scholarly journals Peristaltic Transport of Power-Law Fluid in an Elastic Tapered Tube with Variable Cross-Section Induced by Dilating Peristaltic Wave

2021 ◽  
pp. 1293-1306
Author(s):  
Mohammed Ali Murad ◽  
Ahmed M. Abdulhadi
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Power Law ◽  
Variable Cross Section ◽  
Peristaltic Transport ◽  
Peristaltic Wave ◽  
Variable Cross ◽  
Power Law Fluid ◽  
Opposite Behavior ◽  
Local Shear

The peristaltic transport of power-law fluid in an elastic tapered tube with variable cross-section induced by dilating peristaltic wave is studied. The exact solution of the expression for axial velocity, radial velocity, stream function, local shear stress, volume of flow rate and pressure gradient are obtained under the assumption of long wavelength and low Reynolds number. The effects of all parameters that appear in the problem are analyzed through graphs. The results showed that the flux is sinusoidal in nature and it is an increasing function with the increase of  whereas it is a decreasing function with the increase of . An opposite behavior for shear strain is noticed compared to pressure gradient.  Finally, trapping phenomenon is presented to explain the physical behavior of various parameters. It is noted that the size of the trapping bolus increases with increasing  whereas it decreases as  increases. MATHEMATICA software is used to plot all figures.

Pressure Losses in Power-Law Fluid Flow through a Tube of Variable Cross-Section

2021 ◽  
Vol 56 (1) ◽  
pp. 1-9
Author(s):  
E. I. Borzenko ◽  
I. A. Ryl’tsev ◽  
G. R. Schrager
Keyword(s):  
Fluid Flow ◽  
Cross Section ◽  
Power Law ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Power Law Fluid ◽  
Pressure Losses ◽  
Flow Through

scholarly journals Oscillatory flow of a Casson fluid in an elastic tube with variable cross section

2018 ◽  
Vol 3 (2) ◽  
pp. 571-582 ◽  
Author(s):  
C.K. Selvi ◽  
A.N.S. Srinivas
Keyword(s):  
Pressure Gradient ◽  
Pressure Distribution ◽  
Cross Section ◽  
Oscillatory Flow ◽  
Axial Direction ◽  
Variable Cross Section ◽  
Casson Fluid ◽  
Elastic Parameter ◽  
Elastic Tube ◽  
Variable Cross

AbstractThe aim of this paper was to study an oscillatory flow of a Casson fluid through an elastic tube of variable cross section. The radial displacement of tube wall is taken into consideration. The problem is modelled under the assumption that the variation of the cross section of the tube is slow in the axial direction. Cylindrical coordinate system is chosen to study the problem. The analytical expressions for axial velocity and mass flux as a function of pressure gradient are obtained. The change in pressure distribution for various pressure****radius relationships is analyzed by considering different geometries. The effects of elastic parameter, Womersley parameter and Casson parameter on excess pressure and pressure gradient along axial direction are discussed through graphs. The results reveal that the elastic parameter plays a key role in the variation of pressure along the tube. Womersley parameter has significant effect on pressure distribution. Another important observation is that the amplitude of pressure increases for growing values of Casson parameter for both tapered and constricted tubes. In addition, the pressure oscillates more for the case of locally constricted tube when compared to other geometries.

Peristaltic Transport of a Power-Law Fluid With Variable Consistency

1982 ◽  
Vol 104 (3) ◽  
pp. 182-186 ◽  
Author(s):  
J. B. Shukla ◽  
S. P. Gupta
Keyword(s):  
Pressure Drop ◽  
Friction Force ◽  
Power Law ◽  
Flow Rate ◽  
Peristaltic Transport ◽  
Peristaltic Wave ◽  
Power Law Fluid ◽  
Peripheral Layer

Effects of the consistency variation on the peristaltic transport of a non-Newtonian power-law fluid fluid through a tube have been investigated by taking into account the existence of a peripheral layer. It is shown that the flow rate flux, for zero pressure drop, increases as the amplitude of the peristaltic wave increases but it decreases due to the pseudoplastic nature of the fluid. It is also noted that, for zero pressure drop, the flux does not depend on the consistency of peripheral layer while the friction decreases as this consistency decreases. However, for nonzero pressure drop, the flux increases and the friction force decreases as the consistency of peripheral layer fluid decreases.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

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