scholarly journals Steady Flow of a Second-Grade Fluid in an Annulus with Porous Walls

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
M. Emin Erdoğan ◽  
C. Erdem İmrak
Keyword(s):  
Reynolds Number ◽  
Hypergeometric Functions ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Confluent Hypergeometric Functions ◽  
Moment Coefficient ◽  
Grade Fluid ◽  
Porous Walls ◽  
The Cross ◽  
The Moment

An exact solution of an incompressible second-grade fluid for flow between two coaxial cylinders with porous walls is given. It is assumed that the inner cylinder is rotating with a constant angular velocity and the outer one is at rest. The solution is expressed in terms of the confluent hypergeometric functions and it is valid for all values of the cross-Reynolds number and the elastic number. The solutions for , , and values of the cross-Reynolds number are obtained and a comparison with those of the Newtonian fluid is given. Furthermore, the torque exerted by the fluid on the inner cylinder is calculated. It is shown that the moment coefficient depends on the cross-Reynolds number, the elastic number, and the ratio of the radii of the cylinders. The variation of the moment coefficient with these numbers is discussed.

scholarly journals On the Steady Flow of a Second-Grade Fluid between Two Coaxial Porous Cylinders

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
M. Emin Erdoğan ◽  
C. Erdem İmrak
Keyword(s):  
Exact Solution ◽  
Reynolds Number ◽  
Steady Flow ◽  
Newtonian Fluid ◽  
Velocity Variation ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
The Cross ◽  
Porous Cylinders

An exact solution of an incompressible second-grade fluid for flow between two coaxial porous cylinders is given. The velocity profiles for various values of the cross-Reynolds number and the elastic number are plotted. It is found that for large values of the cross-Reynolds number, the velocity variation near boundaries shows a different behaviour than that of the Newtonian fluid.

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 Peristaltic flow of a fractional second grade fluid through a cylindrical tube

2011 ◽  
Vol 15 (suppl. 2) ◽  
pp. 167-173 ◽  
Author(s):  
Dharmendra Tripathi
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Cylindrical Tube ◽  
Material Constant ◽  
Peristaltic Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Long Wavelength ◽  
Grade Fluid ◽  
Fractional Parameter

The investigation is to explore the transportation of a viscoelastic fluid with fractional second grade model by peristalsis through a cylindrical tube under the assumptions of long wavelength and low Reynolds number. Analytical solution of problem is obtained by using Caputo?s definition. It is assumed that the cross-section of the tube varies sinusoidally along the length of tube. The effects of fractional parameter, material constant and amplitude on the pressure and friction force across one wavelength are discussed numerically with the help of illustrations. It is found that pressure decreases with increase in fractional parameter whereas increases with increase in magnitude of material constant or time. The pressure for the flow of second grade fluid is more than that for the flow of Newtonian fluid.

SECOND‐GRADE FLUID FLOW WITH POWER‐LAW HEAT FLUX AND A HEAT SOURCE

2013 ◽  
Vol 44 (8) ◽  
pp. 687-702 ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir A. Shehzad ◽  
Muhammad Qasim ◽  
F. Alsaadi ◽  
Ahmed Alsaedi
Keyword(s):  
Heat Flux ◽  
Fluid Flow ◽  
Heat Source ◽  
Power Law ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
Power Law Heat Flux

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.

Flow of Second Grade Fluid in a Scraped Surface Heat Exchanger

2016 ◽  
Vol 40 (2) ◽  
pp. e12393 ◽  
Author(s):  
A. Imran ◽  
M.A. Rana ◽  
A.M. Siddiqui ◽  
M. Shoaib
Keyword(s):  
Heat Exchanger ◽  
Surface Heat ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Scraped Surface Heat Exchanger ◽  
Grade Fluid ◽  
Surface Heat Exchanger

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.

The Rayleigh Stokes problem for rectangular pipe in Maxwell and second grade fluid

Meccanica ◽  
2008 ◽  
Vol 43 (5) ◽  
pp. 495-504 ◽  
Author(s):  
S. Nadeem ◽  
S. Asghar ◽  
T. Hayat ◽  
Mazhar Hussain
Keyword(s):  
Stokes Problem ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid
Sign in / Sign up

Export Citation Format

Share Document