Improved One-Dimensional Fin Solutions

Aparecido, J. B.; Cotta, Renato M.

doi:10.1080/01457639008939722

Cited by 50 publications

(27 citation statements)

References 4 publications

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“…Some workers [7][8][9] have studied radial fins with a two-dimensional heat conduction model and have found that when the Biot number based on the thickness of the fin is of the order of 0.1, the error between the one-dimensional and two-dimensional models is negligible. Indeed, it has been established that the fin is effective as a heat transfer enhancement device only when the Biot number is small [10].…”

Section: List Of Symbolsmentioning

confidence: 99%

Thermal Performance of a Functionally Graded Radial Fin

Aziz

Rahman

2009

Int J Thermophys

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This paper investigates the steady-state thermal performance of a radial fin of rectangular profile made of a functionally graded material. The thermal conductivity of the fin varies continuously in the radial direction following a power law. The boundary conditions of a constant base temperature and an insulated tip are assumed. Analytical solutions for the temperature distribution, heat transfer rate, fin efficiency, and fin effectiveness are found in terms of Airy wave functions, modified Bessel functions, hyperbolic functions, or power functions depending on the exponent of the power law. Numerical results illustrating the effect of the radial dependence of the thermal conductivity on the performance of the fin are presented and discussed. It is found that the heat transfer rate, the fin efficiency, and the fin effectiveness are highest when the thermal conductivity of the fin varies inversely with the square of the radius. These quantities, however, decrease as the exponent of the power law increases. The results of the exact solutions are compared with a solution derived by using a spatially averaged thermal conductivity. Because large errors can occur in some cases, the use of a spatially averaged thermal-conductivity model is not recommended.

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Section: List Of Symbolsmentioning

confidence: 99%

Thermal Performance of a Functionally Graded Radial Fin

Aziz

Rahman

2009

Int J Thermophys

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“…Different levels of approximation in such mixed lumped-differential formulations can be used, starting from the plain and classical lumped system analysis, towards improved formulations, obtained through Hermite-type approximations for integrals [1,2]. Such approach has been already exploited in different heat and fluid flow problems [3][4][5][6][7][8][9][10], including phase change problems, extended surfaces (fins), anisotropic heat conduction, heat exchangers analysis, Navier-Stokes equations and drying problems themselves, and shall be reviewed within this section.…”

Section: Improved Lumped-differential Formulations: the Coupled Integmentioning

confidence: 99%

“…First, a problem reformulation strategy is reviewed, based on Hermite integration schemes [1,2] and known as the coupled integral equations approach (CIEA) [3][4][5][6][7][8][9][10], which offers improved lumped-differential formulations in different classes of problems, in comparison with classical lumping schemes, allowing for a reduction on the number of independent variables to be considered in specific formulations, thus reducing simulation costs.…”

Section: Introductionmentioning

confidence: 99%

Improved lumped-differential formulations and hybrid solution methods for drying in porous media

Dantas

Orlande

Cotta

2007

International Journal of Thermal Sciences

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“…It is found that one-dimensional model of fin performance is valid as transverse Biot number is less than unity by 0017 Irey [4]. To expand this valid range, an improved one-dimensional solution was proposed by Aparecido and Cotta [5] who modified those expressions as simple as classical ones but accuracy is significantly improved.…”

Section: Introductionmentioning

confidence: 97%