Laminar Flow in an Annulus With Arbitrary Time-Varying Pressure Gradient and Arbitrary Initial Velocity

1969 ◽  
Vol 36 (2) ◽  
pp. 309-311 ◽  
Author(s):  
Satya Prakash
Keyword(s):  
Pressure Gradient ◽  
Initial Velocity ◽  
Hankel Transform ◽  
Initial Distribution ◽  
Circular Cylinders ◽  
Time Varying ◽  
Annular Space ◽  
Arbitrary Time ◽  
Constant Quantity ◽  
Finite Hankel Transform

In this paper, the problem of incompressible laminar viscous flow in the annular space bounded by two coaxial infinite circular cylinders with an arbitrary time-varying pressure gradient and with an arbitrary initial distribution of velocity has been studied. The present problem generalizes the several earlier works in which the pressure gradient and the initial distribution of velocity have been taken in special forms. The analysis has been made by the use of finite Hankel transform. The case of steady flow when the pressure gradient is constant has been deduced by taking the pressure gradient to be a constant quantity and then letting the time since the start of the motion be infinite. This result has been shown in agreement with the already well-established result.

Laminar Flow of an Incompressible Fluid in a Conduit With Arbitrary Cross Section, Arbitrary Time-Varying Pressure Gradient, and Arbitrary Initial Velocity

1972 ◽  
Vol 94 (1) ◽  
pp. 27-32 ◽  
Author(s):  
H. K. Hepworth ◽  
W. Rice
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Initial Velocity ◽  
Solution Method ◽  
Initial Conditions ◽  
Arbitrary Cross Section ◽  
Computational Time ◽  
Time Varying ◽  
Arbitrary Time ◽  
Gram Determinant

A computer-oriented solution is given for the flow described in the title of the paper. The boundary shape is represented by specification of the coordinates of N points on the boundary; the initial velocity is represented by specification of L values of the velocity in the cross section at time zero; the arbitrary time-varying pressure gradient is implemented by use of Duhamel’s Theorem. In the solution method presented, boundary and initial conditions are satisfied in the least squares sense. The Gram determinant is used to determine eigenvalues and the Gram-Schmidt orthonormalizing procedure is used to construct a set of functions appropriate for a finite series solution. Computer programs are referenced which have been used to investigate the correctness of the solution and the accuracy obtainable with reasonable digital computational time.

Couette Flow of a Generalized Oldroyd-B Fluid due to Constantly Accelerated Shear Stress Coupled with the Pressure Gradient

2011 ◽  
Vol 354-355 ◽  
pp. 179-182
Author(s):  
Chun Rui Li ◽  
Lian Cun Zheng ◽  
Xin Xin Zhang ◽  
Jia Jia Niu
Keyword(s):  
Shear Stress ◽  
Laplace Transform ◽  
Pressure Gradient ◽  
Exact Solutions ◽  
Couette Flow ◽  
Fractional Derivatives ◽  
Hankel Transform ◽  
Time Dependent ◽  
Infinite Cylinder ◽  
Finite Hankel Transform

This paper presented an analysis for the couette flow of a generalized Oldroyd-B fluid within an infinite cylinder subject to a time-dependent shear stress with the influence of the internal constantly decelerated pressure gradient. The exact solutions are established by means of the combine of the sequential fractional derivatives Laplace transform and finite Hankel transform and presented by integral and series form in terms of the Mittag-Leffler function. Moreover, the effects of various parameters are analyzed in detail by graphical illustrations.

Some Exact Solutions for Helical Flows of Maxwell Fluid in an Annular Pipe due to Accelerated Shear Stresses

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Muhammad Jamil ◽  
Constantin Fetecau ◽  
Najeeb Alam Khan ◽  
Amir Mahmood
Keyword(s):  
Exact Solutions ◽  
Large Time ◽  
Maxwell Fluid ◽  
Hankel Transform ◽  
Circular Cylinders ◽  
Shear Stresses ◽  
Material Parameters ◽  
In Series ◽  
Finite Hankel Transform ◽  
Annular Pipe

Some exact solutions corresponding to helical flows of Maxwell fluid between two infinite coaxial circular cylinders are determined by means of finite Hankel transform, presented in series form, satisfied all imposed initial and boundary conditions. The motion is produced by the inner cylinder that applies the torsional and longitudinal time-dependent accelerated shear stresses to the fluid. The corresponding solutions for Newtonian fluid and large-time solutions are also obtained as limiting cases and effect of material parameters on the large-time solutions are discussed. Finally, the influence of pertinent parameters as well as a comparison between Maxwell and Newtonian fluids on the velocity components and shear stresses profiles is also examined by graphical illustrations.

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