A series solution of the fin problem with a temperature-dependent thermal conductivity

Khani, F.; Raji, M.; Hamedi-Nezhad, S.

doi:10.1016/j.cnsns.2008.11.004

Cited by 54 publications

(37 citation statements)

References 23 publications

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“…Kulkarni and Joglekar [5] proposed and implemented a numerical technique based on residue minimization to solve the nonlinear differential equation governing the temperature distribution in a straight convective fin having a temperature-dependent thermal conductivity. Khani et al [6] used HAM to derive approximate analytical solutions for the temperature distribution and efficiency of a convective fin with simultaneous variations of the thermal conductivity and heat transfer coefficient with temperature. Kundu [7] described an analytical method for obtaining the performance characteristics of an annular step fin (ASF) with simultaneous surface heat and mass transfer.…”

Section: Introductionmentioning

confidence: 99%

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%

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

2012

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“…(4) we know that the case n = 0 implies that the heat transfer function is constant. Arslanturk [3] (see also Chiu and Chen [4] and Khani et al [5]) obtains an even power series solution to Eq. (14) using the ADM [11].…”

Section: Series Solutionsmentioning

confidence: 95%

“…2 match those for the variation in fin efficiency in Kim and Huang [9] (see also Refs. [3][4][5][6][7]19]). …”

Section: Approximate Solutionsmentioning

confidence: 97%

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A comparison of two formulations of the fin efficiency for straight fins

Momoniat

2012

Acta Mech Sin

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A formulation of the fin efficiency based on Newton's law of cooling is compared with a formulation based on a ratio of heat transferred from the fin surface to the surrounding fluid to the heat conducted through the base. The first formulation requires that the solution of the nonlinear fin equations for constant heat transfer coefficient and constant thermal conductivity is known, whilst the second formulation of the fin efficiency requires only that a first integral of the model equation is known. This paper shows the first formulation of the fin efficiency contains approximation errors as only power series and approximate solutions to the nonlinear fin equations have been determined. The second formulation of the fin efficiency is exact when the first integrals can be determined.

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“…Due to the nature of the material properties, the thermal conductivity is a temperature-dependent parameter which makes the energy equation nonlinear. Analysis of the real model needs special treatment which is done by Khani et al [4] with series solutions. Furthermore, analytical and exact solutions for one-dimensional fin models with a temperature-dependent thermal conductivity and heat transfer coefficient were obtained in [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

An Analytical Study on a Model Describing Heat Conduction in Rectangular Radial Fin with Temperature-Dependent Thermal Conductivity

et al. 2012

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The coupling of the homotopy perturbation method (HPM) and the variational iteration method (VIM) is a strong technique for solving higher dimensional initial boundary value problems. In this article, after a brief explanation of the mentioned method, the coupled techniques are applied to one-dimensional heat transfer in a rectangular radial fin with a temperature-dependent thermal conductivity to show the effectiveness and accuracy of the method in comparison with other methods. The graphical results show the best agreement of the three methods; however, the amount of calculations of each iteration for the combination of HPM and VIM was reduced markedly for multiple iterations. It was found that the variation of the dimensionless temperature strongly depends on the dimensionless small parameter ε 1 . Moreover, as the dimensionless length increases, the thermal conductivity of the fin decreases along the fin.

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A series solution of the fin problem with a temperature-dependent thermal conductivity

Cited by 54 publications

References 23 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

A comparison of two formulations of the fin efficiency for straight fins

An Analytical Study on a Model Describing Heat Conduction in Rectangular Radial Fin with Temperature-Dependent Thermal Conductivity

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