Electronic instrumentation and atmospheric sciences school, university of veracruz, circuito gonzalo aguirre beltran sn, 9 xalapa, ver, mexico. Abstractin this article, homotopy analysis method ham is used to evaluate the. Hpm has gained reputation as being a powerful tool for solving linear or nonlinear partial differential equations. Introduction the homotopy perturbation method hpm was established by jihuan he in 1999 23.
Solution of temperature distribution in a radiating fin. In this article, we established an application of homotopy perturbation method using laplace transform lthpm to elaborate the analytical solution of heat conduction equation in the heterogeneous castingmould system. An application of homotopy perturbation method for nonlinear. In our previous work, homotopy perturbation method has been used to evaluate thermal performance of. Homotopy perturbation method for solving linear boundary. Application of the homotopy perturbation method for. Application of the homotopy perturbation method for the.
In order to illustrate the potentiality of the approach. Code 1616, lahijan, iran abstract in this article, we have. Application of homotopy perturbation method to nonhomogeneous parabolic. The present paper applies the homotopy perturbation to obtain analytic approximation of distribution of temperature in heat fin radiating, which is compared with the results obtained by adomian decomposition method adm. The homotopy analysis method is based on replacing a nonlinear equation by a. Homotopy perturbation method for thin film flow and heat transfer. Thermal analysis of convectiveradiative fin with temperature. Unlike perturbation methods, the ham has nothing to do with smalllarge physical parameters. Recent development of the homotopy perturbation method. The present work constitutes a guided tour through the mathematics needed for a proper understanding of homotopy perturbation method as applied to various nonlinear problems. Homotopy analysis method in nonlinear differential equations. Request pdf homotopy perturbation method for temperature distribution, fin efficiency and fin effectiveness of convective straight fins homotopy perturbation method is a novel approach that. In our previous work, homotopy perturbation method has been used to evaluate thermal performance of straight fins with constant thermal conductivity.
Pdf comparison of homotopy analysis method and homotopy. Biazar1 department of mathematics, faculty of sciences the university of guilan, p. Temperature distribution and effectiveness of convective radial fins with constant and temperature dependent thermal conductivity are solved by applying homotopy perturbation sumudu transform method hpstm. Here, the fin problem is solved to obtain the distribution of temperature of the fin by homotopy perturbation method and compared with the result obtained by the adomian decomposition method, which is used for solving various nonlinear fin problems 2325. To facilitate the benefits of this proposal, an algorithmic form of the hpm is also designed to handle the same.
Assessment of perturbation and homotopyperturbation. Construction of a homotopy according to the initial guess, a homotopy should be constructed 3. Homotopy perturbation method for solving some initial. New homotopy perturbation method for system of burgers. Mar 31, 2016 in this article, we focus on linear and nonlinear fuzzy volterra integral equations of the second kind and we propose a numerical scheme using homotopy perturbation method hpm to obtain fuzzy approximate solutions to them. This problem consists in the calculation of temperature distribution in the domain, as well as in the reconstruction of functions describing the temperature and heat flux on the boundary, when the temperature measurements in the domain are known. Numerical simulations was performed in the ansys software. Analytical solutions of some twopoint nonlinear elliptic. Application of homotopy perturbation method to biological. Homotopy analysis method in nonlinear differential.
Pdf in this paper, the homotopy analysis method ham is compared with the. Application of homotopy perturbation method in solving. This paper deals with an application of the homotopy perturbation method for the solution of inverse heat conduction problem. The coupling method of the homotopy techniques is called the homotopy perturbation method. In this method, each decomposition of the source function f x, y leads to a new homotopy. Homotopy perturbation method 10, 11 is an analytical method which can be applied to the solution of linear, nonlinear deterministic and stochastic operator equations. We show that a recent application of homotopy perturbation method to a class of ordinary differential equations yields either useless or wrong results. Temperature distribution and effectiveness of convective radial fins with constant and temperaturedependent thermal conductivity are solved by applying homotopy perturbation sumudu transform method hpstm. Temperature and stress distribution in hollow annular disk of uniform. Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. By this method, a rapid convergent series solution can be obtained in most of the cases. Homotopy perturbation method for temperature distribution, fin efficiency and fin effectiveness of convective straight fins with temperaturedependent thermal. This method is the most effective and convenient ones for both linear and nonlinear equations.
This is enabled by utilizing a homotopymaclaurin series to deal with the nonlinearities in the system. The homotopy analysis method employs the concept of the homotopy from topology to generate a convergent series solution for nonlinear systems. One of these semianalytical methods is the homotopy perturbation method hpm. By the homotopy technique in topology, a homotopy can be constructed with an embedding parameter p. Huan he 1415 by coupling the perturbation method and homotopy in topology. A comparison between the differential transform method and homotopy perturbation method for a system of non linear chemistry problems. Adomian decomposition method 1 introduction the idea of hpm was. Besides, we show a table of comparison, between this proposed approximate solution and a numerical of tf, by establishing the accuracy of the results. Comparison of the results obtained by the method reveals that homotopy perturbation method hpm is more effective and easy to use. Pdf application of the homotopy perturbation method for. Optimization of configurations to enhance heat transfer from. Application of homotopy perturbation method to nonlinear. In order to show the ability and reliability of the method some examples are provided. We propose an approximate solution of tf equation, obtained by using the nonlinearities distribution homotopy perturbation method ndhpm.
Homotopy perturbation method for a type of nonlinear coupled. Homotopy perturbation transform method for solving nonlinear. Many analytical methods like homotopy perturbation method hpm. Slota, application of the homotopy perturbation method for calculation of the temperature distribution in the castmould heterogeneous domain, journal of achievements in materials and manufacturing engineering 431 2010 299309. On the application of homotopy perturbation method to.
Solution procedure similar to that of classical perturbation method. Homotopy perturbation method is a novel approach that provides an approximate analytical solution to differential equations in the form of an infinite power series. Based on the improved homotopy perturbation method for. Optimal homotopy perturbation method for nonlinear. He, a coupling method of homotopy technique and perturbation technique for nonlinear problems, international journal of nonlinear mechanics, 35, 3743, 2000. Two new analytical methods to solve nonlinear heat transfer equations are homotopy perturbation method and homotopy analysis method. Application of homotopy perturbation and modified adomian. According to nonlinear fredholm differential and integral equation,it is proposed that the improved homotopy perturbation method is used to solve in this paper, and apply the numerical examples to compare the advantages among homotopy perturbation method, adomian decomposition method and improved homotopy perturbation method. The homotopy perturbation method with an auxiliary term is applied to obtain an approximate analytical solution for the tangent nonlinear packaging system. By applying the perturbation technique the solution of equation 2 can be expressed as a power series in p 23 vv pv pv pv 01 2 3. Muminov4 background hypersingular integral equations hsies arise a variety of mixed boundary value prob. Homotopy perturbation method with an auxiliary term for. The homotopy perturbation method hpm has been used to investigate a variety of mathematical and physical problems, since it is very. Homotopy perturbation method for solving systems of.
Homotopy perturbation method fokkerplanck equation j. Obtaining velocity and temperature distribution from the mathematical. Application of the homotopy perturbation method for calculation of the temperature distribution in thecastmould heterogeneous domain article pdf available november 2010 with 82 reads. In the proposed method, we have chosen initial approximations.
The homotopy analysis method ham is a semianalytical technique to solve nonlinear ordinarypartial differential equations. Homotopy analysis method in nonlinear differential equations presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method ham. The application of the homotopy perturbation method to one. Numerical solution of nonlinear diffusion equation with. Use of homotopy perturbation method for solving multi. The homotopy perturbation method hpm was presented by jihuan he he, 1999 of shanghai university in 1998 which is the coupling method of the homotopy techniques and the perturbation technique. Homotopy perturbation method with an auxiliary term for the. This problem consists in the calculation of temperature distribution in the domain, as well as in the reconstruction of the functions describing temperature and heat flux on the boundary, when the position of the moving interface is known. The results are given in table 1, and also the results of homotopy perturbation method and numerical method n.
The international journal of engineering and science ijes vol. Assessment of homotopy analysis method and homotopy. In this method, the solution is considered as an infinite series expansion where it converges rapidly to the exact solution. Homotopy perturbation method to solve heat conduction equation. The majority of nonlinear problems, especially those having strong nonlinearity, have no small parame. Homotopy perturbation method for thin film flow and heat transfer over an. He 2432 developed the homotopy perturbation method for solving linear, nonlinear, initial and boundary value problems 3338 by merging two techniques, the standard homotopy and the perturbation technique. He 38 developed the homotopy perturbation method for solving linear, nonlinear, ini. Different from perturbation techniques, the ham is valid if a nonlinear problem. M are given in 20 and they are presented in this table. Modified homotopy perturbation method for nonlinear system.
Abstractin this paper, the optimal homotopy perturbation method ohpm is employed to determine an analytic approximate solution for the nonlinear mhd jefferyhamel flow and heat transfer problem. Radiating extended surfaces are widely used to enhance heat transfer between primary surface and the environment. Analytical and numerical study to nonlinear heat transfer equation. The results show that improved homotopy perturbation. Use of homotopy perturbation method for solving multipoint. Application of homotopy perturbation method to non. On the application of homotopy perturbation method to differential equations. Research article approximate solutions of delay differential.
In this paper, we consider the temperature distribution along a. An analytic method for strongly nonlinear problems, namely the homotopy analysis method ham was proposed by liao in 1992, six years earlier than the homotopy perturbation method by he h. He he, 1999, 2003, 2004, 2005 developed the homotopy perturbation method for solving nonlinear initial and boundary value problems by combining the standard homotopy in topology and the perturbation technique. In this paper, we employ a new homotopy perturbation method to obtain the solution of a firstorder inhomogeneous pde. Homotopy perturbation method for a type of nonlinear. Application of homotopy analysis method for solving an. To further raise the accuracy of the solution, this work has expanded the possibility of the energy method for the homotopy perturbation method with an auxiliary term. Application of homotopy analysis method for solving an seirs. An application of homotopy perturbation method for non.
Solution of temperature distribution in a radiating fin using. Homotopy perturbation method for solving partial differential. Optimal homotopy perturbation method for nonlinear differential. Solving natural distribution ventilation network with. Perturbation theory is applicable if the problem at hand cannot be solved exactly, but can be formulated by.
A modification of the homotopy analysis method based on. Perturbation method is based on assuming a small parameter. Enhancement of heat transfer employing fins is important in a multitude of heat. Apr 21, 2018 in this article, we established an application of homotopy perturbation method using laplace transform lthpm to elaborate the analytical solution of heat conduction equation in the heterogeneous castingmould system. Optimization of configurations to enhance heat transfer. The navierstokes equations, taking into account maxwells electromagnetism and heat transfer, lead to two nonlinear ordinary differential equations. It gives a new interpretation of the concept of constant expansion in the homotopy perturbation method. Homotopy perturbation method for solving systems of nonlinear coupled equations a. Fracture porous media, homotopy perturbation method hpm, cocurrent imbibition.
In contrast to the traditional perturbation methods. The homotopy perturbation method hpm combined with trefftz method is employed to find the solution of two kinds of nonlinear. Modified homotopy perturbation method for solving hypersingular integral equations of the first kind z. The solution of the problem is provided with our supposition of an ideal contact between the cast and the mould. The homotopy perturbation method hpm 7,8 has been widely used by scientists and engineers to study the linear and. The homotopy perturbation method hpm applied in this work was proposed by the chinese researcher j. He,comparison of homotopy perturbation method and homotopy analysis method,applied mathematics and computation, 156, 527539,2004. The homotopy perturbation method hpm and the decomposition of a source function are used together to develop this new technique. In this paper, heat transfer from a longitudinal fin with step change has been analysed using a computational fluid dynamics software, fluent. In this paper, the application of the homotopy perturbation method for solving the inverse stefan problem is presented.
We expand the application of the enhanced multistage homotopy perturbation method emhpm to solve delay di erential equations ddes with constant and variable coe cients. Homotopy perturbation method for temperature distribution, fin. Homotopy perturbation transform method for solving. Optimal homotopy asymptotic method for flow and heat transfer of.
Calculation of the neutron diffusion equation by using. Homotopy perturbation method for temperature distribution. Fernandez submitted on 15 aug 2008, last revised 3 sep 2008 this version, v2 abstract. Here, the new method based on the homotopy perturbations will be applied for approximate solving of this system of sp equations. Analysis of the new homotopy perturbation method for linear. The amount of heat dissipation from the fin, fin efficiency and fin effectiveness of crf, rfssc and rfdsc have been determined for five different cases. Second, the ham is a unified method for the lyapunov artificial small parameter method, the delta expansion method, the adomian decomposition method, and the homotopy perturbation method. Siddiqi and 1, 2, b muzammal iftikhar 1department of mathematics, university of the punjab, lahore 54590, pakistan 2department of mathematics, university of education, okara campus, okara 56300, pakistan abstract homotopy perturbation method is used for solving the multipoint boundary. Gholamin department of mathematics, islamic azad university branch of lahijan, p. Rajabi 9 utilized the homotopy perturbation method hpm to calculate the efficiency of. Analysis of the new homotopy perturbation method for.
Nonlinearities distribution homotopy perturbation method. However, we develop a method to obtain the proper decomposition of f x, y which lets us obtain the solution with minimum computation and accelerate the convergence of the solution. In this article, we focus on linear and nonlinear fuzzy volterra integral equations of the second kind and we propose a numerical scheme using homotopy perturbation method hpm to obtain fuzzy approximate solutions to them. Different from classical perturbation method, apm and hpm do not require small parameter and therefore, obtained approximate solutions may be uniformly valid for. Homotopy perturbation method for solving systems of nonlinear. A critical feature of the technique is a middle step that breaks the problem into solvable and perturbation parts.
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