxwell fluid model, through a circular cylinder, is studied. The motion is produced by the cylinder that at the initial moment begins to rotate around its axis with an angular velocity Omegatp, and to slide along the same axis with linear velocity Utp. The solutions that have been obtained using Laplace and finite Hankel transforms and presented in series form in terms of the newly defined special function M(z), satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for ordinary Maxwell and Newtonian fluid obtained as special cases of the present general solution. Finally, the influence of various pertinent parameters on fluid motion as well as the comparison among different fluids models is analyzed by graphical illustrations.

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

2016 ◽  
Vol 8 (5) ◽  
pp. 784-794 ◽  
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.

A Nonlinear Generalized Maxwell Fluid Model for Viscoelastic Materials

2001 ◽  
Vol 68 (5) ◽  
pp. 787-790 ◽  
Author(s):  
D. T. Corr ◽  
M. J. Starr ◽  
R. Vanderby, ◽  
T. M. Best
Keyword(s):  
Fluid Model ◽  
Maxwell Fluid ◽  
Viscoelastic Materials ◽  
Force Equation ◽  
Constant Rate ◽  
Parallel Arrangement ◽  
Noteworthy Feature ◽  
In Series ◽  
Linear Spring ◽  
Generalized Maxwell Fluid

A nonlinear Maxwell fluid model consisting of a linear dashpot in series with a parallel arrangement of a linear spring and a second-order nonlinear spring, was developed. This configuration provides the flexibility necessary to describe both the stiffening and the softening responses of some viscoelastic materials. A noteworthy feature of the model is that under constant rate displacement, the force equation can be solved in closed form, thereby providing a continuous, exact general solution.

Thermal Resistances of Circular Source on Finite Circular Cylinder With Side and End Cooling

2003 ◽  
Vol 125 (2) ◽  
pp. 169-177 ◽  
Author(s):  
M. M. Yovanovich
Keyword(s):  
General Solution ◽  
Circular Cylinder ◽  
Circular Disk ◽  
Spreading Resistance ◽  
Pin Fin ◽  
Special Cases ◽  
Extended Surface ◽  
The One ◽  
Circular Source ◽  
Special Case

General solution for thermal spreading and system resistances of a circular source on a finite circular cylinder with uniform side and end cooling is presented. The solution is applicable for a general axisymmetric heat flux distribution which reduces to three important distributions including isoflux and equivalent isothermal flux distributions. The dimensionless system resistance depends on four dimensionless system parameters. It is shown that several special cases presented by many researchers arise directly from the general solution. Tabulated values and correlation equations are presented for several cases where the system resistance depends on one system parameter only. When the cylinder sides are adiabatic, the system resistance is equal to the one-dimensional resistance plus the spreading resistance. When the cylinder is very long and side cooling is small, the general relationship reduces to the case of an extended surface (pin fin) with end cooling and spreading resistance at the base. The special case of an equivalent isothermal circular source on a very thin infinite circular disk is presented.

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

2010 ◽  
Vol 51 (4) ◽  
pp. 416-429 ◽  
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 ◽  
Similar Solutions ◽  
Generalized Maxwell Fluid

AbstractThe Poiseuille flow of a generalized Maxwell fluid is discussed. The velocity field and shear stress corresponding to the flow in an infinite circular cylinder are obtained by means of the Laplace and Hankel transforms. The motion is caused by the infinite cylinder which is under the action of a longitudinal time-dependent shear stress. Both solutions are obtained in the form of infinite series. Similar solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting cases. Finally, the influence of the material and fractional parameters on the fluid motion is brought to light.

Aerodynamics of a Spinning Sphere

1928 ◽  
Vol 32 (213) ◽  
pp. 777-798 ◽  
Author(s):  
John W. Maccoll
Keyword(s):  
General Solution ◽  
Viscous Fluid ◽  
Mathematical Analysis ◽  
Special Interest ◽  
Equations Of Motion ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Special Cases ◽  
The Right ◽  
Near Future

The full equations of motion for the flow of a viscous fluid have proved too complicated for any general solution to be obtained. It is to be doubted if, in. the near future, the problem of fluid motion will be solved in a general manner, although solutions for a few special cases may be found. In view of this it is of some value to investigate experimentally certain cases which are likely to prove of mathematical interest at a later date; this paper deals with such a problem. By means of the results obtained experimentally the mathematical analysis may be guided along the right lines and a satisfactory analytical solutioa of the problem be obtained.The instrument used in exploring the fluid motion has a special interest of its own as it may prove of use in further aerodynamical investigations where the flow is of three–dimensional character. The development of this instrument, and its performance when tested, are described in Part I.The experiments for the measurement of the forces on the spinning sphere are described in Part II.

A general theory for the motion of a body through a fluid at low Reynolds number

1990 ◽  
Vol 430 (1878) ◽  
pp. 89-104 ◽  
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Stokes Problem ◽  
Low Reynolds Number ◽  
Fluid Motion ◽  
Reynolds Numbers ◽  
Linear Velocity ◽  
Special Cases ◽  
Small Reynolds Numbers ◽  
Low Reynolds

The motion of a body through a viscous fluid at low Reynolds number is considered. The motion is steady relative to axes moving with a linear velocity, U a , and rotating with an angular velocity, Ω a . The fluid motion depends on two (small) Reynolds numbers, R proportional to the linear velocity and T proportional to the angular velocity. The correction to the first approximation (Stokes flow) is a complicated function of R and T ; it is O ( R ) for T ½ ≪ R and O ( T ½ )for T ½ ≫ R . General formulae are derived for the force and couple acting on a body of arbitrary shape. From them all the terms O ( R + T ) or larger can be calculated once the Stokes problem has been solved completely. Some special cases are considered in detail.

scholarly journals Slip Effects on Fractional Viscoelastic Fluids

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Muhammad Jamil ◽  
Najeeb Alam Khan
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Derivatives ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Newtonian Fluids ◽  
Generalized Hypergeometric Functions ◽  
General Solutions ◽  
Slip Effects ◽  
Special Cases ◽  
Wright Generalized Hypergeometric Functions

Unsteady flow of an incompressible Maxwell fluid with fractional derivative induced by a sudden moved plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions obtained for the velocity field and shear stress, written in terms of Wright generalized hypergeometric functions , by using discrete Laplace transform of the sequential fractional derivatives, satisfy all imposed initial and boundary conditions. The no-slip contributions, that appeared in the general solutions, as expected, tend to zero when slip parameter is . Furthermore, the solutions for ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as special cases of general solutions. The solutions for fractional and ordinary Maxwell fluid for no-slip condition also obtained as limiting cases, and they are equivalent to the previously known results. Finally, the influence of the material, slip, and the fractional parameters on the fluid motion as well as a comparison among fractional Maxwell, ordinary Maxwell, and Newtonian fluids is also discussed by graphical illustrations.

scholarly journals Semi-analytical technique for the solution of fractional Maxwell fluid

2017 ◽  
Vol 95 (5) ◽  
pp. 472-478 ◽  
Author(s):  
M. Abdullah ◽  
Asma Rashid Butt ◽  
Nauman Raza ◽  
Ehsan Ul Haque
Keyword(s):  
Circular Cylinder ◽  
Fractional Derivatives ◽  
Bessel Functions ◽  
Maxwell Fluid ◽  
Inverse Transformation ◽  
Physical Parameters ◽  
Time Dynamic ◽  
Analytical Technique ◽  
In Series ◽  
The Impact

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.

scholarly journals Oscillating Flows of Fractionalized Second Grade Fluid

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Muhammad Jamil ◽  
Najeeb Alam Khan ◽  
Abdul Rauf
Keyword(s):  
Fluid Motion ◽  
Newtonian Fluids ◽  
Second Grade ◽  
Classical Solutions ◽  
Second Grade Fluid ◽  
New Exact Solutions ◽  
Special Cases ◽  
Transient Solutions ◽  
In Series ◽  
Grade Fluid

New exact solutions for the motion of a fractionalized (this word is suitable when fractional derivative is used in constitutive or governing equations) second grade fluid due to longitudinal and torsional oscillations of an infinite circular cylinder are determined by means of Laplace and finite Hankel transforms. These solutions are presented in series form in term of generalized Ga,b,c(⋅,t) functions and satisfy all imposed initial and boundary conditions. In special cases, solutions for ordinary second grade and Newtonian fluids are obtained. Furthermore, other equivalent forms of solutions for ordinary second grade and Newtonian fluids are presented and written as sum of steady-state and transient solutions. The solutions for Newtonian fluid coincide with the well-known classical solutions. Finally, by means of graphical illustrations, the influence of pertinent parameters on fluid motion as well as comparison among different models is discussed.

scholarly journals On the flow of MHD generalized maxwell fluid via porous rectangular duct

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 989-1002
Author(s):  
Aamir Farooq ◽  
Muhammad Kamran ◽  
Yasir Bashir ◽  
Hijaz Ahmad ◽  
Azeem Shahzad ◽  
...  
Keyword(s):  
Fluid Model ◽  
Maxwell Fluid ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Rectangular Duct ◽  
Modified Darcy’S Law ◽  
Initial Boundary Value ◽  
Generalized Maxwell Fluid ◽  
Limiting Case ◽  
The Impact

Abstract The purpose of this proposed investigation is to study unsteady magneto hydrodynamic (MHD) mixed initial-boundary value problem for incompressible fractional Maxwell fluid model via oscillatory porous rectangular duct. Considering the modified Darcy’s law, the problem is simplified by using the method of the double finite Fourier sine and Laplace transforms. As a limiting case of the general solutions, the same results can be obtained for the classical Maxwell fluid. Also, the impact of magnetic parameter, porosity of medium, and the impact of various material parameters on the velocity profile and the corresponding tangential tensions are illuminated graphically. At the end, we will give the conclusion of the whole paper.

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