Showing papers on "Homotopy analysis method published in 2017"
TL;DR: In this article, a new model is proposed to investigate the effects of nano-ferroliquid under the influence of low oscillating over a stretchable rotating disk, where the basic governing equations are formulated under the effect of magnetic field and the resulting system of partial differential equations is first reduced in non-dimensional form by using proper transformations and then reduced coupled system of differential equations are solved analytically by means of homotopy analysis method.
198 citations
TL;DR: A numerical algorithm based on fractional homotopy analysis transform method to study the fractional model of Lienard’s equations, which describes the oscillating circuits, is constituted.
149 citations
TL;DR: In this article, the authors analyzed the convective flow of a third grade non-Newtonian fluid due to a linearly stretching sheet subject to a magnetic field and showed that the thermal boundary-layer thickness gets decreased with increasing the Prandtl number.
144 citations
TL;DR: In this article, an analytical investigation of magnetohydrodynamic (MHD) three-dimensional flow of an Oldroyd-B nanofluid in the presence of heat generation/absorption and convective surface boundary condition is provided.
143 citations
TL;DR: In this article, a magnetohydrodynamic thin film nanofluid sprayed on a stretching cylinder with heat transfer is explored, where the basic constitutive equations for the motion and transfer of heat of the thin film with boundary conditions have been converted to nonlinear coupled differential equations with physical conditions by employing appropriate similarity transformations.
Abstract: The magnetohydrodynamic thin film nanofluid sprayed on a stretching cylinder with heat transfer is explored. The spray rate is a function of film size. Constant reference temperature is used for the motion past an expanding cylinder. The sundry behavior of the magnetic nano liquid thin film is carefully noticed which results in to bring changes in the flow pattern and heat transfer. Water-based nanofluids like Al 2 O 3 -H 2 O and CuO-H 2 O are investigated under the consideration of thin film. The basic constitutive equations for the motion and transfer of heat of the nanofluid with the boundary conditions have been converted to nonlinear coupled differential equations with physical conditions by employing appropriate similarity transformations. The modeled equations have been computed by using HAM (Homotopy Analysis Method) and lead to detailed expressions for the velocity profile and temperature distribution. The pressure distribution and spray rate are also calculated. The comparison of HAM solution predicts the close agreement with the numerical method solution. The residual errors show the authentication of the present work. The CuO-H 2 O nanofluid results from this study are compared with the experimental results reported in the literature showing high accuracy especially, in investigating skin friction coefficient and Nusselt number. The present work discusses the salient features of all the indispensable parameters of spray rate, velocity profile, temperature and pressure distributions which have been displayed graphically and illustrated.
130 citations
TL;DR: In this paper, a study for heterogeneous-homogeneous processes in generalized Burgers nanofluid flow past a stretching sheet in the presence of new mass flux condition is presented.
113 citations
TL;DR: A mathematical model has been developed to study the mixed convection on MHD flow of Casson fluid over a nonlinearly permeable stretching sheet with thermal radiation, viscous dissipation, heat source/sink, chemical reaction and suction as discussed by the authors.
107 citations
TL;DR: In this article, a numerical scheme based on q-homotopy analysis transform method to examine the fractional model of regularized long-wave equation is presented. But the proposed technique is a mixture of Q-Homotopy Analysis method, Laplace transform, and homotopy polynomials.
Abstract: The key purpose of the present work is to constitute a numerical scheme based on q-homotopy analysis transform method to examine the fractional model of regularized long-wave equation. The regularized long-wave equation explains the shallow water waves and ion acoustic waves in plasma. The proposed technique is a mixture of q-homotopy analysis method, Laplace transform, and homotopy polynomials. The convergence analysis of the suggested scheme is verified. The scheme provides ℏ and n-curves, which show that the range convergence of series solution is not a local point effects and elucidate that it is superior to homotopy analysis method and other analytical approaches. Copyright © 2017 John Wiley & Sons, Ltd.
102 citations
TL;DR: In this paper, the homotopy perturbation transform method for nonlinear fractional partial differential equations of the Caputo-Fabrizio fractional operator is presented. But the method is not suitable for the case of the limit of the integral order of the time derivative.
Abstract: This work presents the homotopy perturbation transform method for nonlinear fractional partial differential equations of the Caputo-Fabrizio fractional operator. Perturbative expansion polynomials are considered to obtain an infinite series solution. The effectiveness of this method is demonstrated by finding the exact solutions of the fractional equations proposed, for the special case when the limit of the integral order of the time derivative is considered.
96 citations
TL;DR: In this paper, the steady boundary layer flow and heat transfer properties of a thin film second-grade fluid through a porous medium past a stretching sheet concerning the effect of viscous dissipation were investigated.
Abstract: This article inquires into the steady boundary layer flow and heat transfer properties of a thin film second-grade fluid through a porous medium past a stretching sheet concerning the effect of viscous dissipation. The aim of the study is to discuss the impacts of film thickness and porosity in the presence of constant reference temperature which completely affect the flow pattern and bring changes in the cooling/heating. The basic governing equations of the problem have been modeled in terms of suitable similarity transformations which result in nonlinear ordinary differential equations with physical conditions. Solution has been obtained by using HAM (Homotopy Analysis Method) which is frequently used for solving nonlinear differential equations encountered in various applied sciences and is found quite useful. Favorable comparison with previously published research papers is performed to show the correlations for the present work. Skin friction coefficient and Nusselt number are presented through tables which describe the verification for the achieved results showing that the thin liquid film results from this study are in close agreement with the results reported in the literature. The physical influences of all the emerging parameters on velocity and temperature fields have been studied graphically and illustrated clearly. The authentication of the present work has been achieved by evaluating the comparison of HAM solution with the numerical method solution. Results achieved by HAM and residual errors are also discussed numerically and graphically.
91 citations
TL;DR: In this paper, an analytical approach for the non-Newtonian thin film nanofluids bioconvection based on physical mechanisms responsible for the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, is presented.
Abstract: Mixed convection in gravity-driven non-Newtonian nanofluid films (Casson and Williamson) flow containing both nanoparticles and gyrotactic microorganisms along a convectively heated vertical surface is investigated. The actively controlled nanofluid model boundary conditions are used to explore the liquid films flow. The study exhibits an analytical approach for the non-Newtonian thin film nanofluids bioconvection based on physical mechanisms responsible for the nanoparticles and the base fluid, such as Brownian motion and thermophoresis. Both the fluids have almost the same behaviors for the effects of all the pertinent parameters except the effect of Schmidt number on the microorganism density function where the effect is opposite. Ordinary differential equations together with the boundary conditions are obtained through similarity variables from the governing equations of the problem, which are solved by HAM (Homotopy Analysis Method). The solution is expressed through graphs and illustrated which show the influences of all the parameters. The study is relevant to novel microbial fuel cell technologies combining the nanofluid with bioconvection phenomena.
TL;DR: In this paper, the Darcy-Forchheimer flow of water-based carbon nanotubes (CNTs) due to a rotating disk is described by utilizing Darcy Forchheimer model.
TL;DR: In this paper, the problem of oblique stagnation point flow using Jeffery nanofluid as a rheological fluid model was investigated and the effects of thermophoresis and Brownian motion were taken into account.
Abstract: This study investigates the problem of oblique stagnation point flow using Jeffery nanofluid as a rheological fluid model. Effects of thermophoresis and Brownian motion are taken into account. The governing nonlinear partial differential equations for the flow field are obtained and then converted to ordinary differential equations via suitable transformations. Consequential highly non-linear system of differential equations is solved numerically through mid-point integration as a basic scheme along with Richardson's extrapolation as an enhancement scheme and analytical results are also obtained using optimal homotopy analysis Method (OHAM). Non-dimensional velocities, temperature and concentration profiles are expressed through graphs. Numerical values of local skin friction coefficients, local heat and mass flux are tabulated numerically as well as analytically for various physical parameters emerging in our flow problem. The obtained results revealed that both normal and tangential skin friction coefficients decrease with an increase in Jeffery fluid parameter. It is also observed that an enhancement in Thermophoresis and Brownian motion parameters leads to a reduction in heat flux at the wall. Comparison of numerical data is made with previous existing literature to confirm accuracy of present study for the case of Newtonian fluid.
TL;DR: In this paper, an analytical solution for MHD boundary layer flow of a viscous incompressible fluid over an exponentially stretching sheet is developed, where the effect of thermal radiation is included in the energy equation.
Abstract: An analytical solution for MHD boundary layer flow of a viscous incompressible fluid over an exponentially stretching sheet is developed in this study. The effect of thermal radiation is included in the energy equation. Through suitable similarity transformations, the governing equations are transformed into a system of nonlinear ordinary differential equations. Homotopy analysis method (HAM) has been used to get accurate and complete analytic solution. This study reveals that the governing parameters, namely, the magnetic and the radiation parameters have major effects on the flow field, skin friction coefficient, and the heat transfer rate. The magnetic field enhances the dimensionless temperature inside the thermal boundary layer whereas reduces the dimensionless velocity inside the hydrodynamic boundary layer. Heat transfer rate becomes low with magnetic and radiation parameters while the friction factor is increased with magnetic field. Moreover, a comparative study between the previously published and the present results in special cases is conducted and an excellent agreement is found between them.
TL;DR: In this paper, the stagnation point flow of Walters-B fluid induced by a Riga plate is investigated and the optimal values of convergence control parameters are computed by means of Optimal homotopy analysis method (OHAM) via BVPh2.0.
Abstract: In this article, the stagnation point flow of Walters-B fluid induced by a Riga plate is investigated. Heat transfer properties are investigated with thermal radiation effect and Newtonian heating. An electromagnetic actuator is a Riga-plate where a span wise associated array of irregular electrodes and permanent magnets mounted on a flat surface. Lorentz force is parallel to a surface which is generated by this array and it reduces exponentially in the direction normal to the surface. The non-linear ordinary differential equations through the fundamental laws of mass, linear momentum and energy are obtained using the suitable transformation. The optimal values of convergence control parameters are computed by means of Optimal homotopy analysis method (OHAM) via BVPh2.0. Graphical results for the dimensionless velocity and temperature are presented and discussed for various physical parameters. Local skin friction and Local Nusselt numbers are computed analytically using OHAM.
TL;DR: In this paper, the homotopy perturbation method is combined with Laplace transformation to obtain approximate analytical solutions of non-linear differential equations, and an example is given to elucidate the solution process and confirm reliability of the method.
Abstract: Homotopy perturbation method is combined with Laplace transformation to obtain approximate analytical solutions of non-linear differential equations. An example is given to elucidate the solution process and confirm reliability of the method. The result indicates superiority of the method over the conventional homotopy perturbation method due its flexibility in choosing its initial approximation.
TL;DR: A homotopy method for finding the unique positive solution to a multilinear system with a nonsingular M-tensor and a positive right side vector is proposed and its convergence to the desired solution is proved.
TL;DR: In this paper, a nonlinear stretching surface has been employed to create the flow, and convergence series solutions of nonlinear systems are developed through the optimal homotopy analysis method (OHAM).
TL;DR: A mathematical analysis for 3D forced convective flow of Carreau fluid over a bidirectional stretched surface is presented in this article, which reveals that the liquid velocity declines for shear thinning liquids (n 1 ) for the larger values of ratio of stretching rates parameter α and for shears thickening liquids ( n > 1 ) conflicting behavior is detected.
Abstract: A mathematical analysis for 3D forced convective flow of Carreau fluid over a bidirectional stretched surface is presented. The Carreau liquid model is the generalization of linear materials which reveal the aspects of shear thinning ( n 1 ) and shear thickening ( n > 1 ) liquids. Additionally, heat transfer phenomenon is inspected in this research work by utilizing the non-linear thermal radiation and convective surface boundary conditions. The boundary layer equations of 3D Carreau fluid are established by means of usual boundary layer approximations. The governing set of PDEs is rendered into coupled non-linear ODEs via appropriate transformations. Numerical solutions are computed for the resulting non-linear ODEs by employing an effective numerical scheme namely bvp4c function in Matlab. Features of numerous sundry thermophysical parameters on the liquid velocity, temperature, skin friction and Nusselt number are explored and discussed in detail. The present study reveals that the liquid velocity declines for shear thinning liquids ( n 1 ) for the larger values of ratio of stretching rates parameter α and for shear thickening liquids ( n > 1 ) conflicting behavior is detected. It is also pragmatic that thermal radiation parameter R d is an augmenting function of temperature distribution on both situations. To comprehend the legitimacy of numerical results a comparison between bvp4c results with the analytical results obtained by the homotopy analysis method (HAM) is also made in this exploration and alleged an admirable agreement. Furthermore, authentication of numerical outcomes is achieved via benchmarking with previously reported limiting cases and we generally found a splendid correlation with these results.
TL;DR: In this article, the approximate analytical solutions of Lotka-volterra model with fractional derivative have been obtained by using hybrid analytic approach, which is amalgamation of homotopy analysis method, Laplace transform, and homotonous polynomials.
Abstract: In this paper, the approximate analytical solutions of Lotka–Volterra model with fractional derivative have been obtained by using hybrid analytic approach. This approach is amalgamation of homotopy analysis method, Laplace transform, and homotopy polynomials. First, we present an alternative framework of the method that can be used simply and effectively to handle nonlinear problems arising in several physical phenomena. Then, existence and uniqueness of solutions for the fractional Lotka–Volterra equations are discussed. We also carry out a detailed analysis on the stability of equilibrium. Further, we have derived the approximate solutions of predator and prey populations for different particular cases by using initial values. The numerical simulations of the result are depicted through different graphical representations showing that this hybrid analytic method is reliable and powerful method to solve linear and nonlinear fractional models arising in science and engineering. Copyright © 2017 John Wiley & Sons, Ltd.
01 Jun 2017-Microsystem Technologies-micro-and Nanosystems-information Storage and Processing Systems
TL;DR: In this article, the authors proposed a homotopy analysis method (HAM) approach for derivation of analytical solutions for the frequency response of the resonators, and applied the HAM to the proposed Duffing equation, and through this procedure, they derived the first-order and second-order HAM-based analytical solutions.
Abstract: Due to various sources of nonlinearities, micro/nano-electro-mechanical-system (MEMS/NEMS) resonators present highly nonlinear behaviors including softening- or hardening-type frequency responses, bistability, chaos, etc. The general Duffing equation with quadratic and cubic nonlinearities serves as a characterizing model for a wide class of MEMS/NEMS resonators as well as lots of other engineering and physical systems. In this paper, after brief reviewing of various sources of nonlinearities in micro/nano-resonators and discussing how they contribute to the Duffing-type nonlinearities, we propose a Homotopy Analysis Method (HAM) approach for derivation of analytical solutions for the frequency response of the resonators. Toward this aim, we first apply the HAM to the proposed Duffing equation, and through this procedure, we derive the first-order and second-order HAM-based analytical solutions for the frequency response of the resonator. As the main novelty, we show that the second-order solution benefits from a tunable parameter, known as the convergence-control parameter, which is a distinguishing aspect of the HAM and plays a key role in enhancing the accuracy of the obtained analytical expressions in strongly nonlinear problems. We use the obtained analytical solutions for the study of nonlinear dynamics in two types of electrostatically actuated MEMS resonators proposing hardening, softening or mixed behaviors near their primary resonance frequency. Numerical simulations are performed to validate the analytical results.
TL;DR: In this paper, the Soret and Dufour effects on the double-diffusive convective boundary layer flow of a nanofluid past a moving wedge in the presence of suction were investigated.
Abstract: Purpose
The purpose of this study is to investigate the Soret and Dufour effects on the double-diffusive convective boundary layer flow of a nanofluid past a moving wedge in the presence of suction.
Design/methodology/approach
The similarity transformation is applied to convert the governing nonlinear partial differential equations into ordinary differential equations. Then, they are solved numerically by the fourth-order Runge–Kutta–Gill method along with the shooting technique and the Newton–Raphson method. In addition, the ordinary differential equations are also analytically solved by the homotopy analysis method.
Findings
The results for dimensionless velocity, temperature, solutal concentration and nanoparticle volume fraction profiles, as well as local skin friction coefficient and local Nusselt and local Sherwood numbers are presented through the plots for various combinations of pertinent parameters involved in the study. The heat transfer rate increases on increasing the Soret parameter and it decreases on increasing the Dufour parameter. The mass transfer behaves oppositely to heat transfer.
Practical implication
In engineering applications, a wedge is used to hold objects in place, such as engine parts in the gate valves. A gate valve is the valve that opens by lifting a wedge-shaped disc to control the timing and quantity of fluid flow into an engine.
Originality/value
No such investigation is available in literature, and therefore, the results obtained are novel.
TL;DR: Here the authors are concerned with the Darcy-Forchheimer three-dimensional flow of carbon nanotubes in a rotating frame and the skin-friction coefficients and local Nusselt number are enhanced for larger values of nanoparticles volume fraction.
Abstract: Here we are concerned with the Darcy-Forchheimer three-dimensional flow of carbon nanotubes in a rotating frame. Flow is generated by stretching of the surface. Xue model is adopted for nanofluid transport mechanism. Results for single wall carbon nanotubes (SWCNTs) and multi wall carbon nanotubes are achieved and compared. Flow saturating porous space obeys Darcy-Forchheimer expression. Boundary layer approximations are invoked to simplify governing partial differential system. Optimal homotopy analysis method (OHAM) is utilized for solutions of governing model. The optimal values of auxiliary parameters are computed. Plots have been displayed in order to analyze how the velocities and temperature fields get affected by various flow parameters. Skin-friction coefficients and local Nusselt number are presented through numerical data for both SWCNTs and MWCNTs. Moreover the skin-friction coefficients and local Nusselt number are enhanced for larger values of nanoparticles volume fraction.
TL;DR: In this article, the effect of Cattaneo Christov heat flux with heat generation/absorption on three dimensional Maxwell fluid flow past a bidirectional stretched surface in the presence of magnetohydrodynamic (MHD) was examined.
TL;DR: In this article, the Tiwari-Das nanofluid scheme has been used to investigate the laminar free-convective flow and heat transfer of an electrically conducting nano-drone in the presence of a transverse magnetic field over a rotating down-pointing vertical cone.
TL;DR: It is witnessed that nanoparticle concentration is diminishing function of chemical reaction parameter and mounting values of thermal and solutal stratification lowers the temperature and concentration fields respectively.
Abstract: This exploration addresses MHD stagnation point Powell Eyring nanofluid flow with double stratification. The effects of thermal radiation and chemical reaction are added in temperature and nanoparticle concentration fields respectively. Furthermore, appropriate transformations are betrothed to obtain nonlinear differential equations from the system of partial differential equations and an analytical solution of system of coupled differential equations is obtained by means of the renowned Homotopy Analysis method. Through graphical illustrations, momentum, energy and concentration distributions are conversed for different prominent parameters. Comparison in limiting case is also part of present study to validate the obtained results. It is witnessed that nanoparticle concentration is diminishing function of chemical reaction parameter. Moreover, mounting values of thermal and solutal stratification lowers the temperature and concentration fields respectively.
TL;DR: The results demonstrate that the proposed methodology is very useful and simple in the determination of the solution of the K-S equations of fractional order.
Abstract: In this study, we discuss the application of an analytical technique namely modified homotopy analysis transform method (MHATM) for solving coupled one- dimensional time-fractional Keller-Segel (K-S) equations. The MHATM is a new analytical technique based on homotopy polynomial. We provide a convergence analysis of MHATM and the solution obtained by the proposed method is verified through different graphical representations. The results demonstrate that the proposed methodology is very useful and simple in the determination of the solution of the K-S equations of fractional order.
TL;DR: In this paper, a new application of multivariate Padé approximation method has been used for solving European vanilla call option pricing problem, according to the relations of "smaller than" or "greater than", between stock price and exercise price of the option.
Abstract: In this study, a new application of multivariate Padé approximation method has been used for solving European vanilla call option pricing problem. Padé polynomials have occurred for the fractional Black-Scholes equation, according to the relations of “smaller than”, or “greater than”, between stock price and exercise price of the option. Using these polynomials, we have applied the multivariate Padé approximation method to our fractional equation and we have calculated numerical solutions of fractional Black-Scholes equation for both of two situations. The obtained results show that the multivariate Padé approximation is a very quick and accurate method for fractional Black-Scholes equation. The fractional derivative is understood in the Caputo sense.
TL;DR: In this article, the boundary layer flow and heat transfer of a Maxwell fluid over an exponential stretching surface with thermal stratifications are analyzed using Cattaneo-Christov heat flux model instead of Fourier law of heat conduction.
Abstract: This article presents a research for boundary layer flow and heat transfer of a Maxwell fluid over an exponential stretching surface with thermal stratifications. The effect of homogeneous and heterogeneous reaction are incorporated. Cattaneo–Christov heat flux model is used instead of Fourier law of heat conduction, which is recently proposed by Christov. This model predicts the impacts of thermal relaxation time on boundary layer. The transformed boundary layer equations are solved analytically by using Optimal homotopy analysis method. The effect of non-dimensional fluid relaxation time, thermal relaxation time, Prandtl number, Schmidt number and strength of homogeneous and heterogeneous reaction are demonstrated and exhibited graphically. The comparison of Cattaneo–Christov heat flux model and the Fourier’s law of heat conduction is also displayed.
TL;DR: In this paper, the exact and approximate analytical solution of Nizhnik-Novikov-Veselov system which may be considered as a model for an incompressible fluid with newly defined conformable derivative by using $$G'/G$$expansion method and homotopy analysis method (HAM) respectively.
Abstract: The main purpose of this paper is to find the exact and approximate analytical solution of Nizhnik–Novikov–Veselov system which may be considered as a model for an incompressible fluid with newly defined conformable derivative by using $$G'/G$$
expansion method and homotopy analysis method (HAM) respectively. Authors used conformable derivative because of its applicability and lucidity. It is known that, the NNV system of equations is an isotropic Lax integrable extension of the well-known KdV equation and has physical significance. Also, NNV system of equations can be derived from the inner parameter-dependent symmetry constraint of the KP equation. Then the exact solutions obtained by using $$G'/G$$
expansion method are compared with the approximate analytical solutions attained by employing HAM.