Mathematical model for the ciliary-induced transport of seminal liquids through the ductuli efferentes

2017 ◽  
Vol 10 (03) ◽  
pp. 1750031 ◽  
Author(s):  
A. A. Farooq ◽  
A. M. Siddiqui
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Couple Stress ◽  
Reproductive Tract ◽  
Couple Stress Fluid ◽  
Graphical Form ◽  
Axially Symmetric ◽  
Governing System ◽  
Ciliary Motion ◽  
Two Dimensional Flow

This study describes the consequences of the ciliary motion on the transport of seminal liquid through the ductus efferentes of the male reproductive tract. By assuming the seminal liquid as a couple stress fluid, we have formulated a mathematical model for a two-dimensional flow through an axially symmetric tube whose inner surface is ciliated in the form of a metachronal wave. The governing system consists of nonlinear coupled partial differential equations which is reduced to a system of ordinary differential equations by utilizing the long wavelength approximation in an environment of the inertia free flow. Exact solutions for the velocity distribution, the pressure gradient and the stream function are obtained in terms of the couple stress parameters and the ciliary metachronism. Special attention is given to the pumping and the trapping characteristics due to the cilia motility. The study reveals that the ciliary pumping has to be more efficient to transport a couple stress fluid as compared to a Newtonian fluid. Moreover, the theoretical results for the couple stress fluid are found to be in good agreement with those reported by [T. J. Lardner and W. J. Shack, Cilia transport, Bull. Math. Biophys. 34 (1972) 325–335]. The analytical results are also displayed in graphical form.

scholarly journals Swirling flow of couple stress fluid due to a rotating disk

2019 ◽  
Vol 8 (1) ◽  
pp. 261-269 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Nadeem Alam Khan ◽  
Saif Ullah ◽  
Farah Naz
Keyword(s):  
Differential Equations ◽  
Couple Stress ◽  
Swirling Flow ◽  
Nonlinear Differential Equations ◽  
Rotating Disk ◽  
Tangential Component ◽  
Couple Stress Fluid ◽  
Governing System ◽  
Fluid Parameter ◽  
Homotopy Analysis

AbstractThe main objective of the present investigation is to examine the couple stress fluid flow occurring as a result of rotation of a disk. On implementing a suitable transformation, the governing system of partial differential equations (PDEs) is converted into nonlinear differential equations of a single independent variable. These equations are solved analytically by virtue of the Homotopy Analysis Method (HAM) which gives solutions in the form of a series. The solution of most of the governing problems is determined in terms of the absolute exponential and decaying functions by means of this powerful technique. To support analytic results, some graphs are plotted for determining the convergence of the solution. Also the graphical interpretation of velocity profiles corresponding to the effects of pertinent parameters are shown and discussed in detail. The numerical results are calculated for evaluation of the influence of fluid parameter. It can also be anticipated that the radial and axial velocity components show decreasing behavior due to rise in the values of couple stress parameter which conflict the behavior of the tangential component of velocity.

scholarly journals Soret and dufour effects on free convection flow of a couple stress fluid in a vertical channel with chemical reaction

2013 ◽  
Vol 19 (1) ◽  
pp. 45-55 ◽  
Author(s):  
D. Srinivasacharya ◽  
K. Kaladhar
Keyword(s):  
Differential Equations ◽  
Chemical Reaction ◽  
Couple Stress ◽  
Vertical Channel ◽  
Couple Stress Fluid ◽  
Convection Flow ◽  
Parallel Plates ◽  
Soret And Dufour Effects ◽  
Similarity Transformations ◽  
Dufour Number

The Soret and Dufour effects in the presence of chemical reaction on natural convection heat and mass transfer of a couple stress fluid in a vertical channel formed by two vertical parallel plates is presented. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using Homotopy Analysis Method (HAM). Profiles of dimensionless velocity, temperature and concentration are shown graphically for various values of Dufour number, Soret number, Couple stress parameter and chemical reaction parameter.

scholarly journals Analytical solution of MHD free convective flow of couple stress fluid in an annulus with Hall and ion-slip effects

2011 ◽  
Vol 16 (4) ◽  
pp. 477-487 ◽  
Author(s):  
Darbhashayanam Srinivasacharya ◽  
Kolla Kaladhar
Keyword(s):  
Differential Equations ◽  
Couple Stress ◽  
Circular Cylinders ◽  
Couple Stress Fluid ◽  
Electrically Conducting ◽  
Linear Partial Differential Equations ◽  
Similarity Transformations ◽  
Slip Effects ◽  
Homotopy Analysis ◽  
Ion Slip

This paper presents the Hall and Ion-slip effects on electrically conducting couple stress fluid flow between two circular cylinders in the presence of a temperature dependent heat source. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations and then solved using homotopy analysis method (HAM). The effects of the magnetic parameter, Hall parameter, Ion-slip parameter and couple stress fluid parameter on velocity and  temperature are discussed and shown graphically.

scholarly journals Off-Centered Stagnation Point Flow of a Couple Stress Fluid towards a Rotating Disk

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Fatima Riaz
Keyword(s):  
Differential Equations ◽  
Couple Stress ◽  
Similarity Transformation ◽  
Rotating Disk ◽  
Analytical Approximation ◽  
Couple Stress Fluid ◽  
Analysis Method ◽  
Convergence Region ◽  
Homotopy Analysis ◽  
Special Case

An investigation has been made to study the off-centered stagnation flow of a couple stress fluid over a rotating disk. The model developed for the governing problem in the form of partial differential equations has been converted to ordinary differential equations with the use of suitable similarity transformation. The analytical approximation has been made with the most promising analytical approach, homotopy analysis method (HAM). The convergence region of the obtained solution is determined and plotted. The effects of couple stress and nondimensional parameters have been observed on the flows of couple stress fluid. Also comparison has been made with the Newtonian fluid as the special case of considered problem.

scholarly journals PERISTALTIC TRANSPORT OF A COUPLE STRESS FLUID: SOME APPLICATIONS TO HEMODYNAMICS

2012 ◽  
Vol 12 (03) ◽  
pp. 1250048 ◽  
Author(s):  
S. MAITI ◽  
J. C. MISRA
Keyword(s):  
Frictional Force ◽  
Couple Stress ◽  
Amplitude Ratio ◽  
Circulatory System ◽  
Peristaltic Transport ◽  
Porous Channel ◽  
Couple Stress Fluid ◽  
Graphical Form ◽  
Physical Parameters ◽  
Stress Effect

The paper deals with a theoretical investigation of the peristaltic transport of a couple stress fluid in a porous channel. The study is motivated toward investigating the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. The velocity, pressure gradient, stream function, and frictional force of blood are investigated, when the Reynolds number is small and the wavelength is large, by using appropriate analytical and numerical methods. Effects of different physical parameters reflecting porosity, Darcy number, couple stress parameter, as well as amplitude ratio on velocity profiles, pumping action and frictional force, streamlines pattern, and trapping of blood are studied with particular emphasis. The computational results are presented in graphical form. The results are found to be in good agreement with those reported by Shapiro et al.52 that was carried out for a non-porous channel without consideration of couple stress effect. The present study puts forward an important observation that for peristaltic transport of a couple stress fluid during free pumping, flow reversal can be considerably controlled by suitably adjusting the couple stress effect of the fluid/Darcy permeability of the channel. It is also possible to avoid the occurrence of trapping, by reducing the permeability.

MATHEMATICAL MODELING OF BLOOD FLOW THROUGH STENOSED TUBE

2008 ◽  
Vol 08 (01) ◽  
pp. 27-32 ◽  
Author(s):  
V. K. VERMA ◽  
M. P. SINGH ◽  
V. K. KATIYAR
Keyword(s):  
Mathematical Modeling ◽  
Blood Flow ◽  
Cross Section ◽  
Newtonian Fluid ◽  
Couple Stress ◽  
Slip Velocity ◽  
Couple Stress Fluid ◽  
Constant Cross Section ◽  
Axially Symmetric ◽  
Flow Through

In the present study, blood flow in a stenosed tube is modeled. Blood is assumed to be represented by couple stress fluid. The growth projects into the lumen of the artery and blood flow is disturbed; thus, a potential coupling develops between the growth and the blood flow through the artery. An analysis of the effect of an axially symmetric growth into the lumen of a tube of constant cross-section through which a Newtonian fluid is steadily flowing is presented. The importance of the effect of slip velocity in stenosed tube is highlighted.

scholarly journals Analysis of couple stress fluid flow with variable viscosity using two homotopy-based methods

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 134-145
Author(s):  
Alamgeer Khan ◽  
Muhammad Farooq ◽  
Rashid Nawaz ◽  
Muhammad Ayaz ◽  
Hijaz Ahmad ◽  
...  
Keyword(s):  
Differential Equations ◽  
Couple Stress ◽  
Homotopy Perturbation Method ◽  
Variable Viscosity ◽  
Coupled System ◽  
Velocity Shear ◽  
Couple Stress Fluid ◽  
Governing Equations ◽  
Optimal Homotopy Asymptotic Method ◽  
Velocity Average

Abstract In this article, the generalized plane Couette flow of Vogel’s model of incompressible, non-isothermal, couple stress fluid flowing steadily between two parallel walls is investigated. The governing equations are reduced to ordinary differential equations. To investigate the non-linear coupled system of differential equations, the optimal homotopy asymptotic method with DJ polynomial and asymptotic homotopy perturbation method have been used. Important flow properties are presented and discussed. We have obtained expressions for velocity, average velocity, shear stress, volume flux and temperature. The results gained employing these techniques are in the form of infinite series; thus, the results can be easily calculated. Comparison of various results, obtained through the suggested approaches, is carried out and an excellent agreement is achieved.

scholarly journals Comparative study of generalized couette flow of couple stress fluid using optimal homotopy asymptotic method and new iterative method

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Muhammad Farooq ◽  
Alamgeer Khan ◽  
Rashid Nawaz ◽  
Saeed Islam ◽  
Muhammad Ayaz ◽  
...  
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Couette Flow ◽  
Asymptotic Method ◽  
Couple Stress ◽  
Research Work ◽  
Couple Stress Fluid ◽  
Parallel Plates ◽  
Optimal Homotopy Asymptotic Method ◽  
New Iterative Method

AbstractIn this research work, we have studied the steady generalized Couette flow of couple stress fluid between two parallel plates considering the non-isothermal effects. The governing equations that are, continuity, momentum and energy equations are reduced to ordinary differential equations. The Optimal Homotopy Asymptotic Method (OHAM) and New Iterative Method (NIM) are used to solve this coupled system of differential equations. Using the said methods, we have obtained expressions for velocity profile, temperature distribution, volume flux, average velocity and shear stress. The results of OHAM and NIM are compared numerically as well as graphically and a tremendous agreement is attained.

Analysis of the Working Process and Mechanical Losses in a Stirling Engine for a Solar Power Unit

1999 ◽  
Vol 121 (2) ◽  
pp. 121-127 ◽  
Author(s):  
Kh. Kh. Makhkamov ◽  
D. B. Ingham
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Power Unit ◽  
Computational Simulation ◽  
Mass Conservation ◽  
Stirling Engine ◽  
Computational Results ◽  
Working Process ◽  
Euler’S Method ◽  
Governing System

In this paper a second level mathematical model for the computational simulation of the working process of a 1-kW Stirling engine has been used and the results obtained are presented. The internal circuit of the engine in the calculation scheme was divided into five chambers, namely, the expansion space, heater, regenerator, cooler and the compression space, and the governing system of ordinary differential equations for the energy and mass conservation were solved in each chamber by Euler’s method. In additional, mechanical losses in the construction of the engine have been determined and the computational results show that the mechanical losses for this particular design of the Stirling engine may be up to 50% of the indicated power of the engine.

Sign in / Sign up

Export Citation Format

Share Document