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.

Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Due to a Time-Dependent Couple

2011 ◽  
Vol 66 (1-2) ◽  
pp. 40-46 ◽  
Author(s):  
Corina Fetecau ◽  
Muhammad Imran ◽  
Constantin Fetecau
Keyword(s):  
Exact Solutions ◽  
Couette Flow ◽  
Bessel Functions ◽  
Time Dependent ◽  
Second Grade ◽  
Governing Equations ◽  
Material Parameters ◽  
Taylor Couette ◽  
Similar Solutions ◽  
Taylor Couette Flow

Taylor-Couette flow in an annulus due to a time-dependent torque suddenly applied to one of the cylinders is studied by means of finite Hankel transforms. The exact solutions, presented under series form in terms of usual Bessel functions, satisfy both the governing equations and all imposed initial and boundary conditions. They can easily be reduced to give similar solutions for Maxwell, second grade, and Newtonian fluids performing the same motion. Finally, some characteristics of the motion, as well as the influence of the material parameters on the behaviour of the fluid, are emphasized by graphical illustrations.

Micropolar Fluid Flow Between Two Inclined Parallel Plates

2017 ◽  
Author(s):  
Abbas Hazbavi ◽  
Sajad Sharhani
Keyword(s):  
Fluid Flow ◽  
Pressure Gradient ◽  
Micropolar Fluid ◽  
Constant Heat Flux ◽  
Hydrodynamic Characteristics ◽  
Parallel Plates ◽  
Governing Equations ◽  
Micropolar Fluid Flow ◽  
Flow Through ◽  
The Magnetic Field

In this study, the hydrodynamic characteristics are investigated for magneto-micropolar fluid flow through an inclined channel of parallel plates with constant pressure gradient. The lower plate is maintained at constant temperature and upper plate at a constant heat flux. The governing equations which are continuity, momentum and energy are are solved numerically by Explicit Runge-Kutta. The effect of characteristic parameters is discussed on velocity and microrotation in different diagrams. The nonlinear parameter affected the velocity microrotation diagrams. An increase in the value of Hartmann number slows down the movement of the fluid in the channel. The application of the magnetic field induces resistive force acting in the opposite direction of the flow, thus causing its deceleration. Also the effect of pressure gradient is investigated on velocity and microrotation in different diagrams.

General Solutions for the Unsteady Flow of Second-Grade Fluids over an Infinite Plate that Applies Arbitrary Shear to the Fluid

2011 ◽  
Vol 66 (12) ◽  
pp. 753-759 ◽  
Author(s):  
Constantin Fetecau ◽  
Corina Fetecau ◽  
Mehwish Rana
Keyword(s):  
Shear Stress ◽  
Unsteady Flow ◽  
Infinite Plate ◽  
Unsteady Motion ◽  
Newtonian Fluids ◽  
Second Grade ◽  
Moving Plate ◽  
General Solutions ◽  
Similar Solutions ◽  
Second Grade Fluids

General solutions corresponding to the unsteady motion of second-grade fluids induced by an infinite plate that applies a shear stress ƒ (t) to the fluid are established. These solutions can immediately be reduced to the similar solutions for Newtonian fluids. They can be used to obtain known solutions from the literature or any other solution of this type by specifying the function ƒ (.). Furthermore, in view of a simple remark, general solutions for the flow due to a moving plate can be developed.

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.

Unsteady Flow of Two Immiscible Fluids under an Oscillatory Time-dependent Pressure Gradient in a Channel with One Porous Floor

2006 ◽  
Vol 1 (2) ◽  
pp. 194-203 ◽  
Author(s):  
Sai K.S., . ◽  
N.S. Swamy . ◽  
H.R. Nataraja . ◽  
S.B. Tiwari . ◽  
B. Nageswara Rao .
Keyword(s):  
Unsteady Flow ◽  
Pressure Gradient ◽  
Immiscible Fluids ◽  
Time Dependent

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.

scholarly journals On semi-inverse solutions for the time-dependent flows of a second-grade fluid

2006 ◽  
Vol 2006 ◽  
pp. 1-22 ◽  
Author(s):  
Muhammad R. Mohyuddin ◽  
S. Asghar ◽  
T. Hayat ◽  
A. M. Siddiqui
Keyword(s):  
Stream Function ◽  
Analytical Solutions ◽  
Time Dependent ◽  
Polar Coordinates ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Inverse Solutions ◽  
Grade Fluid

This paper deals with analytical solutions for the time-dependent equations arising in a second-grade fluid. The solutions have been developed by assuming certain forms of the stream function. Expressions for velocity components are obtained for flows in plane polar, axisymmetric cylindrical, and axisymmetric spherical polar coordinates. The obtained solutions are compared with existing results.

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