Analytical solution by Laplace-ritz variational method for non-Newtonian nanofluid inside a circular tube

2018 ◽  
Vol 135 ◽  
pp. 596-608
Author(s):  
Antar Tahiri ◽  
Kacem Mansouri
Keyword(s):  
Analytical Solution ◽  
Variational Method ◽  
Circular Tube

scholarly journals A variational method to study the Zakharov equation

2005 ◽  
Vol 2005 (22) ◽  
pp. 3703-3709 ◽  
Author(s):  
Arun Kumar
Keyword(s):  
Analytical Solution ◽  
Variational Method ◽  
Trial Function ◽  
Good Description ◽  
Elliptic Functions ◽  
Jacobian Elliptic Functions ◽  
Zakharov Equation ◽  
Static Limit ◽  
Spatially Periodic ◽  
Linear And Nonlinear

A variational method given by Ritz has been applied to the Zakharov equation to construct an analytical solution. The solution of Zakharov equation gives a good description of both linear and nonlinear evolutions of instabilities generated in waves due to modulation. The spatially periodic trial function is chosen in the form of combination of Jacobian elliptic functions with the dependence of its parameters subject to optimization. This Zakharov equation is reduced to nonlinear Schrödinger equation in the static limit.

Development of a Periodic Flow in a Rigid Tube

1968 ◽  
Vol 90 (3) ◽  
pp. 395-399 ◽  
Author(s):  
P. J. Florio ◽  
W. K. Mueller
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Axial Velocity ◽  
Circular Tube ◽  
Approximate Analytical Solution ◽  
Experimental Results ◽  
Oscillating Flow ◽  
Periodic Flow ◽  
Mean Flow ◽  
Rigid Tube

The development of a pulsating velocity field in a rigid, circular tube was experimentally investigated. The wall pressure and the radial variation of the axial velocity were measured at several axial locations. The measured inlet velocities were compared with the fully developed velocities. The experimental results show that, for the range of parameters investigated, the developing pulsating flow can be considered to be simply a superposition of a developing mean flow and a fully developed oscillating flow. These results are in agreement with a previous approximate analytical solution by Atabek and Chang.

Analytical Solution for a Class of Quadrilateral Stepped Slider Bearings

1984 ◽  
Vol 106 (1) ◽  
pp. 140-144
Author(s):  
J. J. Blech ◽  
I. Etsion
Keyword(s):  
Finite Difference ◽  
Analytical Solution ◽  
Variational Method ◽  
Analytical Approximation ◽  
Slider Bearings ◽  
Aspect Ratios ◽  
Finite Difference Solution ◽  
Difference Solution

Analytical solution is presented for a class of quadrilateral stepped slider bearings. The solution is based on a variational method type of approximation. Results are compared with a finite difference solution to establish the range of validity of the analytical approximation. Bearings performance are presented for various aspect ratios and compared with the performance of the conventional rectangular stepped slider. A range of aspect ratios is found where the quadrilateral bearing is superior to the rectangular one.

scholarly journals An analytical solution for steady flow of a Quemada fluid in a circular tube

1993 ◽  
Vol 32 (4) ◽  
pp. 422-426 ◽  
Author(s):  
A. S. Popel ◽  
G. Enden
Keyword(s):  
Analytical Solution ◽  
Steady Flow ◽  
Circular Tube
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