scholarly journals Analytic solution of Stokes second problem for second-grade fluid

2006 ◽  
Vol 2006 ◽  
pp. 1-8 ◽  
Author(s):  
S. Asghar ◽  
S. Nadeem ◽  
K. Hanif ◽  
T. Hayat
Keyword(s):  
Analytical Solution ◽  
Laplace Transformation ◽  
Material Parameter ◽  
Analytic Solution ◽  
Second Grade ◽  
Perturbation Techniques ◽  
Second Grade Fluid ◽  
Transient Solutions ◽  
Grade Fluid ◽  
Stokes Second Problem

Using Laplace transformation and perturbation techniques, analytical solution is obtained for unsteady Stokes' second problem. Expressions for steady and transient solutions are explicitly determined. These solutions depend strongly upon the material parameter of second-grade fluid. It is shown that phase velocity decreases by increasing material parameter of second-grade fluid.

Similarity solution of second grade fluid flow over a moving cylinder

2021 ◽  
Author(s):  
Nadeem Abbas ◽  
M. Y. Malik ◽  
Sohail Nadeem ◽  
Shafiq Hussain ◽  
A. S. El-Shafa
Keyword(s):  
Boundary Layer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Material Parameter ◽  
Second Grade ◽  
Physical Parameters ◽  
Stretching Cylinder ◽  
Second Grade Fluid ◽  
Moving Cylinder ◽  
Grade Fluid

Stagnation point flow of viscoelastic second grade fluid over a stretching cylinder under the thermal slip and magnetic hydrodynamics effects are studied. The mathematical model has been developed under the assumption of non-Newtonian viscoelastic fluid flow over a stretching cylinder by means of the boundary layer approximations. The developed model further reduced through the similarity transformations and constructs the model of nonlinear ordinary differential equations. The system of nonlinear differential equations is dimensionless and solved through the numerical technique bvp5c methods. The results of the physical parameters are found and interpreted in the form of tables and graphs. The velocity shows that the graph of curves enhances away from the surface when the values material parameter [Formula: see text] increase, which means the momentum boundary layer increases for enhancing the material parameter [Formula: see text]. The temperature gradient reduced due enhancing the values of material parameter [Formula: see text] because thermal boundary layer reduced for higher values of material parameter [Formula: see text].

scholarly journals Analytical solution for the flow of second grade fluid over a stretching sheet

AIP Advances ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 055313 ◽  
Author(s):  
Muhammad Rafiq ◽  
Muhammad Kamran ◽  
Naveed Ahmed ◽  
Syed Tauseef Mohyud-Din ◽  
Yasir Bashir ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Stretching Sheet ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid

On the Analytic Solution of Magnetohydrodynamic Flow of a Second Grade Fluid Over a Shrinking Sheet

2007 ◽  
Vol 74 (6) ◽  
pp. 1165-1171 ◽  
Author(s):  
T. Hayat ◽  
Z. Abbas ◽  
M. Sajid
Keyword(s):  
Series Solution ◽  
Analytic Solution ◽  
Second Grade ◽  
Shrinking Sheet ◽  
Series Solutions ◽  
Analysis Method ◽  
Second Grade Fluid ◽  
Homotopy Analysis ◽  
Grade Fluid ◽  
Layer Flow

In this study, we derive an analytical solution describing the magnetohydrodynamic boundary layer flow of a second grade fluid over a shrinking sheet. Both exact and series solutions have been determined. For the series solution, the governing nonlinear problem is solved using the homotopy analysis method. The convergence of the obtained solution is analyzed explicitly. Graphical results have been presented and discussed for the pertinent parameters.

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.

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