Differential transformation approach to thermal conductive problems with discontinuous boundary condition

Jang, Ming-Jyi; Yeh, Yen Liang; Chen, Chieh Li; Yeh, Wei Chih

doi:10.1016/j.amc.2010.03.079

Cited by 28 publications

(21 citation statements)

References 7 publications

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“…Joneidi et al [16] used the DTM to obtain an analytical solution for the efficiency of a convective straight fin with a temperature-dependent thermal conductivity. Jang et al [17] investigated a two-dimensional transient heat conduction problem with discontinuous boundary and initial conditions. Rashidi et al [18] applied the DTM to find the analytic solution for the problem of mixed convection about an inclined flat plate embedded in a porous medium.…”

Section: Introductionmentioning

confidence: 99%

“…3, where the concept of a differential transform is briefly described. The method was subsequently used to obtain analytical solutions of higher-order ordinary differential equations, partial differential equations, difference equations, and integro-differential equations [13][14][15][16][17][18][19][20][21]. Chu and Chen [13] applied a hybrid method of a differential transform and finite difference method to solve a transient heat conduction problem which had complex nonlinear terms.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Solution for Convective–Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity

2012

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In this article, heat transfer in a moving fin with variable thermal conductivity, which is losing heat by simultaneous convection and radiation to its surroundings, is analyzed. The calculations are carried out by using the differential transformation method (DTM) which is an analytical solution technique that can be applied to various types of differential equations. The effects of parameters such as the Peclet number, Pe, thermal conductivity parameter, a, convection-conduction parameter, N c , radiation-conduction parameter, N r , dimensionless convection sink temperature, θ a , and dimensionless radiation sink temperature, θ s , on the temperature distribution are illustrated and explained. The analytical solution is found to be in good agreement with the direct numerical solution. Moreover, the results demonstrate that the DTM is very effective in generating analytical solutions for even highly nonlinear problems.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical Solution for Convective–Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity

2012

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“…These are all case examples in which the one-dimensional DTM was applied. In contrast, Jang et al [34] employed the two-dimensional DTM to analyze one-dimensional transient heat conduction in a finite region. Some of the papers mentioned above investigated not only the heat conduction but also the resulting thermal stress response [24,31].…”

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confidence: 95%

Application of Differential Transform Method to Thermoelastic Problem for Annular Disks of Variable Thickness with Temperature-Dependent Parameters

Chiba

2012

Int J Thermophys

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This article analyzes the one-dimensional steady temperature field and related thermal stresses in an annular disk of variable thickness that has a temperature-dependent heat transfer coefficient and is capable of temperature-dependent internal heat generation. The temperature dependencies of the thermal conductivity, Young's modulus, and the coefficient of linear thermal expansion of the disk are considered, whereas Poisson's ratio is assumed to be constant. The differential transform method (DTM) is employed to analyze not only the nonlinear heat conduction but also the resulting thermal stresses. Analytical solutions are developed for the temperature and thermal stresses in the form of simple power series. Numerical calculations are performed for an annular cooling/heating fin of variable thickness. Numerical results show that the sufficiently converged analytical solutions are in good agreement with the solutions obtained by the Adomian decomposition method and give the effects of the temperature-dependent parameters on the temperature and thermal stress profiles in the disk. The DTM is useful as a new analytical method for solving thermoelastic problems for a body with temperature-dependent parameters including material properties.

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“…By introducing expression (26) in (25), boundary conditions become redundant since they already verified by the proposed expansion (26). Consecutively, and by majoring the quadrature terms, the problem is transformed in a linear system with unknown real variables | =1⋅⋅⋅ 0 .…”

Section: Solution Using the Boubaker Polynomials Expansion Scheme (Bpmentioning

confidence: 99%

“…Joneidi et al [25] provided analytical solution to fin efficiency of convective straight fins with temperaturedependent thermal conductivity by DTM. Jang et al [26] investigated and characterized a two-dimensional thermal conductive boundary value problem with discontinuous boundary and initial conditions. Rashidi et al [27] applied DTM to find the analytic solution for the problem of mixed convection about an inclined flat plate embedded in a porous medium.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Radiative Radial Fin with Temperature-Dependent Thermal Conductivity Using Nonlinear Differential Transformation Methods

Torabi

Yaghoobi

Colantoni

et al. 2013

Chinese Journal of Engineering

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Radiative radial fin with temperature-dependent thermal conductivity is analyzed. The calculations are carried out by using differential transformation method (DTM), which is a seminumerical-analytical solution technique that can be applied to various types of differential equations, as well as the Boubaker polynomials expansion scheme (BPES). By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related boundary conditions are transformed into a set of algebraic equations. The principle of differential transformation is briefly introduced and then applied to the aforementioned equations. Solutions are subsequently obtained by a process of inverse transformation. The current results are then compared with previously obtained results using variational iteration method (VIM), Adomian decomposition method (ADM), homotopy analysis method (HAM), and numerical solution (NS) in order to verify the accuracy of the proposed method. The findings reveal that both BPES and DTM can achieve suitable results in predicting the solution of such problems. After these verifications, we analyze fin efficiency and the effects of some physically applicable parameters in this problem such as radiation-conduction fin parameter, radiation sink temperature, heat generation, and thermal conductivity parameters.

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Differential transformation approach to thermal conductive problems with discontinuous boundary condition

Cited by 28 publications

References 7 publications

Analytical Solution for Convective–Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity

Analytical Solution for Convective–Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity

Application of Differential Transform Method to Thermoelastic Problem for Annular Disks of Variable Thickness with Temperature-Dependent Parameters

Analysis of Radiative Radial Fin with Temperature-Dependent Thermal Conductivity Using Nonlinear Differential Transformation Methods

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