Influence of metachronal wave on hyperbolic tangent fluid model with inclined magnetic field

2019 ◽  
Vol 16 (09) ◽  
pp. 1950139 ◽  
Author(s):  
Safia Akram ◽  
Farkhanda Afzal ◽  
Muhammad Imran
Keyword(s):  
Newtonian Fluid ◽  
Fluid Model ◽  
Perturbation Technique ◽  
Pressure Rise ◽  
Weissenberg Number ◽  
Hyperbolic Tangent ◽  
Regular Perturbation ◽  
Tangent Hyperbolic Fluid ◽  
Wavelength Approximation ◽  
Induced Flow

The purpose of this paper is to discuss the theoretical study of a nonlinear problem of cilia induced flow by considering the fluid as anincompressible non-Newtonian fluid (hyperbolic tangent fluid) model by means of ciliated walls. The leading equations of present flow problem are simplified under the consideration of long-wavelength approximation. We have utilized regular perturbation technique to solve the simplified leading equations of hyperbolic tangent fluid model. The analytical solution is computed for stream function and numerical solution is computed for the rise in pressure. The characteristics of the ciliary system on tangent hyperbolic fluid are analyzed graphically and discussed in detail. It has been found that when [Formula: see text], the results of pressure rise coincide with the results of Newtonian fluid. It has also been observed that the size of the trapping bolus decreases with an increase in Hartmann number and Weissenberg number.

Peristaltic Transport of a Hyperbolic Tangent Fluid Model in an Asymmetric Channel

2009 ◽  
Vol 64 (9-10) ◽  
pp. 559-567 ◽  
Author(s):  
Sohail Nadeem ◽  
Safia Akram
Keyword(s):  
Pressure Gradient ◽  
Fluid Model ◽  
Pressure Rise ◽  
Weissenberg Number ◽  
Physical Parameters ◽  
Asymmetric Channel ◽  
Governing Equations ◽  
Hyperbolic Tangent ◽  
Regular Perturbation ◽  
Narrow Part

In the present analysis, we have modeled the governing equations of a two dimensional hyperbolic tangent fluid model. Using the assumption of long wavelength and low Reynolds number, the governing equations of hyperbolic tangent fluid for an asymmetric channel have been solved using the regular perturbation method. The expression for pressure rise has been calculated using numerical integrations. At the end, various physical parameters have been shown pictorially. It is found that the narrow part of the channel requires a large pressure gradient, also in the narrow part the pressure gradient decreases with the increase in Weissenberg number We and channel width d.

scholarly journals An Analytical Approach to Study the Blood Flow over a Nonlinear Tapering Stenosed Artery in Flow of Carreau Fluid Model

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Riaz Ahmad ◽  
Asma Farooqi ◽  
Rashada Farooqi ◽  
Nawaf N. Hamadneh ◽  
Md Fayz-Al-Asad ◽  
...  
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Analytical Approach ◽  
Fluid Model ◽  
Perturbation Technique ◽  
Fluid Velocity ◽  
Weissenberg Number ◽  
Carreau Fluid ◽  
Regular Perturbation ◽  
Stenosed Artery

The current study provides an analytical approach to analyze the blood flow through a stenosed artery by using the Carreau fluid model. The flow governing equations are derived under the consideration of mild stenosis. Mathematical analysis has been carried out by considering the blood as non-Newtonian nature. Then, the analytical solution has been investigated by using the regular perturbation technique. The solutions obtained by this perturbation are up to the second-order in dimensionless Weissenberg number We . The performed computations of various parameter values such as velocity, wall shear stress, shear stress, and resistance impedance at the stenotic throat are discussed in detail for different values of Weissenberg number We . The obtained results demonstrate that for shear-thinning fluid, the fluid velocity increases with the increasing parameter m while opposite behavior is observed with the increase in We . Hence, the presented numerical analysis reveals many aspects of the flow by considering the blood as a non-Newtonian Carreau fluid model, and the presented model can be equally applicable to other bio-mathematical studies.

scholarly journals A novel mathematical modeling with solution for movement of fluid through ciliary caused metachronal waves in a channel

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Wasim Ullah Khan ◽  
Ali Imran ◽  
Muhammad Asif Zahoor Raja ◽  
Muhammad Shoaib ◽  
Saeed Ehsan Awan ◽  
...  
Keyword(s):  
Fluid Transport ◽  
Fluid Model ◽  
Transverse Velocity ◽  
Perturbation Technique ◽  
Wave Length ◽  
Pressure Rise ◽  
Nano Fluid ◽  
Symmetric Channel ◽  
Ciliary Motion ◽  
Induced Flow

AbstractIn the present research, a novel mathematical model for the motion of cilia using non-linear rheological fluid in a symmetric channel is developed. The strength of analytical perturbation technique is employed for the solution of proposed physical process using mectachoronal rhythm based on Cilia induced flow for pseudo plastic nano fluid model by considering the low Reynolds number and long wave length approximation phenomena. The role of ciliary motion for the fluid transport in various animals is explained. Analytical expressions are gathered for stream function, concentration, temperature profiles, axial velocity, and pressure gradient. Whereas, transverse velocity, pressure rise per wave length, and frictional force on the wall of the tubule are investigated with aid of numerical computations and their outcomes are demonstrated graphically. A comprehensive analysis for comparison of Perturb and numerical solution is done. This analysis validates the analytical solution.

An investigation of non-Newtonian fluid flow due to metachronal beating of cilia in a tube

2015 ◽  
Vol 08 (02) ◽  
pp. 1550016 ◽  
Author(s):  
A. M. Siddiqui ◽  
A. A. Farooq ◽  
M. A. Rana
Keyword(s):  
Newtonian Fluid ◽  
Flow Rate ◽  
Fluid Model ◽  
Volume Flow Rate ◽  
Weissenberg Number ◽  
Volume Flow ◽  
Physical Parameters ◽  
Regular Perturbation ◽  
Ciliary Motion ◽  
Viscous Fluid Model

The aim of this study is to explain theoretically the role of ciliary motion on the transport of epididymal fluid through the ductus efferentes of the male reproductive track. For this purpose, a mathematical model has been developed for the flow of a non-Newtonian fluid in an axisymmetric tube due to metachronal wave of cilia motion for the more realistic consequences. Carreau viscous fluid model is considered to see the rheological effects on the pumping characteristics of the flow. Regular perturbation method has been employed to obtain the analytical expressions for the stream function, the velocity field and a relation between the pressure difference and the volume flow rate. It is found that the volume flow rate is influenced significantly by Weissenberg number We and the cilia length parameter ε. The computational results are presented graphically to see the effects of various physical parameters. Finally, the analysis is applied and compared with the observed value of the flow rate of spermatic fluid in the ductus efferentes of the male reproductive track. The volume flow rate is reported closed to the estimated value 6 × 10-3 ml/h in the human ductus efferentes when We = 0.5 and ε is near by 0.25.

scholarly journals Williamson Fluid Model for the Peristaltic Flow of Chyme in Small Intestine

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Sohail Nadeem ◽  
Sadaf Ashiq ◽  
Mohamed Ali
Keyword(s):  
Small Intestine ◽  
Fluid Model ◽  
Flow Characteristics ◽  
Pressure Rise ◽  
Intestinal Wall ◽  
Peristaltic Flow ◽  
Weissenberg Number ◽  
Regular Perturbation ◽  
Williamson Fluid ◽  
Axial Pressure Gradient

Mathematical model for the peristaltic flow of chyme in small intestine along with inserted endoscope is considered. Here, chyme is treated as Williamson fluid, and the flow is considered between the annular region formed by two concentric tubes (i.e., outer tube as small intestine and inner tube as endoscope). Flow is induced by two sinusoidal peristaltic waves of different wave lengths, traveling down the intestinal wall with the same speed. The governing equations of Williamson fluid in cylindrical coordinates have been modeled. The resulting nonlinear momentum equations are simplified using long wavelength and low Reynolds number approximations. The resulting problem is solved using regular perturbation method in terms of a variant of Weissenberg numberWe. The numerical solution of the problem is also computed by using shooting method, and comparison of results of both solutions for velocity field is presented. The expressions for axial velocity, frictional force, pressure rise, stream function, and axial pressure gradient are obtained, and the effects of various emerging parameters on the flow characteristics are illustrated graphically. Furthermore, the streamlines pattern is plotted, and it is observed that trapping occurs, and the size of the trapped bolus varies with varying embedded flow parameters.

scholarly journals Convective Heat/Mass Transfer Analysis on Johnson-Segalman Fluid in a Symmetric Curved Channel with Peristalsis: Engineering Applications

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1475
Author(s):  
Humaira Yasmin ◽  
Naveed Iqbal ◽  
Aiesha Hussain
Keyword(s):  
Newtonian Fluid ◽  
Peristaltic Flow ◽  
Weissenberg Number ◽  
Concentration Profiles ◽  
Convective Conditions ◽  
Curved Channel ◽  
Regular Perturbation ◽  
Flexible Walls ◽  
Physical Level ◽  
Parameter Values

The peristaltic flow of Johnson–Segalman fluid in a symmetric curved channel with convective conditions and flexible walls is addressed in this article. The channel walls are considered to be compliant. The main objective of this article is to discuss the effects of curvilinear of the channel and heat/mass convection through boundary conditions. The constitutive equations for Johnson–Segalman fluid are modeled and analyzed under lubrication approach. The stream function, temperature, and concentration profiles are derived. The analytical solutions are obtained by using regular perturbation method for significant number, named as Weissenberg number. The influence of the parameter values on the physical level of interest is outlined and discussed. Comparison is made between Jhonson-Segalman and Newtonian fluid. It is concluded that the axial velocity of Jhonson-Segalman fluid is substantially higher than that of Newtonian fluid.

scholarly journals Theoretical Study of Heat Transfer on Peristaltic Transport of Non-Newtonian Fluid Flowing in a Channel: Rabinowitsch Fluid Model

2018 ◽  
Vol 3 (4) ◽  
pp. 450-471 ◽  
Author(s):  
U. P. Singh ◽  
Amit Medhavi ◽  
R. S. Gupta ◽  
Siddharth Shankar Bhatt
Keyword(s):  
Heat Transfer ◽  
Pressure Gradient ◽  
Friction Force ◽  
Newtonian Fluid ◽  
Theoretical Study ◽  
Fluid Model ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Long Wavelength ◽  
Velocity Pressure

The present investigation is concerned with the problem of heat transfer and peristaltic flow of non-Newtonian fluid using Rabinowitsch fluid model through a channel under long wavelength and low Reynolds number approximation. Expressions for velocity, pressure gradient, pressure rise, friction force and temperature have been obtained. The effect of different parameters on velocity, pressure gradient, pressure rise, streamlines, friction force and temperature have been discussed through graphs.

Application of Rabinowitsch Fluid Model for the Mathematical Analysis of Peristaltic Flow in a Curved Channel

2015 ◽  
Vol 70 (7) ◽  
pp. 513-520 ◽  
Author(s):  
Ehnber Naheed Maraj ◽  
Sohail Nadeem
Keyword(s):  
Current Problem ◽  
Fluid Model ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Shear Stresses ◽  
Curved Channel ◽  
Long Wavelength ◽  
Long Wavelength Approximation ◽  
Dimensional Parameters ◽  
Wavelength Approximation

AbstractThe present work is the mathematical investigation of peristaltic flow of Rabinowitsch fluid in a curved channel. The current problem is modeled and solutions for non-dimensional differential equation are obtained under low Reynolds number and long wavelength approximation. The effects of long lasting non-dimensional parameters on exact solution for velocity profile, pressure rise and shear stresses are studied graphically in the last section. Tables are also incorporated for shear stresses at the walls of the curved channel.

Metachronal Wave of Cilia Transport in a Curved Channel

2015 ◽  
Vol 70 (1) ◽  
pp. 33-38 ◽  
Author(s):  
Sohail Nadeem ◽  
Hina Sadaf
Keyword(s):  
Viscous Fluid ◽  
Pressure Rise ◽  
Viscous Effects ◽  
Curved Channel ◽  
Long Wavelength ◽  
Metachronal Wave ◽  
Long Wavelength Approximation ◽  
Two Dimensional Flow ◽  
Wavelength Approximation ◽  
Induced Flow

AbstractIn this article, the mechanism of cilia-induced flow is discussed through a mathematical model. In this analysis two-dimensional flow of a viscous fluid is observed in a curved channel with ciliated walls. The features of ciliary structures are determined by the dominance of viscous effects over inertial effects using the long-wavelength approximation. The flow is modeled in both fixed and wave frame references. The exact solution is calculated for the velocity profile and the flow properties for the viscous fluid are determined as a function of the cilia and metachronal wave velocity. Results for the pressure rise, pressure gradient and stream function are constructed and analyzed graphically.

Dispersion coefficient in an electro-osmotic flow of a viscoelastic fluid through a microchannel with a slowly varying wall zeta potential

2018 ◽  
Vol 839 ◽  
pp. 348-386 ◽  
Author(s):  
J. C. Arcos ◽  
F. Méndez ◽  
E. G. Bautista ◽  
O. Bautista
Keyword(s):  
Dispersion Coefficient ◽  
Fluid Model ◽  
Perturbation Technique ◽  
Debye Length ◽  
Rheological Behaviour ◽  
Governing Equations ◽  
Regular Perturbation ◽  
Axial Distribution ◽  
Osmotic Flow ◽  
Electro Osmotic Flow

The dispersion coefficient of a passive solute in a steady-state pure electro-osmotic flow (EOF) of a viscoelastic liquid, whose rheological behaviour follows the simplified Phan-Thien–Tanner (sPTT) model, along a parallel flat plate microchannel, is studied. The walls of the microchannel are assumed to have modulated and low $\unicode[STIX]{x1D701}$ potentials, which vary slowly in the axial direction in a sinusoidal manner. The flow field required to obtain the dispersion coefficient was solved using the lubrication approximation theory (LAT). The solution of the electric potential is based on the Debye–Hückel approximation for a symmetric $(z:z)$ electrolyte. The viscoelasticity of the fluid is observed to notably amplify the axial distribution of the effective dispersion coefficients due to the variation in the $\unicode[STIX]{x1D701}$ potentials of the walls. The problem was formulated for two cases: when the Debye layer thickness (EDL) was on the order of unity (thick EDL) and in the limit where the thickness of the EDL was very small compared with the height of the microchannel (thin EDL limit). Due to the coupling between the nonlinear governing equations and the sPTT fluid model, they were replaced by their approximate linearized forms and solved in the limit of $\unicode[STIX]{x1D700}\ll 1$ using the regular perturbation technique. Here $\unicode[STIX]{x1D700}$ is the amplitude of the sinusoidal function of the $\unicode[STIX]{x1D701}$ potentials. Additionally, the numerical solution of the simplified governing equations was also obtained for $\unicode[STIX]{x1D700}=O(1)$ and compared with the approximate solution, showing excellent agreement for $0\leqslant \unicode[STIX]{x1D700}\leqslant 0.3$. Note that the dispersion coefficient primarily depends on the Deborah number, on the ratio of the half-height of the microchannel to the Debye length, and on the assumed variation in the $\unicode[STIX]{x1D701}$ potentials of the walls.

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