Showing papers on "Homotopy analysis method published in 2016"
TL;DR: In this paper, the characteristics of generalized Burgers fluid over a stretched surface Cattaneo-Christov heat flux model is utilized for the formulation of the energy equation instead of Fourier's law of heat conduction, which can foresee the impacts of thermal relaxation time on the boundary layer phenomenon.
211 citations
TL;DR: In this article, the boundary layer Cattaneo-Christov double-diffusion model of heat and mass transfer in an upper-convected Maxwell nanofluid over a stretching sheet is presented.
179 citations
TL;DR: In this article, an analytical method based on the generalized Taylors series formula together with residual error function, namely residual power series method (RPSM), is proposed for finding the numerical solution of the coupled system of time-fractional nonlinear Boussinesq-Burger's equations.
Abstract: In this paper, an analytical method based on the generalized Taylors series formula together with residual error function, namely residual power series method (RPSM), is proposed for finding the numerical solution of the coupled system of time–fractional nonlinear Boussinesq–Burger’s equations. The Boussinesq–Burger’s equations arise in studying the fluid flow in a dynamic system and describe the propagation of the shallow water waves. Subsequently, the approximate solutions of time-fractional nonlinear coupled Boussinesq–Burger’s equations obtained by RPSM are compared with the exact solutions as well as the solutions obtained by modified homotopy analysis transform method. Then, we provide a rigorous convergence analysis and error estimate of RPSM. Numerical simulations of the results are depicted through different graphical representations and tables showing that present scheme is reliable and powerful in finding the numerical solutions of coupled system of fractional nonlinear differential equations like Boussinesq–Burger’s equations.
171 citations
TL;DR: In this paper, a two-dimensional heat transfer flow of a nanofluid in the neighborhood of a stagnation point flow in the presence of mixed convection is investigated, where the mathematical model consists of continuity and the momentum equations, while a new model is proposed to see the effects aggregations on water base Al2O3 nan ofluid over permeable wedge.
Abstract: Two-dimensional heat transfer flow of a nanofluid in the neighborhood of a stagnation point flow in the presence of mixed convection is investigated. The mathematical model consists of continuity and the momentum equations, while a new model is proposed to see the effects aggregations on water base Al2O3 nanofluid over permeable wedge. The variable wall temperature is taken into account. The Mathematica package based on homotopy analysis method is used to solve this problem. Several aspects of the aggregation parameters on velocity and temperature profiles of nanofluid are investigated and shown graphically with respect to the physical parameters involved in it. The tabular results are demonstrated for heat transfer rate and skin friction coefficient. © 2015 Curtin University of Technology and John Wiley & Sons, Ltd.
163 citations
TL;DR: In this article, a q-homotopy analysis transform method was proposed to solve time and space-fractional coupled Burgers' equations, which produces many more opportunities by appropriate selection of auxiliary parameters ℏ and n (n ⩾ 1 ) to solve strongly nonlinear differential equations.
Abstract: In this paper, we constitute a homotopy algorithm basically extension of homotopy analysis method with Laplace transform, namely q-homotopy analysis transform method to solve time- and space-fractional coupled Burgers’ equations. The suggested technique produces many more opportunities by appropriate selection of auxiliary parameters ℏ and n ( n ⩾ 1 ) to solve strongly nonlinear differential equations. The proposed technique provides ℏ and n -curves, which describe that the convergence range is not a local point effects and finds elucidated series solution that makes it superior than HAM and other analytical techniques.
144 citations
TL;DR: In this article, the effects of homogeneous-heterogeneous reactions in boundary layer flow of nanofluids with different base fluids are investigated in water, kerosene and engine oils.
142 citations
TL;DR: In this paper, the motion of temperature dependent plastic dynamic viscosity and thermal conductivity of steady incompressible laminar free convective magnetohydrodynamic (MHD) Casson fluid flow over an exponentially stretching surface with suction and exponentially decaying internal heat generation was studied.
141 citations
TL;DR: In this paper, the heat and mass transfer characteristics of three-dimensional steady flow of Burgers nanofluid over a bidirectional stretching surface are examined. And the impact of nonlinear thermal radiation and heat generation/absorption is delved.
121 citations
TL;DR: In this paper, a two-dimensional Darcy-Forchheimer flow of Maxwell fluid induced by a stretching surface is modeled and analyzed using homotopy analysis method to derive convergent homotopic solutions for velocity and temperature distributions.
Abstract: Purpose
The objectives of present communication are threefolds. First is to model and analyze the two-dimensional Darcy-Forchheimer flow of Maxwell fluid induced by a stretching surface. Temperature-dependent thermal conductivity is taken into account. Second is to examine the heat transfer process through non-classical flux by Cattaneo-Christov theory. Third is to derive convergent homotopic solutions for velocity and temperature distributions. The paper aims to discuss these issues.
Design/methodology/approach
The resulting non-linear system is solved through the homotopy analysis method.
Findings
An increment in Deborah number β causes a reduction in velocity field f′(η) while opposite behavior is observed for temperature field θ(η). Velocity field f′(η) and thickness of momentum boundary layer are decreased when the authors enhance the values of porosity parameter λ while opposite behavior is noticed for temperature profile θ(η). Temperature field θ(η) is inversely proportional to the thermal relaxation parameter γ. The numerical values of temperature gradient at the sheet − θ′(0) are higher for larger values of thermal relaxation parameter γ.
Originality/value
To the best of author’s knowledge, no such consideration has been given in the literature yet.
119 citations
TL;DR: In this article, the authors proposed a rapid and effective way of working out the optimum convergence control parameter in the homotopy analysis method (HAM) for solving algebraic, highly nonlinear differentialdifference, integro-differential, and ordinary or partial differential equations or systems.
Abstract: A rapid and effective way of working out the optimum convergence control parameter in the homotopy analysis method (HAM) is introduced in this paper. As compared with the already known ways of evaluating the convergence control parameter in HAM either through the classical constant h − curves ( h is the convergence control parameter) or from the classical squared residual error as frequently used in the literature, a novel description is proposed to find out an optimal value for the convergence control parameter yielding the same optimum values. In most cases, the new method is shown to perform quicker and better against the residual error method when integrations are much harder to evaluate. Examples involving solution of algebraic, highly nonlinear differentialdifference, integro-differential, and ordinary or partial differential equations or systems, all from the literature demonstrate the validity and usefulness of the introduced technique
115 citations
TL;DR: In this article, a combination of the Laplace transform and homotopy methods was used to find the approximate solutions of the FPDE in the Liouville-Caputo and Caputo-Fabrizio sense.
Abstract: In this work, we present an analysis based on a combination of the Laplace transform and homotopy methods in order to provide a new analytical approximated solutions of the fractional partial differential equations (FPDEs) in the Liouville-Caputo and Caputo-Fabrizio sense. So, a general scheme to find the approximated solutions of the FPDE is formulated. The effectiveness of this method is demonstrated by comparing exact solutions of the fractional equations proposed with the solutions here obtained.
TL;DR: In this article, homotopy perturbation method (HPM) is applied to solve fractional partial differential equations (PDEs) with proportional delay in t and shrinking in x.
TL;DR: In this article, a numerical polynomial homotopy continuation method is proposed to find all the solutions of power flow equations without ever encountering a bifurcation, which is embarrassingly parallelisable.
Abstract: The manuscript addresses the problem of finding all solutions of power flow equations or other similar non-linear system of algebraic equations. This problem arises naturally in a number of power systems contexts, most importantly the direct methods for transient stability analysis and voltage stability assessment. Here, the authors introduce a novel form of homotopy continuation method called the numerical polynomial homotopy continuation method that is mathematically guaranteed to find all the solutions without ever encountering a bifurcation. Since finding real solutions is much more challenging, first the authors embed the real form of power flow equation in complex space, and then track the generally unphysical solutions with complex values of real and imaginary parts of the voltages. The solutions converge to physical real form in the end of the homotopy. The so-called gamma-trick mathematically rigorously ensures that all the paths are well-behaved along the paths, so unlike other continuation approaches, no special handling of bifurcations is necessary. The method is embarrassingly parallelisable. The authors demonstrate the technique performance by solving several test cases up to the 14 buses. Finally, they discuss possible strategies for scaling the method to large size systems, and propose several applications for security assessments.
TL;DR: In this paper, the authors presented the procedure to obtain analytical solutions of Lienard type model of a fluid transmission line represented by the Caputo-Fabrizio fractional operator.
Abstract: This paper presents the procedure to obtain analytical solutions of Lienard type model of a fluid transmission line represented by the Caputo-Fabrizio fractional operator. For such a model, we derive a new approximated analytical solution by using the Laplace homotopy analysis method. Both the efficiency and the accuracy of the method are verified by comparing the obtained solutions with the exact analytical solution. Good agreement between them is confirmed.
TL;DR: In this article, the two-dimensional flow of Powell-Eyring fluid with variable thermal conductivity is considered and both numerical and analytic solutions are obtained and compared by homotopy analysis method.
Abstract: This article is concerned with the two-dimensional flow of Powell–Eyring fluid with variable thermal conductivity. The flow is caused due to a stretching cylinder. Temperature dependent thermal conductivity is considered. Both numerical and analytic solutions are obtained and compared. Analytic solution is found by homotopy analysis method. Numerical solution by shooting technique is presented. Discussion to different physical parameters for the velocity and temperature is assigned. It is observed that the velocity profile enhances for larger magnetic parameter. It is also further noted that for increasing the value of Prandtl number temperature profile decreases.
TL;DR: In this article, the authors investigated the Cattaneo-Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet.
Abstract: We investigate the Cattaneo–Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformations. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method (OHAM). The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo–Christov heat flux model than those in the Fourier's law of heat conduction.
TL;DR: In this article, a mathematical model for stagnation point flow of nanofluids over an impermeable stretching sheet with variable thickness is presented, and the optimal values of convergence control parameters and corresponding individual and total residual errors are computed by means of homotopy analysis method (HAM) based BVPh 2.0.
Abstract: This work concentrates on the mathematical modeling for stagnation point flow of nanofluids over an impermeable stretching sheet with variable thickness. Carbon nanotubes [single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs)] as the nanoparticles are utilized. Water and kerosene oil are taken as the base fluids. Heat transfer through melting effect is discussed. Transformation procedure is adapted to obtain the non-linear ordinary differential equations from the fundamental laws of mass, linear momentum and energy. The optimal values of convergence control parameters and corresponding individual and total residual errors for SWCNTs and MWCNTs are computed by means of homotopy analysis method (HAM) based BVPh 2.0. Characteristics of different involved parameters on the velocity, temperature, skin friction coefficient and Nusselt number are discussed. Higher velocity profile is observed for wall thickness parameter in case of water carbon nanotubes when compared with the kerosene o...
TL;DR: The slip effects on the axisymmetric flow of an electrically conducting viscous fluid in the presence of a magnetic field over a non-linear radially stretching sheet is dealt with by introducing new similarity transformations.
Abstract: This article deals with the slip effects on the axisymmetric flow of an electrically conducting viscous fluid in the presence of a magnetic field over a non-linear radially stretching sheet. By introducing new similarity transformations, the governing partial differential equations are reduced to an ordinary differential equation. The resulting ordinary differential equation is then solved analytically using the homotopy analysis method and numerically by shooting method to show the accuracy of the analytical solution. The significant effects of various parameters on velocity field are discussed in detail. The shear stress at the wall together with some other physical parameters is tabulated and compared with existing literature, which shows an excellent agreement.
TL;DR: In this article, an analysis for the unsteady boundary layer flow and heat transfer of power law fluid model over a radially stretching sheet is presented, where a uniform magnetic field is applied perpendicular to the direction of the flow with the aid of new similarity transformations, the governing time dependent nonlinear boundary layer equations are converted into nonlinear ordinary differential equations.
TL;DR: In this article, the unsteady boundary layer flow and heat transfer of an incompressible Oldroyd-B nanofluid thin film due to a stretching sheet have been investigated analytically.
TL;DR: In this article, the authors introduced the more general convective heat and mass conditions in mixed convection flow with nanoparticles and showed the effects of different parameters on the velocity, temperature and concentration profiles.
TL;DR: In this paper, the governing partial differential equations for momentum, energy and micro-rotation are presented and transformed into ordinary differential equations by means of similarity transformations and local skin friction co-efficient and local heat fluxes are computed analytically using optimal homotopy analysis method (OHAM) as well as numerically through mid-point integration scheme and they are found to be in excellent agreement.
TL;DR: The classical Buongiorno model that involves Brownian motion and thermophoretic diffusivities is modified by considering nanoparticle volume fraction distribution, and the effects of second order velocity slip and nanoparticles migration on nanofluids between two rotating parallel plates are analyzed.
TL;DR: In this paper, the Cattaneo-Christov heat and mass flux models were applied to the steady three-dimensional flow of Burgers fluid over a bidirectional stretching surface.
TL;DR: In this article, the magneto-hydrodynamic flow of viscous fluid in a channel with non-parallel walls is studied and the effects of different emerging parameters on temperature and concentration profiles are analyzed.
TL;DR: In this paper, the authors investigate the nonlinear radiation effects in a time-dependent two-dimensional flow of a Casson fluid squeezed between two parallel disks when the upper disk is taken to be impermeable and the lower one is porous.
TL;DR: In this article, the boundary layer flow and heat transfer characteristic in power law fluid model over unsteady radially stretching sheet under the influence of convective boundary conditions is examined.
Abstract: This paper examines the boundary layer flow and heat transfer characteristic in power law fluid model over unsteady radially stretching sheet under the influence of convective boundary conditions. A uniform magnetic field is applied transversely to the direction of the flow. The governing time dependent nonlinear boundary layer equations are reduced into nonlinear ordinary differential equations with the help of similarity transformations. The transformed coupled ordinary differential equations are then solved analytically by homotopy analysis method (HAM) and numerically by shooting procedure. Effects of various governing parameters like, power law index n , magnetic parameter M , unsteadiness A , suction/injection S , Biot number γ and generalized Prandtl number Pr on velocity, temperature, local skin friction and the local Nusselt number are studied and discussed. It is found from the analysis that the magnetic parameter diminishes the velocity profile and the corresponding thermal boundary layer thickness.
TL;DR: In this paper, the entropy generation via two important slip mechanism Brownian motion and thermophoresis diffusion in non-Newtonian nanofluid flow is analyzed by momentum equation along with a newly formed equation for nanoparticle distribution.
Abstract: The primary objective of the present analysis is to investigate the entropy generation via two important slip mechanism Brownian motion and thermophoresis diffusion in non-Newtonian nanofluid flow. These effects are analyzed by momentum equation along with a newly formed equation for nanoparticle distribution. Conventional energy equation is modified for the nanofluid by incorporation nanoparticles effects. The condition for zero normal flux of nanoparticles at the stretching sheet is defined to impulse the particles away from surface. To measure the disorder in the thermodynamic system an entropy generation analysis is discussed for present Jeffery nanofluid model. In order to solve the governing equations, compatible similarity transformations are used to obtain a set of higher order non-linear differential equations. An optimal homotopy analysis method (OHAM) and Keller Box Method are used to solve the given system of higher order nonlinear differential equations. Effect of emerging parameters such as Prandtl number, Schmidt number, Brownian motion and thermophoresis on temperature and concentration are shown through graphs. Variations in the entropy generation for different emerging parameters are discussed in detail with the help of graphical results. Also, the coefficient of skin friction, Nusselt number, Sherwood number and characteristic entropy generation rate are presented through graphs.
TL;DR: In this article, a three-dimensional flow of an elastico-viscous nanofluid under the influence of mass transfer and chemical reaction is studied and the effects of thermophoresis and Brownian motion are also present.
TL;DR: In this paper, the authors considered the flow of ferrofluid due to a rotating disk in the presence of homogeneous-heterogeneous reactions and computed convergence series solutions using homotopy analysis method (HAM) for the resulting nonlinear problems.