Influence of Starling's Hypothesis and Joule Heating on Peristaltic Flow of an Electrically Conducting Casson Fluid in a Permeable Microvessel

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
A. Sutradhar ◽  
J. K. Mondal ◽  
P. V. S. N. Murthy ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Joule Heating ◽  
Axial Velocity ◽  
Perturbation Technique ◽  
Casson Fluid ◽  
Order Ordinary Differential Equation ◽  
Long Wavelength ◽  
Electrically Conducting ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation ◽  
Microvessel Wall

Peristaltic transport of electrically conducting blood through a permeable microvessel is investigated by considering the Casson model in the presence of an external magnetic field. The reabsorption process across the permeable microvessel wall is regarded to govern by Starling's hypothesis. Under the long wavelength approximation and low-Reynolds number assumption, the nonlinear governing equations along with the boundary conditions are solved using a perturbation technique. Starling's hypothesis at the microvessel wall provides a second-order ordinary differential equation to be solved numerically for pressure distribution which in turn gives the stream function and temperature field. Also, the location of the interface between the plug and core regions is obtained from the axial velocity. Due to an increasing reabsorption process, the axial velocity is found to increase initially but decreases near the outlet. The temperature is appreciably intensified by virtue of the Joule heating produced due to the electrical conductivity of blood.

Magnetothermodynamic Peristaltic Flow of Bingham Non-Newtonian Fluid in Eccentric Annuli with Slip Velocity and Temperature Jump Conditions

2013 ◽  
Vol 29 (3) ◽  
pp. 493-506 ◽  
Author(s):  
M. F. El-Sayed ◽  
N. T. M. Eldabe ◽  
A. Y. Ghaly ◽  
H. M. Sayed
Keyword(s):  
Newtonian Fluid ◽  
Axial Velocity ◽  
Slip Velocity ◽  
Temperature Jump ◽  
Peristaltic Flow ◽  
Long Wavelength ◽  
Electrically Conducting ◽  
Flow And Heat Transfer ◽  
Wavelength Approximation ◽  
External Uniform Magnetic Field

AbstractIn this paper, we studied the peristaltic flow and heat transfer of an incompressible, electrically conducting Bingham Non-Newtonian fluid in an eccentric uniform annulus in the presence of external uniform magnetic field with slip velocity and temperature jump at the wall conditions. The viscous and Joule dissipations are taken into account. The inner tube is rigid and moving with a constant axial velocity, while the outer tube has a sinusoidal wave traveling down its wall. Under zero Reynolds number condition with the long wavelength approximation, the axial velocity and the stream function are obtained analytically. A numerical solution for the governing partial differential equation of energy is performed in order to analyze the temperature distribution. The effects of all parameters of the problem are numerically discussed and graphically explained.

Magnetohydrodynamic Flow of a Carreau Fluid in a Channel with DifferentWave Forms

2011 ◽  
Vol 66 (3-4) ◽  
pp. 215-222 ◽  
Author(s):  
Tasawar Hayat ◽  
Najma Saleem ◽  
Said Mesloub ◽  
Nasir Ali
Keyword(s):  
Magnetic Field ◽  
Peristaltic Motion ◽  
Carreau Fluid ◽  
Long Wavelength ◽  
Electrically Conducting ◽  
Long Wavelength Approximation ◽  
Wave Forms ◽  
Wavelength Approximation ◽  
Fluid Behaviour ◽  
Pumping And Trapping

In this investigation, we discuss the peristaltic motion based on the constitutive equations of a Carreau fluid in a channel. The fluid is electrically conducting in the presence of a uniform applied magnetic field. Four different wave forms are chosen. The fluid behaviour is studied using long wavelength approximation. Detailed analysis is performed for various emerging parameters on pumping and trapping phenomena. The present results reduce favourably with the currently available results of hydrodynamic case when the Hartman number is chosen zero.

Peristaltic thrusting of a thermal-viscosity nanofluid through a resilient vertical pipe

2020 ◽  
Vol 75 (8) ◽  
pp. 727-738 ◽  
Author(s):  
Ramzy M. Abumandour ◽  
Islam M. Eldesoky ◽  
Mohamed H. Kamel ◽  
Mohamed M. Ahmed ◽  
Sara I. Abdelsalam
Keyword(s):  
Pressure Gradient ◽  
Hartmann Number ◽  
Amplitude Ratio ◽  
Variable Viscosity ◽  
Friction Forces ◽  
Long Wavelength ◽  
Viscosity Parameter ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation ◽  
Theoretical Results

AbstractIn the article, the effects of the thermal viscosity and magnetohydrodynamic on the peristalsis of nanofluid are analyzed. The dominant neutralization is deduced through long wavelength approximation. The analytical solution of velocity and temperature is extracted by using steady perturbation. The pressure gradient and friction forces are obtained. Numerical results are calculated and contrasted with the debated theoretical results. These results are calculated for various values of Hartmann number, variable viscosity parameter and amplitude ratio. It is observed that the pressure gradient is reduced with an increase in the thermal viscosity parameter and that the Hartmann number enhances the pressure difference.

Tensile Stability of Medial Arterial Tissues

2016 ◽  
Vol 83 (5) ◽  
Author(s):  
Alan J. Levy ◽  
Xinyu Zhang
Keyword(s):  
Smooth Muscle ◽  
Constitutive Models ◽  
Constitutive Parameter ◽  
Axial Stretch ◽  
Long Wavelength ◽  
Arterial Tissue ◽  
Long Wavelength Approximation ◽  
Geometrical Imperfections ◽  
Wavelength Approximation ◽  
Nominal Load

Tensile stability of healthy medial arterial tissue and its constituents, subject to initial geometrical and/or material imperfections, is investigated based on the long wavelength approximation. The study employs existing constitutive models for elastin, collagen, and vascular smooth muscle which comprise the medial layer of large elastic (conducting) arteries. A composite constitutive model is presented based on the concept of the musculoelastic fascicle (MEF) which is taken to be the essential building block of medial arterial tissue. Nonlinear equations governing axial stretch and areal stretch imperfection growth quantities are obtained and solved numerically. Exact, closed-form results are presented for both initial and terminal rates of imperfection growth with nominal load. The results reveal that geometrical imperfections, in the form of area nonuniformities, and material imperfections, in the form of constitutive parameter nonuniformities, either decrease or increase only slightly with increasing nominal load; a result which is to be expected for healthy tissue. By way of contrast, an examination of a simple model for elastin with a degrading stiffness gives rise to unbounded imperfection growth rates at finite values of nominal load. The latter result indicates how initial geometrical and material imperfections in diseased tissues might behave, a topic of future study by the authors.

TRIVIALITY OF THE HIGGS FIELD

1989 ◽  
Vol 04 (05) ◽  
pp. 1037-1053 ◽  
Author(s):  
KERSON HUANG
Keyword(s):  
Monte Carlo ◽  
Perturbation Theory ◽  
Critical Review ◽  
Higgs Field ◽  
Higgs Sector ◽  
Long Wavelength ◽  
The Standard Model ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation ◽  
Function Potential

We give a critical review of the "triviality" of the λϕ4 theory, i.e., the vanishing of the renormalized self-coupling. Evidence from perturbation theory and Monte-Carlo simulations are cited. It is noted that (a) the theory is "trivial" but not entirely free, for there is spontaneous symmetry breaking; (b) perturbation theory is unreliable. Soluble examples with similar behavior are compared, in particular the Lee model and the 3D δ function potential. The latter case is especially important, for it shows that triviality is a symptom that the interaction is too singular, and suggests a cure. The import for the Higgs sector of the standard model is discussed. It is argued that, like the Fermi pseudopotential, the Higgs field is a long-wavelength approximation that should be used in lowest order perturbation theory only.

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