A reliable convergent Adomian decomposition method for heat transfer through extended surfaces

PurposeThis paper aims to revisite the traditional Adomian decomposition method frequently used for the solution of highly nonlinear extended surface problems in order to understand the heat transfer enhancement phenomenon. It is modified to include a parameter adjusting and controlling the convergence of the resulting Adomian series.Design/methodology/approachIt is shown that without such a convergence control parameter, some of the published data in the literature concerning the problem are lacking accuracy or the worst is untrustful. With the proposed amendment over the classical Adomian decomposition method, it is easy to gain the range of parameters guaranteeing the convergence of the Adomian series.FindingsWith the presented improvement, the reliable behavior of the fin tip temperature and the fin efficiency of the most interested from practical perspective are easily predicted.Originality/valueThe relevant future studies involving the fin problems covering many physical nonlinear properties must be properly treated as guided in this paper, while the Adomian decomposition method is adopted for the solution procedure.

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Solution of jamming transition problem using adomian decomposition method

Engineering Computations ◽

10.1108/ec-12-2016-0437 ◽

2018 ◽

Vol 35 (5) ◽

pp. 1950-1964 ◽

Cited By ~ 1

Author(s):

Erman Şentürk ◽

Safa Bozkurt Coşkun ◽

Mehmet Tarık Atay

Keyword(s):

Decomposition Method ◽

Numerical Solutions ◽

Initial Conditions ◽

Adomian Decomposition Method ◽

Numerical Function ◽

Content Type ◽

Jamming Transition ◽

Transition Problem ◽

Adomian Decomposition ◽

Highly Nonlinear

Purpose The purpose of the study is to obtain an analytical approximate solution for jamming transition problem (JTP) using Adomian decomposition method (ADM). Design/methodology/approach In this study, the jamming transition is presented as a result of spontaneous deviations of headway and velocity that is caused by the acceleration/breaking rate to be higher than the critical value. Dissipative dynamics of traffic flow can be represented within the framework of the Lorenz scheme based on the car-following model in the one-lane highway. Through this paper, an analytical approximation for the solution is calculated via ADM that leads to a solution for headway deviation as a function of time. Findings A highly nonlinear differential equation having no exact solution due to JTP is considered and headway deviation is obtained implementing a number of different initial conditions. The results are discussed and compared with the available data in the literature and numerical solutions obtained from a built-in numerical function of the mathematical software used in the study. The advantage of using ADM for the problem is presented in the study and discussed on the basis of the results produced by the applied method. Originality/value This is the first study to apply ADM to JTP.

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Numerical solution of large deflection beams by using the Laplace Adomian decomposition method

Engineering Computations ◽

10.1108/ec-01-2021-0044 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Ming-Xian Lin ◽

Chia-Hsiang Tseng ◽

Chao Kuang Chen

Keyword(s):

Decomposition Method ◽

Large Deflection ◽

Adomian Decomposition Method ◽

Nonlinear Behavior ◽

Bernoulli Beam ◽

Rapid Convergence ◽

Content Type ◽

Adomian Decomposition ◽

Euler Bernoulli Beam ◽

Better Than

PurposeThis paper presents the problems using Laplace Adomian decomposition method (LADM) for investigating the deformation and nonlinear behavior of the large deflection problems on Euler-Bernoulli beam.Design/methodology/approachThe governing equations will be converted to characteristic equations based on the LADM. The validity of the LADM has been confirmed by comparing the numerical results to different methods.FindingsThe results of the LADM are found to be better than the results of Adomian decomposition method (ADM), due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms. LADM are presented for two examples for large deflection problems. The results obtained from example 1 shows the effects of the loading, horizontal parameters and moment parameters. Example 2 demonstrates the point loading and point angle influence on the Euler-Bernoulli beam.Originality/valueThe results of the LADM are found to be better than the results of ADM, due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms.

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Adomian decomposition method to magnetohydrodynamics natural convection heat generating/absorbing slip flow through a porous medium

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-08-2018-0153 ◽

2019 ◽

Vol 15 (3) ◽

pp. 673-684 ◽

Cited By ~ 4

Author(s):

Abiodun O. Ajibade ◽

Jeremiah Jerry Gambo

Keyword(s):

Porous Medium ◽

Natural Convection ◽

Decomposition Method ◽

Slip Flow ◽

Adomian Decomposition Method ◽

Convection Heat ◽

Content Type ◽

Adomian Decomposition ◽

Flow Through ◽

Effect Parameter

Purpose The purpose of this paper is to analyze magnetohydrodynamics fully developed natural convection heat-generating/absorbing slip flow through a porous medium. Adomian decomposition method was applied to find the solutions to the problem. Design/methodology/approach In this study, Adomian decomposition method was used. Findings Results show that heat generation parameter enhanced the temperature and velocity of the fluid in the annulus. Moreover, slip effect parameter increases the velocity of the fluid. Originality/value Originality is in the application of Adomian decomposition method which allowed the slip at interface.

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Thermal Prediction of Convective-Radiative Porous Fin Heatsink of Functionally Graded Material Using Adomian Decomposition Method

Computation ◽

10.3390/computation7010019 ◽

2019 ◽

Vol 7 (1) ◽

pp. 19 ◽

Cited By ~ 5

Author(s):

George Oguntala ◽

Gbeminiyi Sobamowo ◽

Yinusa Ahmed ◽

Raed Abd-Alhameed

Keyword(s):

Functionally Graded Material ◽

Decomposition Method ◽

Adomian Decomposition Method ◽

Functionally Graded ◽

Electronic Systems ◽

Fin Efficiency ◽

Porous Fin ◽

Adomian Decomposition ◽

Graded Material ◽

Inhomogeneity Index

In recent times, the subject of effective cooling have become an interesting research topic for electronic and mechanical engineers due to the increased miniaturization trend in modern electronic systems. However, fins are useful for cooling various low and high power electronic systems. For improved thermal management of electronic systems, porous fins of functionally graded materials (FGM) have been identified as a viable candidate to enhance cooling. The present study presents an analysis of a convective–radiative porous fin of FGM. For theoretical investigations, the thermal property of the functionally graded material is assumed to follow linear and power-law functions. In this study, we investigated the effects of inhomogeneity index of FGM, convective and radiative variables on the thermal performance of the porous heatsink. The results of the present study show that an increase in the inhomogeneity index of FGM, convective and radiative parameter improves fin efficiency. Moreover, the rate of heat transfer in longitudinal FGM fin increases as β increases. The temperature prediction using the Adomian decomposition method is in excellent agreement with other analytical and method.

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Heat transfer through converging-diverging channels using Adomian decomposition method

Engineering Applications of Computational Fluid Mechanics ◽

10.1080/19942060.2020.1830857 ◽

2020 ◽

Vol 14 (1) ◽

pp. 1373-1384

Author(s):

Hayette Saifi ◽

Mohamed Rafik Sari ◽

Mohamed Kezzar ◽

Mahyar Ghazvini ◽

Mohsen Sharifpur ◽

...

Keyword(s):

Heat Transfer ◽

Decomposition Method ◽

Adomian Decomposition Method ◽

Adomian Decomposition

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Closed-form solution for a rectangular stepped fin involving all variable thermal parameters and nonlinear boundary conditions

Proceedings of the Institution of Mechanical Engineers Part E Journal of Process Mechanical Engineering ◽

10.1177/0954408916652438 ◽

2016 ◽

Vol 231 (5) ◽

pp. 992-1010 ◽

Cited By ~ 4

Author(s):

Kuljeet Singh ◽

Ranjan Das ◽

Rohit K Singla

Keyword(s):

Heat Transfer ◽

Boundary Conditions ◽

Decomposition Method ◽

Nonlinear Boundary ◽

Adomian Decomposition Method ◽

Nonlinear Boundary Conditions ◽

Thermal Parameters ◽

Physical Parameters ◽

Temperature Dependent ◽

Adomian Decomposition

In this paper, the implementation of the Adomian decomposition method is demonstrated to solve a nonlinear heat transfer problem for a stepped fin involving all temperature-dependent means of heat transfer and nonlinear boundary conditions. Unlike conventional insulated tip assumption, to make the present problem more practical, the fin tip is assumed to disperse heat by convection and radiation. Thermal parameters such as the thermal conductivity, the surface heat transfer coefficient and the surface emissivity are considered to be temperature-dependent. Adomian polynomials are first obtained and then a set of Adomian decomposition method results is validated with pertinent results of the differential transformation method reported in the literature. Effects of different thermo-physical parameters on the temperature distribution and the efficiency have been exemplified. The study reveals that for a given set of conditions, the stepped fin may perform better than the straight fin.

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