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 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.

Entropy generation analysis in flow of thixotropic nanofluid

2019 ◽  
Vol 29 (12) ◽  
pp. 4507-4530 ◽  
Author(s):  
Muhammad Ijaz Khan ◽  
Salman Ahmad ◽  
Tasawar Hayat ◽  
M. Waleed Ahmad Khan ◽  
Ahmed Alsaedi
Keyword(s):  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Entropy Generation ◽  
Hartmann Number ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Content Type ◽  
Flow Variables

Purpose The purpose of this paper is to address entropy generation in flow of thixotropic nonlinear radiative nanoliquid over a variable stretching surface with impacts of inclined magnetic field, Joule heating, viscous dissipation, heat source/sink and chemical reaction. Characteristics of nanofluid are described by Brownian motion and thermophoresis effect. At surface of the sheet zero mass flux and convective boundary condition are considered. Design/methodology/approach Considered flow problem is mathematically modeled and the governing system of partial differential equations is transformed into ordinary ones by using suitable transformation. The transformed ordinary differential equations system is figure out by homotopy algorithm. Outcomes of pertinent flow variables on entropy generation, skin friction, concentration, temperature, velocity, Bejan, Sherwood and Nusselts numbers are examined in graphs. Major outcomes are concluded in final section. Findings Velocity profile increased versus higher estimation of material and wall thickness parameter while it decays through larger Hartmann number. Furthermore, skin friction coefficient upsurges subject to higher values of Hartmann number and magnitude of skin friction coefficient decays via materials parameters. Thermal field is an increasing function of Hartmann number, radiation parameter, thermophoresis parameter and Eckert number. Originality/value The authors have discussed entropy generation in flow of thixotropic nanofluid over a variable thicked surface. No such consideration is yet published in the literature.

3D stagnation point flow of Maxwell fluid towards an off-centered rotating disk

2016 ◽  
Vol 12 (2) ◽  
pp. 345-361 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Sidra Khan ◽  
Fatima Riaz
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Perturbation Technique ◽  
Maxwell Fluid ◽  
Rotating Disk ◽  
Deborah Number ◽  
Stagnation Point Flow ◽  
Graphical Form ◽  
Rotational Parameter ◽  
Content Type

Purpose – The purpose of this paper is to study the three dimensional, steady and incompressible flow of non-Newtonian rate type Maxwell fluid, for stagnation point flow toward an off-centered rotating disk. Design/methodology/approach – The governing partial differential equations are transformed to a system of non-linear ordinary differential equations by conventional similarity transformations. The non-perturbation technique, homotopy analysis method (HAM) is employed for the computation of solutions. And, the solution is computed by using the well-known software Mathematica 10. Findings – The effects of rotational parameter and Deborah number on radial, azimuthal and induced velocity functions are investigated. The results are presented in graphical form. The convergence control parameter is also plotted for velocity profiles. The comparison with the previous results is also tabulated. The skin friction coefficients are also computed for different values of Deborah number. Originality/value – This paper studies the effect of rotation and Deborah number on off-centered rotating disk has been observed and presented graphically.

scholarly journals A New Dynamic Model of a Two-Wheeled Two-Flexible-Beam Inverted Pendulum Robot

2020 ◽  
Author(s):  
Amin Mehrvarz ◽  
Mohammad Javad Khodaei ◽  
William Clark ◽  
Nader Jalili
Keyword(s):  
Differential Equations ◽  
High Performance ◽  
Inverted Pendulum ◽  
Equations Of Motion ◽  
Flexible Beam ◽  
Governing Equations ◽  
Natural Modes ◽  
Wheeled Inverted Pendulum ◽  
Highly Nonlinear ◽  
New Type

Abstract Inverted pendulums are traditional dynamic problems. If an inverted pendulum is used in a moving cart, a new type of exciting issues will appear. One of these problems is two-wheeled inverted pendulum systems. Because of their small size, high performance in quick driving, and their stability with controller, researchers and engineers are interested in them. In this paper, a new configuration of one specific robot is modeled, and its dynamic behavior is analyzed. The proposed model can move in two directions, and with a proper controller can keep its stability during the operation. In this robot, two cantilever beams are on the two-wheeled base, and they are excited by voltages to the attached piezoelectric actuators. The mathematical model of this system is obtained using the extended Hamilton’s Principle. The results show that the governing equations of motion are highly nonlinear and contain several coupled partial differential equations (PDEs). In order to extract the natural modes of the beams, the undamped, unforced equations of motion and boundary conditions of the beams are used. If a limited number of modes (N1 and N2) are selected for each beam, the coupled PDEs will be changed to N1 + N2 + 5 ordinary differential equations (ODEs). These complex equations are solved numerically, and the natural frequencies of the system are extracted. The system is then simulated in both lateral and horizontal plane movements. The simulation shows that the governing equations are correct, and the system is ready for designing a proper controller. It should be mentioned that in the future works, the derived equations will be validated experimentally, and a suitable control strategy will be applied to the system to make it automated and more applicable.

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 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.

On the Analytic Solution of Magnetohydrodynamic (MHD) Flow by a Moving Wedge in Porous Medium

2018 ◽  
Vol 389 ◽  
pp. 128-137 ◽  
Author(s):  
Hamza Berrehal ◽  
Abdelaziz Maougal ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi
Keyword(s):  
Porous Medium ◽  
Nonlinear Boundary ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Governing Equations ◽  
Third Order ◽  
Moving Wedge ◽  
Optimal Homotopy Asymptotic Method ◽  
Layer Flow ◽  
Similarity Method

This paper is devoted to find analytic approximate solution by optimal homotopy asymptotic method (OHAM) for the problem of nonlinear boundary layer flow. Two-dimensional magneto-hydrodynamic (MHD) flow of a viscous fluid over a moving wedge in porous medium with suction/injection is investigated. Governing equations are transformed by similarity method into a third order Falkner-Skan equation and solved analytically using OHAM. This approach is highly efficient, ensuring a very rapid convergence of the solution only after one iteration. Graphical results are presented to discuss the effects of various parameters on velocity profiles. Further, the skin friction coefficient is also tabulated and compared with the corresponding results available in literature. Our results were found in an excellent agreement.

Stokes’ first problem for MHD flow of Casson nanofluid

2017 ◽  
Vol 13 (1) ◽  
pp. 2-10
Author(s):  
Syed Tauseef Mohyud-din ◽  
Umar Khan ◽  
Naveed Ahmed ◽  
M.M. Rashidi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Mhd Flow ◽  
Governing Equations ◽  
Content Type ◽  
Buongiorno’S Model ◽  
Linear Ordinary Differential Equations ◽  
Flux Condition ◽  
Non Linear ◽  
Flow Heat

Purpose The purpose of this paper is to present investigation of the flow, heat and mass transfer of a nanofluid over a suddenly moved flat plate using Buongiorno’s model. This study is different from some of the previous studies as the effects of Brownian motion and thermophoresis on nanoparticle fraction are passively controlled on the boundary rather than actively. Design/methodology/approach The partial differential equations governing the flow are reduced to a system of non-linear ordinary differential equations. Viable similarity transforms are used for this purpose. A well-known numerical scheme called Runge-Kutta-Fehlberg method coupled with shooting procedure has been used to find the solution of resulting system of equations. Discussions on the effects of different emerging parameters are provided using graphical aid. A table is also given that provides the results of different parameters on local Nusselt and Sherwood numbers. Findings A revised model for Stokes’ first problem in nanofluids is presented in this paper. This model considers a zero flux condition at the boundary. Governing equations after implementing the similarity transforms get converted into a system of non-linear ordinary differential equations. Numerical solution using RK-Fehlberg method is also carried out. Emerging parameters are analyzed graphically. Figures indicate a quite significant change in concentration profile due to zero flux condition at the wall. Originality/value This work can be extended for other problems involving nanofluids for the better understanding of different properties of nanofluids.

scholarly journals Application of response surface methodology on the nanofluid flow over a rotating disk with autocatalytic chemical reaction and entropy generation optimization

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tahir Mehmood ◽  
Muhammad Ramzan ◽  
Fares Howari ◽  
Seifedine Kadry ◽  
Yu-Ming Chu
Keyword(s):  
Response Surface Methodology ◽  
Friction Coefficient ◽  
Response Surface ◽  
Skin Friction ◽  
Chemical Reaction ◽  
Rotating Disk ◽  
Skin Friction Coefficient ◽  
Engine Oil ◽  
Suction Parameter ◽  
Highly Nonlinear

AbstractThe role of nanofluids is of fundamental significance in the cooling process of small electronic devices including microchips and other associated gadgets in microfluidics. With such astounding applications of nanofluids in mind, it is intended to examine the flow of magnetohydrodynamic nanofluid comprising a novel combination of multi-walled carbon nanotubes and engine oil over a stretched rotating disk. The concentration equation is modified by considering the autocatalytic chemical reaction. The succor of the bvp4c numerical technique amalgamated with the response surface methodology is secured for the solution of a highly nonlinear system of equations. The sensitivity analysis is performed using a response surface methodology. The significant impacts of the prominent arising parameters versus involved fields are investigated through graphical illustrations. It is observed that the skin friction coefficient and local Nusselt number are positively sensitive to nanoparticle volume fraction while it is positively sensitive to the suction parameter. It is negatively sensitive to the Magnetic parameter. The skin friction coefficient is negatively sensitive to all input parameters.

scholarly journals IMPACT OF SUCTION/INJECTION AND HEAT TRANSFER ON UNSTEADY MHD FLOW OVER A STRETCHABLE ROTATING DISK

2020 ◽  
Vol 50 (3) ◽  
pp. 159-165
Author(s):  
K. V. Prasad ◽  
Hanumesh Vaidya ◽  
O D Makinde ◽  
Kuppalapalle Vajravelu ◽  
V Ramajini
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Rotating Disk ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Optimal Homotopy Analysis Method ◽  
Similarity Transformations

In this article, the unsteady magnetohydrodynamic two-dimensional boundary layer flow and heat transfer over a stretchable rotating disk with mass suction/injection is investigated. Temperature-dependent physical properties and convective boundary conditions are taken into account. The governing coupled nonlinear partial differential equations are transformed into a system of ordinary differential equations by adopting the well-known similarity transformations. Further, the solutions are obtained through the semi-analytical method called an Optimal Homotopy Analysis Method (OHAM). The obtained results are discussed graphically to predict the features of the involved key parameters which are monitoring the flow model. The skin friction coefficient and Nusselt number are also examined. The validation of the present work is verified with the earlier published results and is found to be in excellent agreement. It is noticed that an increase in the viscosity parameter leads to decay in momentum boundary layer thickness, and the inverse trend is observed in the case of the temperature profile.

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