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.

Theoretical analysis of MHD Carreau liquid over a heated rotating disk under Von-Karman transformations

2019 ◽  
Vol 16 (2) ◽  
pp. 390-408 ◽  
Author(s):  
Memoona Bibi ◽  
Muhammad Sohail ◽  
Rahila Naz
Keyword(s):  
Differential Equations ◽  
Coupled System ◽  
Rotating Disk ◽  
Analytical Approximation ◽  
Skin Friction Coefficient ◽  
Governing Equations ◽  
Content Type ◽  
Highly Nonlinear ◽  
Contour Plots ◽  
Optimal Homotopy Asymptotic Method

Purpose The purpose of this paper is to perform an analytical approximation for the flow of magnetohydrodynamic Carreau fluid with the association of nanoparticles over a rotating disk. The disk is moving with a constant uniform speed. Governing equations are obtained by using these assumptions in the form of partial differential equations with boundary conditions. These coupled, highly nonlinear equations are transformed into a coupled system of ordinary differential equations by engaging similarity transformation in the rotating frame of reference. Design/methodology/approach An efficient and reliable scheme, namely optimal homotopy asymptotic method, is used to obtain the solutions of the arising physical problem, which is further analyzed graphically. After computing the solutions of the arising problem, plots of velocities, temperature and concentration are discussed briefly. Findings It has been observed that dimensionless velocity reduced due to magnetic effect between the boundary layer and escalating values of the magnetic parameter upsurges the temperature and concentration profiles. Contour plots and numerical results are given for local numbers like skin friction coefficient, Nusselt number and Sherwood number. Originality/value The work presented in this manuscript is neither published nor submitted anywhere for the consideration/publications. It is a novel work.

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.

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.

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 Extension of Optimal Homotopy Asymptotic Method with Use of Daftardar–Jeffery Polynomials to Coupled Nonlinear-Korteweg-De-Vries System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Rashid Nawaz ◽  
Zawar Hussain ◽  
Abraiz Khattak ◽  
Adam Khan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Asymptotic Method ◽  
Nonlinear Partial Differential Equations ◽  
Coupled System ◽  
Higher Order ◽  
Partial Differential ◽  
De Vries ◽  
Optimal Homotopy Asymptotic Method

In this paper, Daftardar–Jeffery Polynomials are introduced in the Optimal Homotopy Asymptotic Method for solution of a coupled system of nonlinear partial differential equations. The coupled nonlinear KdV system is taken as test example. The results obtained by the proposed method are compared with the multistage Optimal Homotopy Asymptotic Method. The results show the efficiency and consistency of the proposed method over the Optimal Homotopy Asymptotic Method. In addition, accuracy of the proposed method can be improved by taking higher order approximations.

scholarly journals Effects of Heat and Mass Transfer on the Peristaltic Transport of MHD Couple Stress Fluid through Porous Medium in a Vertical Asymmetric Channel

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
K. Ramesh ◽  
M. Devakar
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Couple Stress ◽  
Couple Stress Fluid ◽  
Asymmetric Channel ◽  
Governing Equations ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Frictional Forces ◽  
Generation Parameter

The intrauterine fluid flow due to myometrial contractions is peristaltic type motion and the myometrial contractions may occur in both symmetric and asymmetric directions. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitude, and phase due to the variation of channel width, wave amplitudes and phase differences. In this paper, we study the effects of heat and mass transfer on the peristaltic transport of magnetohydrodynamic couple stress fluid through homogeneous porous medium in a vertical asymmetric channel. The flow is investigated in the wave frame of reference moving with constant velocity with the wave. The governing equations of couple stress fluid have been simplified under the long wave length approximation. The exact solutions of the resultant governing equations have been derived for the stream function, temperature, concentration, pressure gradient, and heat transfer coefficients. The pressure difference and frictional forces at both the walls are calculated using numerical integration. The influence of diverse flow parameters on the fluid velocity, pressure gradient, temperature, concentration, pressure difference, frictional forces, heat transfer coefficients, and trapping has been discussed. The graphical results are also discussed for four different wave shapes. It is noticed that increasing of couple stresses and heat generation parameter increases the size of the trapped bolus. The heat generation parameter increases the peristaltic pumping and temperature.

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.

Application of Modified Couple Stress Theory and Homotopy Perturbation Method in Investigation of Electromechanical Behaviors of Carbon Nanotubes

2016 ◽  
Vol 9 (1) ◽  
pp. 23-42 ◽  
Author(s):  
Mir Masoud Seyyed Fakhrabadi
Keyword(s):  
Carbon Nanotubes ◽  
Perturbation Method ◽  
Couple Stress ◽  
Homotopy Perturbation Method ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Governing Equations ◽  
Stress Theory ◽  
Homotopy Perturbation ◽  
Modified Couple Stress

AbstractThe paper presents the size-dependant behaviors of the carbon nanotubes under electrostatic actuation using the modified couple stress theory and homotopy perturbation method. Due to the less accuracy of the classical elasticity theorems, the modified couple stress theory is applied in order to capture the size-dependant properties of the carbon nanotubes. Both of the static and dynamic behaviors under static DC and step DC voltages are discussed. The effects of various dimensions and boundary conditions on the deflection and pull-in voltages of the carbon nanotubes are to be investigated in detail via application of the homotopy perturbation method to solve the nonlinear governing equations semi-analytically.

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