scholarly journals Starting solutions for some simple oscillating motions of second-grade fluids

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
C. Fetecau ◽  
Corina Fetecau
Keyword(s):  
Rectangular Cross Section ◽  
Navier Stokes ◽  
Second Grade ◽  
Governing Equations ◽  
Transient Solutions ◽  
Grade Fluid ◽  
Stokes Fluid ◽  
Starting Solutions ◽  
Second Grade Fluids ◽  
Special Case

The exact starting solutions corresponding to the motions of a second-grade fluid, due to the cosine and sine oscillations of an infinite edge and of an infinite duct of rectangular cross-section as well as those induced by an oscillating pressure gradient in such a duct, are determined by means of the double Fourier sine transforms. These solutions, presented as sum of the steady-state and transient solutions, satisfy both the governing equations and all associate initial and boundary conditions. In the special case whenα1→0, they reduce to those for a Navier-Stokes fluid.

Starting solutions for the motion of second grade fluids due to oscillating shear stresses

2015 ◽  
Vol 4 (2) ◽  
Author(s):  
Muhammad Jamil
Keyword(s):  
Analytic Solutions ◽  
Second Grade ◽  
Shear Stresses ◽  
Exact Analytic Solutions ◽  
Transient Solutions ◽  
Grade Fluid ◽  
Starting Solutions ◽  
Second Grade Fluids ◽  
Graphical Illustration ◽  
Special Case

AbstractExact analytic solutions for the motion of second grade fluid between two infinite coaxial cylinders are established. The motion is produced by the inner cylinder that at time t = 0+ applies torsional and longitudinal oscillating shear stresses to the fluid. The exact analytic solutions, obtained with the help of Laplace and finite Hankel transforms, and presented as a sum of the steady-state and transient solutions, satisfy both the governing equations and all associate initial and boundary conditions. In the special case when a1 to 0 they reduce to those for a Newtonian fluid. Finally, the effect of various parameters of interest on transient parts of velocity components, velocity profiles as well as comparison between second grade and Newtonian fluids is discussed through graphical illustration.

ON BOUNDARY PERMEATION IN NAVIER–STOKES AND SECOND GRADE INCOMPRESSIBLE FLUIDS

2006 ◽  
Vol 16 (01) ◽  
pp. 59-75 ◽  
Author(s):  
RIËTTE MARITZ ◽  
NIKO SAUER
Keyword(s):  
Mathematical Model ◽  
Incompressible Fluids ◽  
Contact Forces ◽  
Navier Stokes ◽  
Second Grade ◽  
Normal Stresses ◽  
Permeable Walls ◽  
Fluid Boundary ◽  
Stokes Fluid ◽  
Second Grade Fluids

A mathematical model for the phenomenon of penetration of fluid into permeable walls is developed for second grade fluids. The model is based on mechanical principles which involve normal stresses at the boundary and contact forces at the fluid-boundary interface. Stability of the rest state is proved. The results are compared to that for the simplified case of a Navier–Stokes fluid.

Effects of Hall current on unsteady MHD flows of a second grade fluid

Open Physics ◽  
2010 ◽  
Vol 8 (3) ◽  
Author(s):  
Masud Ahmad ◽  
Haider Zaman ◽  
Naila Rehman
Keyword(s):  
Uniform Magnetic Field ◽  
Hall Current ◽  
Second Grade ◽  
Governing Equations ◽  
Second Grade Fluid ◽  
Sine Transform ◽  
Fourier Sine Transform ◽  
Transient Solutions ◽  
Grade Fluid ◽  
Limiting Case

AbstractThe aim of this present paper is to construct exact solutions corresponding to the motion of magnetohydrodynamic (MHD) fluid in the presence of Hall current, due to cosine and sine oscillations of a rigid plate as well as those induced by an oscillating pressure gradient. A uniform magnetic field is applied transversely to the flow. By using Fourier sine transform steady state and transient solutions are presented. These solutions satisfy the governing equations and all associated initial and boundary conditions. The results for a hydrodynamic second grade fluid can be obtained as a limiting case when B 0 → 0 and for a Newtonian fluid when α 1 → 0.

Transient Free Convection Mass Transfer of Second-grade Fluid Flow with Wall Transpiration

CFD Letters ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 35-52
Author(s):  
Mohamad Alif Ismail ◽  
Mohamad Hidayad Ahmad Kamal ◽  
Lim Yeou Jiann ◽  
Anati Ali ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Schmidt Number ◽  
Second Grade ◽  
Concentration Profiles ◽  
Governing Equations ◽  
Second Grade Fluid ◽  
Wall Suction ◽  
Viscoelastic Parameter ◽  
Grade Fluid ◽  
Wall Injection

The study of mass transfer in the non-Newtonian fluid is essential in understanding the engine lubrication, the cooling system of electronic devices, and the manufacturing process of the chemical industry. Optimal performance of the practical applications requires the appropriate conditions. The unsteady transient free convective flow of second-grade fluid with mass transfer and wall transpiration is concerned in the present communication. The behavior of the second-grade fluid under the influence of injection or suction is discussed. Suitable non-dimensional variables are utilized to transform the governing equations into non-dimensional governing equations. A Maple solver “pdsolve” that is using the centered implicit scheme of a finite difference method is utilized to solve the dimensionless governing equations numerically. The effects of wall injection or suction parameter, second-grade fluid viscoelastic parameter, Schmidt number, and modified Grashof number on the velocity and concentration profiles are graphically displayed and analyzed. The results show that with increasing wall suction, viscoelastic parameter, and Schmidt number, the velocity and concentration profiles decrease. Whereas, the velocity profiles show an opposite tendency in situations of wall injection. The wall suction has increased the skin friction and also the rate of mass diffusion in the second-grade fluid.

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.

On the Unsteady Flow of Two Incompressible Immiscible Second Grade Fluids between Two Parallel Plates

2014 ◽  
Vol 1016 ◽  
pp. 546-553
Author(s):  
Abdul M. Siddiqui ◽  
Maya K. Mitkova ◽  
Ali R. Ansari
Keyword(s):  
Unsteady Flow ◽  
Pressure Gradient ◽  
Analytical Solutions ◽  
Interface Velocity ◽  
Time Dependent ◽  
Second Grade ◽  
Parallel Plates ◽  
Governing Equations ◽  
Layer Flow ◽  
Second Grade Fluids

Unsteady, pressure driven in the gap between two parallel plates flow of two non-Newtonian incompressible second grade fluids is considered. The governing equations are established for the particular two-layer flow and analytical solutions of the equations that satisfy the imposed boundary conditions are obtained. The velocity of each fluid is expressed as function of the material constants, time dependent pressure gradient and other characteristics of the fluids. As part of the solution, an expression for the interface velocity is derived. We analyze the shift of the velocity maximum from one to another fluid as a function of variety of values of fluids’ parameters.

scholarly journals A note on “Taylor–Couette flow of a generalized second grade fluid due to a constant couple”

2010 ◽  
Vol 15 (2) ◽  
pp. 155-158 ◽  
Author(s):  
C. Fetecau ◽  
A. U. Awan ◽  
M. Athar
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Unsteady Flow ◽  
Couette Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
New Form ◽  
Second Grade Fluids

In this brief note, we show that the unsteady flow of a generalized second grade fluid due to a constant couple, as well as the similar flow of Newtonian and ordinary second grade fluids, ultimately becomes steady. For this, a new form of the exact solution for velocity is established. This solution is presented as a sum of the steady and transient components. The required time to reach the steady-state is obtained by graphical illustrations.

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