Peaceman-Rachford ADI Scheme for the Two-Dimensional Flow of a Second-Grade Fluid

2009 ◽  
Author(s):  
E. Momoniat ◽  
C. Harley ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Second Grade ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Grade Fluid ◽  
Adi Scheme

scholarly journals Unsteady stagnation point flow of a non-Newtonian second-grade fluid

2003 ◽  
Vol 2003 (60) ◽  
pp. 3797-3807 ◽  
Author(s):  
F. Labropulu ◽  
X. Xu ◽  
M. Chinichian
Keyword(s):  
Finite Difference ◽  
Stagnation Point ◽  
Infinite Plate ◽  
Second Grade ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
Harmonic Oscillations ◽  
Finite Difference Technique ◽  
Two Dimensional Flow ◽  
Grade Fluid

The unsteady two-dimensional flow of a viscoelastic second-grade fluid impinging on an infinite plate is considered. The plate is making harmonic oscillations in its own plane. A finite difference technique is employed and solutions for small and large frequencies of the oscillations are obtained.

scholarly journals A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Asim Khan ◽  
Norhashidah Hj. Mohd Ali ◽  
Nur Nadiah Abd Hamid
Keyword(s):  
Finite Difference ◽  
Stokes Problem ◽  
Stability And Convergence ◽  
Second Grade ◽  
Group Method ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
The Matrix ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

Abstract In this article, a new explicit group iterative scheme is developed for the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid. The proposed scheme is based on the high-order compact Crank–Nicolson finite difference method. The resulting scheme consists of three-level finite difference approximations. The stability and convergence of the proposed method are studied using the matrix energy method. Finally, some numerical examples are provided to show the accuracy of the proposed method.

scholarly journals Three dimensional flow and mass transfer analysis of a second grade fluid in a porous channel with a lower stretching wall

2016 ◽  
Vol 21 (2) ◽  
pp. 359-376
Author(s):  
N.A. Khan ◽  
F. Naz
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Three Dimensional ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Grade Fluid ◽  
Suction Or Injection

AbstractThis investigation analyses a three dimensional flow and mass transfer of a second grade fluid over a porous stretching wall in the presence of suction or injection. The equations governing the flow are attained in terms of partial differential equations. A similarity transformation has been utilized for the transformation of partial differential equations into the ordinary differential equations. The solutions of the nonlinear systems are given by the homotopy analysis method (HAM). A comparative study with the previous results of a viscous fluid has been made. The convergence of the series solution has also been considered explicitly. The influence of admissible parameters on the flows is delineated through graphs and appropriate results are presented. In addition, it is found that instantaneous suction and injection reduce viscous drag on the stretching sheet. It is also shown that suction or injection of a fluid through the surface is an example of mass transfer and it can change the flow field.

Some Exact Analytical Solutions for Two-Dimensional Flow of an Incompressible Second Grade Fluid

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Saif Ullah
Keyword(s):  
Analytical Solutions ◽  
Separation Of Variables ◽  
Point Of View ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Exact Analytical Solutions ◽  
Contour Plots ◽  
Two Dimensional Flow ◽  
Grade Fluid ◽  
Physical Features

This investigation deals with some exact analytical solutions of the incompressible second grade fluid by using the method based on the separation of variables. In many cases, this method can derive exact analytical solutions easier than other methods. A family of solutions is derived in this paper, which governs scientific and engineering experimentations. The derived solutions represent the flows having streamlines as a family of ellipses, parabolas, concentric circles, and rectangular hyperbolas. From practical point of view, these flows have applications in many manufacturing processes in industry. Some physical features of the derived solutions are also illustrated by their contour plots.

A series solution of the boundary value problem arising in the application of fluid mechanics

2018 ◽  
Vol 28 (10) ◽  
pp. 2480-2490 ◽  
Author(s):  
Yasir Khan
Keyword(s):  
Differential Equation ◽  
Reynolds Number ◽  
Transverse Direction ◽  
Hydrodynamic Flow ◽  
Porous Channel ◽  
Second Grade ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
Content Type ◽  
Grade Fluid

Purpose This paper aims to study the two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the homotopy perturbation method (HPM). Design/methodology/approach The governing Navier–Stokes equations of the flow are reduced to a third-order nonlinear ordinary differential equation by a suitable similarity transformation. Analytic solution of the resulting differential equation is obtained using the HPM. Mathematica software is used to visualize the flow behavior. The effects of the various parameters on velocity field are analyzed through appropriate graphs. Findings It is found that x component of the velocity increases with the increase of the Hartman number when the transverse direction variable ranges from 0 to 0.2 and the reverse behavior is observed when transverse direction variable takes values between 0.2 and 0.5. It is noted that the y component of the velocity increases rapidly with the increase of the transverse direction variable. The y component of the velocity increases marginally with the increase of the Hartman number M. The effect of the Reynolds number R on the x and y components of the velocity is quite opposite to the effect of the Hartman number on the x and y components of the velocity and the effect of the parameter on the x and y components of the velocity is similar to that of the Reynolds number. Originality/value To the best of the author’s knowledge, nobody had tried before two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the HPM.

scholarly journals Study of two dimensional boundary layer flow of a thin film second grade fluid with variable thermo-physical properties in three dimensions space

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5387-5405 ◽  
Author(s):  
Noor Khan
Keyword(s):  
Thin Film ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Second Grade ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
Similarity Transformations ◽  
Dimensional Boundary ◽  
Grade Fluid ◽  
Layer Flow

The formation of three dimensional study from two dimensional study due to high intensified magnetic field is investigated for a thin film second-grade fluid with variable fluid properties. The effects of Soret, Dufour, thermophoresis, thermal radiation and viscous dissipation are taken into account in the problem. Similarity transformations are employed to convert the governing equations into dimensionless form which have been solved by using homotopy analysis method (HAM). Quite real results are achieved with the help of emerging parameters which are shown through different graphs for velocities, temperature and concentration profiles.

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