Flow of a Conducting Fluid with Suspension of Particles in Cylinders with Arbitrary Time Varying Pressure Gradient

1980 ◽  
Vol 30 (4) ◽  
pp. 171-182 ◽  
Author(s):  
S. C. Gupta ◽  
M. C. Agarwal
Keyword(s):  
Pressure Gradient ◽  
Conducting Fluid ◽  
Time Varying ◽  
Arbitrary Time

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.

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.

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