scholarly journals Flows with Slip of Oldroyd-B Fluids over a Moving Plate

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Abdul Shakeel ◽  
Sohail Ahmad ◽  
Hamid Khan ◽  
Nehad Ali Shah ◽  
Sami Ul Haq
Keyword(s):  
Integral Transform ◽  
Fluid Velocity ◽  
Translational Motion ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Analytic Solutions ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Moving Plate ◽  
Grade Fluid

A general investigation has been made and analytic solutions are provided corresponding to the flows of an Oldroyd-B fluid, under the consideration of slip condition at the boundary. The fluid motion is generated by the flat plate which has a translational motion in its plane with a time-dependent velocity. The adequate integral transform approach is employed to find analytic solutions for the velocity field. Solutions for the flows corresponding to Maxwell fluid, second-grade fluid, and Newtonian fluid are also determined in both cases, namely, flows with slip on the boundary and flows with no slip on the boundary, respectively. Some of our results were compared with other results from the literature. The effects of several emerging dimensionless and pertinent parameters on the fluid velocity have been studied theoretically as well as graphically in the paper.

scholarly journals Analytical Solutions for the Flow of a Fractional Second Grade Fluid due to a Rotational Constantly Accelerating Shear

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
M. Kamran ◽  
M. Imran ◽  
M. Athar
Keyword(s):  
Fluid Motion ◽  
Analytic Solutions ◽  
Second Grade ◽  
Governing Equations ◽  
Second Grade Fluid ◽  
Coaxial Cylinders ◽  
Exact Analytic Solutions ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
Similar Solutions

Exact analytic solutions are obtained for the flow of a generalized second grade fluid in an annular region between two infinite coaxial cylinders. The fractional calculus approach in the governing equations of a second grade fluid is used. The exact analytic solutions are constructed by means of Laplace and finite Hankel transforms. The motion is produced by the inner cylinder which is rotating about its axis due to a constantly accelerating shear. The solutions that have been obtained satisfy both the governing equations and all imposed initial and boundary conditions. Moreover, they can be easily specialized to give similar solutions for second grade and Newtonian fluids. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between the three models, is underlined by graphical illustrations.

Mechanical and thermal energies transport flow of a second grade fluid with novel fractional derivative

2021 ◽  
pp. 095440892110535
Author(s):  
Mushtaq Ahmad ◽  
Muhammad I Asjad ◽  
Kottakkaran S Nisar ◽  
Ilyas Khan
Keyword(s):  
Integral Transform ◽  
Large Time Behavior ◽  
Second Grade ◽  
Convection Flow ◽  
Time Behavior ◽  
Second Grade Fluid ◽  
Dual Nature ◽  
The Laplace Transform ◽  
Grade Fluid ◽  
Unsteady Natural Convection

In this study, an unsteady natural convection flow of second-grade fluid over a vertical plate with Newtonian heating by constant proportional Caputo non-integer order derivative is presented. After developing a dimensionless flow model, the set of governing equations are solved with the help of integral transform, namely the Laplace transform and closed solutions are obtained. Also, some graphs of temperature and velocity field are drawn to see the subjectively of fractional parameter [Formula: see text] and other involved parameters of interest. It also shows dual nature for small and large time behavior due to the power-law kernel. Further, a comparative analysis between the temperature as well as the velocity fields with existing literature has been presented. Further, as a result, it is concluded that constant proportional Caputo derivative shows more decaying nature of the fluid flow properties than classical Caputo and Caputo-Fabrizio fractional derivatives.

scholarly journals Three-Dimensional Couette Flow of a Second-Grade Fluid Along Periodic Injection/Suction

Coatings ◽  
2019 ◽  
Vol 9 (9) ◽  
pp. 553 ◽  
Author(s):  
Muhammad Afzal Rana ◽  
Yasar Ali ◽  
Babar Ahmad ◽  
Muhammad Touseef Afzal Rana
Keyword(s):  
Transverse Direction ◽  
Flow Direction ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
Main Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Suction Velocity ◽  
Grade Fluid ◽  
Main Flow Direction

This work explores the three-dimensional laminar flow of an incompressible second-grade fluid between two parallel infinite plates. The assumed suction velocity comprises a basic steady dispersal with a superimposed weak transversally fluctuating distribution. Because of variation of suction velocity in transverse direction on the wall, the problem turns out to be three-dimensional. Analytic solutions for velocity field, pressure and skin friction are presented and effects of dimensionless parameters emerging in the model are discussed. It is observed that the non-Newtonian parameter plays dynamic part to rheostat the velocity component along main flow direction.

Flow of an Electrically Conducting Second-Grade Fluid under an Oscillating Rigid Moving Plate

2006 ◽  
Vol 1 (2) ◽  
pp. 184-193
Author(s):  
Swamy N.S., . ◽  
H.R. Nataraja . ◽  
K.S. Sai . ◽  
S.B. Tiwari . ◽  
B. Nageswara Rao .
Keyword(s):  
Second Grade ◽  
Second Grade Fluid ◽  
Moving Plate ◽  
Electrically Conducting ◽  
Grade Fluid

Flow of Second Grade Fluid between two Walls Induced by Rectified Sine Pulses Shear Stress

2015 ◽  
Vol 31 (5) ◽  
pp. 573-582
Author(s):  
Q. Sultan ◽  
M. Nazar ◽  
I. Ahmad ◽  
U. Ali
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Fluid Motion ◽  
Mhd Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Fourier Cosine ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Grade Fluid

AbstractThis paper concerns with the unsteady MHD flow of a second grade fluid between two parallel walls through porous media induced by rectified sine pulses shear stress. The analytical expressions for the velocity field and the adequate shear stress are determined by means of the Laplace transform technique and Fourier cosine and sine transforms and are written as a sum of steady state and transient solutions. The influence of side walls on the fluid motion, the distance between walls for which the velocity of the fluid in the middle of the channel is negligible, and the required time to reach the steady state are presented by graphical illustrations. As the second grade fluid parameter → 0 the problem reduces to the Newtonian fluids performing the same motion.

Nonorthogonal Stagnation-point Flow of a Second-grade Fluid Past a Lubricated Surface

2016 ◽  
Vol 71 (3) ◽  
pp. 273-280 ◽  
Author(s):  
Khalid Mahmood ◽  
Muhammad Sajid ◽  
Nasir Ali
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Weissenberg Number ◽  
Stagnation Point Flow ◽  
Partial Slip ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid

AbstractThe stagnation-point flow of a second-grade fluid past a power law lubricated surface is considered in this paper. It is assumed that the fluid impinges on the wall obliquely. A suitable choice of similarity transformations reduces the governing partial differential equations into ordinary differential equations. The thin lubrication layer suggests that the interface conditions between the fluid and the lubricant can be imposed on the boundary. An implicit finite difference scheme known as the Keller-Box method is employed to obtain the numerical solutions. The effects of slip parameter and Weissenberg number on the fluid velocity and streamlines is discussed in the graphs. The limiting cases of partial-slip and no-slip can be deduced from the present solutions.

Exact Solutions of Electro-Osmotic Flow of Generalized Second-Grade Fluid with Fractional Derivative in a Straight Pipe of Circular Cross Section

2014 ◽  
Vol 69 (12) ◽  
pp. 697-704 ◽  
Author(s):  
Shaowei Wang ◽  
Moli Zhao ◽  
Xicheng Li ◽  
Xi Chen ◽  
Yanhui Ge
Keyword(s):  
Fractional Derivative ◽  
Integral Transform ◽  
Capillary Tube ◽  
Circular Cross Section ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Osmotic Flow ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
Electro Osmotic Flow

AbstractThe transient electro-osmotic flow of generalized second-grade fluid with fractional derivative in a narrow capillary tube is examined. With the help of the integral transform method, analytical expressions are derived for the electric potential and transient velocity profile by solving the linearized Poisson-Boltzmann equation and the Navier-Stokes equation. It was shown that the distribution and establishment of the velocity consists of two parts, the steady part and the unsteady one. The effects of retardation time, fractional derivative parameter, and the Debye-Hückel parameter on the generation of flow are shown graphically.

An Explicit Analytic Solution of Steady Three-Dimensional Stagnation Point Flow of Second Grade Fluid Toward a Heated Plate

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
Ahmer Mehmood ◽  
Asif Ali
Keyword(s):  
Stagnation Point ◽  
Analytic Solution ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
Stagnation Point Flow ◽  
Second Grade ◽  
Heated Plate ◽  
Second Grade Fluid ◽  
Homotopy Analysis ◽  
Grade Fluid

We present a purely analytic solution to the steady three-dimensional viscous stagnation point flow of second grade fluid over a heated flat plate moving with some constant speed. The analytic solution is obtained by a newly developed analytic technique, namely, homotopy analysis method. By giving a comparison with the existing results, it is shown that the obtained analytic solutions are highly accurate and are in good agreement with the results already present in literature. Also, the present analytic solution is uniformly valid for all values of the dimensionless second grade parameter α. The effects of α and the Prandtl number Pr on velocity and temperature profiles are discussed through graphs.

scholarly journals The unsteady mixed convection flow of rotating second grade fluid in porous medium with ramped wall temperature

2017 ◽  
Vol 13 (4) ◽  
pp. 798-802
Author(s):  
Ahmad Qushairi Mohamad ◽  
Ilyas Khan ◽  
Nor Athirah Mohd Zin ◽  
Zulkhibri Ismail ◽  
Sharidan Shafie
Keyword(s):  
Mixed Convection ◽  
Wall Temperature ◽  
Fluid Velocity ◽  
Second Grade ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Second Grade Fluid ◽  
Porosity Parameter ◽  
Unsteady Mixed Convection ◽  
Grade Fluid

The effects of ramped wall temperature, rotation and porosity on mixed convection flow of incompressible second grade fluid are studied. The momentum equation is modelled in a problem of rotating fluid with constant angular velocity subjected to initial and oscillating boundary conditions. The energy equation is also introduced. Some suitable non-dimensional variables are used to write equations into non-dimensional form. Laplace transform method is used to solve these equations in order to obtain the analytical solutions of velocity and temperature profiles. Computations are carried out and presented graphically to analyse the effect of second grade fluid parameter, rotation parameter, porosity parameter, Prandtl number and Grashof number on the profiles. It is found that, for larger values of porosity parameter, the fluid velocity will increase for both primary and secondary velocities. The results also show that, velocity for ramped wall temperature is lower compared to isothermal temperature. It is worth to mention that, the exact solutions obtained in this study can be used to check correctness of the results obtained through numerical schemes.

scholarly journals Transient electro-osmotic flow of generalized second-grade fluids under slip boundary conditions

2017 ◽  
Vol 95 (12) ◽  
pp. 1313-1320 ◽  
Author(s):  
Xiaoping Wang ◽  
Haitao Qi ◽  
Huanying Xu
Keyword(s):  
Boundary Conditions ◽  
Velocity Distribution ◽  
Fluid Velocity ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Osmotic Flow ◽  
Slip Boundary ◽  
Grade Fluid ◽  
Second Grade Fluids ◽  
Electro Osmotic Flow

This work investigates the transient slip flow of viscoelastic fluids in a slit micro-channel under the combined influences of electro-osmotic and pressure gradient forcings. We adopt the generalized second-grade fluid model with fractional derivative as the constitutive equation and the Navier linear slip model as the boundary conditions. The analytical solution for velocity distribution of the electro-osmotic flow is determined by employing the Debye–Hückel approximation and the integral transform methods. The corresponding expressions of classical Newtonian and second-grade fluids are obtained as the limiting cases of our general results. These solutions are presented as a sum of steady-state and transient parts. The combined effects of slip boundary conditions, fluid rheology, electro-osmotic, and pressure gradient forcings on the fluid velocity distribution are also discussed graphically in terms of the pertinent dimensionless parameters. By comparison with the two cases corresponding to the Newtonian fluid and the classical second-grade fluid, it is found that the fractional derivative parameter β has a significant effect on the fluid velocity distribution and the time when the fluid flow reaches the steady state. Additionally, the slip velocity at the wall increases in a noticeable manner the flow rate in an electro-osmotic flow.

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