Residue minimization technique to analyze the efficiency of convective straight fins having temperature-dependent thermal conductivity

Kulkarni, D. B.; Joglekar, M. M.

doi:10.1016/j.amc.2009.08.011

Cited by 21 publications

(18 citation statements)

References 16 publications

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“…Arslanturk [8] obtained correlation equations for optimum design of annular fins with temperaturedependent thermal conductivity. Kulkarni and Joglekar [9] proposed and implemented a numerical technique based on residue minimization to solve the nonlinear differential equation, which governs the temperature distribution in straight convective fins having temperature-dependent thermal conductivity. Khani et al [10] used HAM to evaluate the analytical approximate solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient.…”

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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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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show abstract

“…Under these assumptions, the energy balance equation of rectangular fin is given by [1][2][3][4][5][6][7][8][9][10][11] ‫ܣ‬ ݀ ࣲ݀ ൬‫ܭ‬ሺܶሻ ݀ܶ ࣲ݀ ൰ − ܲℎሺܶ − ܶ ሻ = 0,…”

Section: Introductionmentioning

confidence: 99%

“…Here, we take the heat transfer coefficient ℎ as a constant and the thermal conductivity ݇(ܶ) as a linear function of temperature [1][2][3][4][5][6][7][8][9] …”

Section: Introductionmentioning

confidence: 99%

“…(6) with boundary conditions (8) and (10) are investigated using the Parameterized Perturbation method in [1], by using optimal homotopy asymptotic method in [2], by using the homotopy analysis method in [3,4], by using the Residue minimization technique in [5], by using the variational iteration method in [6] and by using the decomposition method in [7,8].…”

mentioning

confidence: 99%

“…(3) dimensionless; the following transformations are introduced [1][2][3][4][5][6][7][8][9][10][11][12][13][14] …”

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confidence: 99%

See 2 more Smart Citations

Exact solution of fin problem with linear temperature-dependent thermal conductivity

Kader¹,

Latif²,

Nour³

2016

J. Appl. Math. Comput. Mech.

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In this paper, we obtain the general exact solution of a nonlinear fin equation which governs heat transfer in a rectangular fin with linear temperature-dependent thermal conductivity using the partial Noether method. The relationship between the fin efficiency and the thermo-geometric fin parameter is obtained. Additionally, we obtained the relationship among the fin effectiveness, the thermo-geometric fin parameter and the Biot number.

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Analytical approaches for thermal analysis of radiative fin with a step change in thickness and variable thermal conductivity

Torabi

Yaghoobi

2012

Heat Trans. Asian Res.

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In this paper, heat transfer in a straight fin with a step change in thickness and variable thermal conductivity which is losing heat by radiation to its surroundings is analyzed. The calculations are carried out by using the differential transformation method (DTM) and variational iteration method (VIM) that can be applied to various types of differential equations. The results obtained employing the DTM and VIM are compared with a finite difference technique with Richardson extrapolation which is an accurate numerical solution to verify the accuracy of the proposed methods. As an important result, it is depicted that the DTM results are more accurate in comparison with those obtained by VIM. After these verifications the effects of parameters such as thickness parameter α, dimensionless fin semi‐thickness δ, length ratio λ, thermal conductivity parameter β, and radiation–conduction parameter Nr, on the temperature distribution and fin efficiency are illustrated and explained. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (http://wileyonlinelibrary.com/journal/htj. DOI 10.1002/htj.21000

show abstract

Residue minimization technique to analyze the efficiency of convective straight fins having temperature-dependent thermal conductivity

Cited by 21 publications

References 16 publications

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

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

Exact solution of fin problem with linear temperature-dependent thermal conductivity

Analytical approaches for thermal analysis of radiative fin with a step change in thickness and variable thermal conductivity

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