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1.
The problem of magneto‐hydrodynamic fluid flow past a nonlinear stretching sheet in the presence of a transverse magnetic field is analyzed. The governing equations are transformed into a nonlinear ordinary differential equation that is solved using a novel spectral homotopy analysis method and the Matlab in‐built numerical solverttbvp4c. The new technique removes some known limitations of the homotopy analysis method and offers a more systematic way of selecting initial approximations and the optimal auxiliary parameter ?. A comparison with the numerical solution confirms the robustness, the computational efficiency, and the accuracy of the technique. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
2.
P. D. Ariel 《国际流体数值方法杂志》1992,15(11):1295-1312
A technique combining the features of parameter differentiation and finite differences is presented to compute the flow of viscoelastic fluids. Two flow problems are considered: (i) three-dimensional flow near a stagnation point and (ii) axisymmetric flow due to stretching of a sheet. Both flows are characterized by a boundary value problem in which the order of the differential equation exceeds the number of boundary conditions. The exact numerical solutions are obtained using the technique described in the paper. Also, the first-order perturbation solutions (in terms of the viscoelastic fluid parameter) are derived. A comparison of the results shows that the perturbation method is inadequate in predicting some of the vital characteristic features of the flows, which can possibly be revealed only by the exact numerical solution. 相似文献
3.
基于精细积分技术的非线性动力学方程的同伦摄动法 总被引:2,自引:0,他引:2
将精细积分技术(PIM)和同伦摄动方法(HPM)相结合,给出了一种求解非线性动力学方程的新的渐近数值方法。采用精细积分法求解非线性问题时,需要将非线性项对时间参数按Taylor级数展开,在展开项少时,计算精度对时间步长敏感;随着展开项的增加,计算格式会变得越来越复杂。采用同伦摄动法,则具有相对筒单的计算格式,但计算精度较差,应用范围也限于低维非线性微分方程。将这两种方法相结合得到的新的渐近数值方法则同时具备了两者的优点,既使同伦摄动方法的应用范围推广到高维非线性动力学方程的求解,又使精细积分方法在求解非线性问题时具有较简单的计算格式。数值算例表明,该方法具有较高的数值精度和计算效率。 相似文献
4.
This letter is concerned with the plane and axisymmetric stagnation-point flows and heat transfer of an electrically-conducting
fluid past a stretching sheet in the presence of the thermal radiation and heat generation or absorption. The analytical solutions
for the velocity distribution and dimensionless temperature profiles are obtained for the various values of the ratio of free
stream velocity and stretching velocity, heat source parameter, Prandtl number, thermal radiation parameter, the suction and
injection velocity parameter and magnetic parameter and dimensionality index in the series form with the help of homotopy
analysis method (HAM). Convergence of the series is explicitly discussed. In addition, shear stress and heat flux at the surface
are calculated. 相似文献
5.
This study presents an analysis of the axisymmetric flow of a non-Newtonian fluid over a radially stretching sheet. The momentum equations for two-dimensional flow are first modeled for Sisko fluid constitutive model, which is a combination of power-law and Newtonian fluids. The general momentum equations are then simplified by invoking the boundary layer analysis. Then a non-linear ordinary differential equation governing the axisymmetric boundary layer flow of Sisko fluid over a radially stretching sheet is obtained by introducing new suitable similarity transformations. The resulting non-linear ordinary differential equation is solved analytically via the homotopy analysis method (HAM). Closed form exact solution is then also obtained for the cases n=0 and 1. Analytical results are presented for the velocity profiles for some values of governing parameters such as power-law index, material parameter and stretching parameter. In addition, the local skin friction coefficient for several sets of the values of physical parameter is tabulated and analyzed. It is shown that the results presented in this study for the axisymmetric flow over a radially non-linear stretching sheet of Sisko fluid are quite general so that the corresponding results for the Newtonian fluid and the power-law fluid can be obtained as two limiting cases. 相似文献
6.
Analysis of hydromagnetic flow of a dusty fluid over a stretching sheet is carried out with a view to throw adequate light on the effects of fluid-particle interaction, particle loading, and suction on the flow characteristics. The equations of motion are reduced to coupled non-linear ordinary differential equations by similarity transformations. These coupled non-linear ordinary differential equations are solved numerically on an IBM 4381 with double precession, using a variable order, variable step-size finite-difference method. The numerical solutions are compared with their approximate solutions, obtained by a perturbation technique. For small values of β the exact (numerical) solution is in close agreement with that of the analytical (approximate) solution. It is observed that, even in the presence of a transverse magnetic field and suction, the transverse velocity of both the fluid and particle G phases decreases with an increase in the fluid-particle interaction parameter, β, or the particle-loading parameter, k. Moreover, the particle density is maximum at the surface of the stretching sheet, and the shearing stress increases with an increase in β or k. 相似文献
7.
In this paper, the homotopy perturbation method (HPM) is developed to obtain approximate analytical solutions of a fractional Boussinesq equation with initial condition. The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made, the comparisons show that the HPM is very effective and convenient and overcomes the difficulty of traditional methods. The numerical results show that the approaches are easy to implement and accurate when applied to space‐ and time‐fractional equations. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
8.
This article reports the laminar axisymmetric flow of nanofluid over a non-linearly stretching sheet. The model used for nanofluid contains the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The recently proposed boundary condition is considered which requires the mass flux of nanoparticles at the wall to be zero. Analytic solutions of the arising boundary value problem are obtained by optimal homotopy analysis method. Moreover the numerical solutions are computed by Keller–Box method. Both the solutions are found in excellent agreement. The behavior of Brownian motion on the fluid temperature and wall heat transfer rate is insignificant. Further the nanoparticle volume fraction distribution is found to be negative near the vicinity of the stretching sheet. 相似文献
9.
10.
Semih Küçükarslan 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(5):433-440
In this paper, numerical analysis of the (2+1)-dimensional dispersive long-wave equation (DLWE) is studied by using the homotopy
perturbation method (HPM). For this purpose, the available analytical solutions obtained by multiple traveling-wave solution
will be compared to show the validity and accuracy of the presented numerical algorithm. The obtained results prove the convergence
and accuracy of the HPM for the numerically analyzed (2+1)-dimensional DLWE system. 相似文献
11.
M. Sajid T. Hayat S. Asghar K. Vajravelu 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(2):127-134
An analysis is performed for the boundary-layer flow of a viscous fluid over a nonlinear axisymmetric stretching sheet. By
introducing new nonlinear similarity transformations, the partial differential equations governing the flow are reduced to
an ordinary differential equation. The resulting ordinary differential equation is solved using the homotopy analysis method
(HAM). Analytic solution is given in the form of an infinite series. Convergence of the obtained series solution is explicitly
established. The solution for an axisymmetric linear stretching sheet is obtained as a special case. 相似文献
12.
This paper is concerned with two-dimensional stagnation-point steady flow of an incompressible viscous fluid towards a stretching sheet whose velocity is proportional to the distance from the slit. The governing system of partial differential equations is first transformed into a system of dimensionless ordinary differential equations. Analytical solutions of the velocity distribution and dimensionless temperature profiles are obtained for different ratios of free stream velocity and stretching velocity, Prandtl number, Eckert number and dimensionality index in series forms using homotopy analysis method(HAM). It is shown that a boundary layer is formed when the free stream velocity exceeds the stretching velocity, and an inverted boundary layer is formed when the free stream velocity is less than the stretching velocity. Graphs are presented to show the effects of different parameters. 相似文献
13.
14.
S. A. Shehzad T. Hayat A. Alsaedi 《Journal of Applied Mechanics and Technical Physics》2016,57(4):672-680
This article addresses the boundary layer flow of a thixotropic fluid past an exponentially stretching sheet with heat transfer. The governing partial differential equations are reduced to an ordinary differential equation whose solution is found by the homotopy analysis method. The numerical values of the skin friction coefficient and Nusselt number are compared with available data. 相似文献
15.
U. S. Mahabaleshwar K. R. Nagaraju P. N. Vinay Kumar Dumitru Baleanu Giulio Lorenzini 《Continuum Mechanics and Thermodynamics》2017,29(2):559-567
In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems. 相似文献
16.
In this paper, shooting method and homotopy perturbation technique are applied for the flow analysis of temporal energy transport in a deformation channel with isothermal walls. An incompressible viscous fluid fills the space inside the channel. Analytical and numerical solutions are developed for the momentum and energy equations. The viscous dissipation effects are taken into account. Graphs for pertinent flow parameters are sketched and discussed. Comparison between the analytical and numerical solutions indicates an excellent agreement. It is noticed that behaviors of Prandtl and Eckert numbers on the temperature are qualitatively similar. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
17.
Summary The steady laminar flow of a viscous incompressible fluid through a two-dimensional channel, having fluid sucked or injected with different velocities through its uniformly porous parallel walls is considered. A solution for small suction Reynolds number has been given by the authors in a previous paper. The purpose of this paper is to present a solution valid for large Reynolds numbers for the cases of (i) suction at both walls, and (ii) suction at one wall and injection at the other. A technique of matching outer and inner expansions is used to obtain an asymptotic solution for both of these cases. Further a perturbation solution for the case of suction at one wall and injection at the other is obtained by choosing the difference between two wall velocities as the perturbation parameter. Both asymptotic and perturbation solutions are confirmed by exact numerical solutions. As expected, the resulting solutions show the presence of the usual suction boundary layers in both types of flow considered in this paper. 相似文献
18.
The aim of this paper is to obtain new solitary solutions with compact support for Boussinesq‐like B(2n, 2n) equations with fully nonlinear dispersion using the homotopy perturbation method (HPM). The special case B(2, 2) is chosen to illustrate the concrete scheme of the HPM in B(2n, 2n) equations. General formulas for the solutions of B(2n, 2n) equations are established. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
19.
The present investigation derives the exact and series solutions for steady thin film flow of a third‐grade fluid. The series solution is constructed by a homotopy analysis method. The obtained solutions are compared and an excellent agreement between these is achieved. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
20.
Tiegang Fang 《International Journal of Non》2011,46(9):1116-1426
In this paper, we investigate the steady momentum and heat transfer of a viscous fluid flow over a stretching/shrinking sheet. Exact solutions are presented for the Navier-Stokes equations. The new solutions provide a more general formulation including the linearly stretching and shrinking wall problems as well as the asymptotic suction velocity profiles over a moving plate. Interesting non-linear phenomena are observed in the current results including both exponentially decaying solution and algebraically decaying solution, multiple solutions with infinite number of solutions for the flow field, and velocity overshoot. The energy equation ignoring viscous dissipation is solved exactly and the effects of the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking strength on the temperature profiles and wall heat flux are also presented and discussed. The exact solution of this general flow configuration is a rare case for the Navier-Stokes equation. 相似文献