Thermal performance of a functionally graded radial fin

A. Aziz, M. M. Rahman

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1637-1648
Number of pages12
JournalInternational Journal of Thermophysics
Volume30
Issue number5
DOIs
Publication statusPublished - Oct 2009

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fins
thermal conductivity
heat transfer
exponents
hyperbolic functions
Bessel functions
temperature distribution
wave functions
boundary conditions
radii
profiles

Keywords

  • Fin effectiveness
  • Fin efficiency
  • Functionally graded radial fin
  • Heat transfer rate
  • Spatially averaged thermal-conductivity model

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Thermal performance of a functionally graded radial fin. / Aziz, A.; Rahman, M. M.

In: International Journal of Thermophysics, Vol. 30, No. 5, 10.2009, p. 1637-1648.

Research output: Contribution to journalArticle

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