An exact solution to steady heat conduction in a two-dimensional annulus on a one-dimensional fin: Application to frosted heat exchangers with round tubes

A. D. Sommers, A. M. Jacobi

Research output: Contribution to journalArticlepeer-review

Abstract

The fin efficiency of a high-thermal-conductivity substrate coated with a low-thermal-conductivity layer is considered, and an analytical solution is presented and compared to alternative approaches for calculating fin efficiency. This model is appropriate for frost formation on a round-tube-and-fin metallic heat exchanger, and the problem can be cast as conduction in a composite two-dimensional circular cylinder on a one-dimensional radial fin. The analytical solution gives rise to an eigenvalue problem with an unusual orthogonality condition. A one-term approximation to this new analytical solution provides fin efficiency calculations of engineering accuracy for a range of conditions, including most frosted-coated metal fins. The series solution and the one-term approximation are of sufficient generality to be useful for other cases of a low-thermal-conductivity coating on a high-thermal-conductivity substrate.

Original languageEnglish (US)
Pages (from-to)397-404
Number of pages8
JournalJournal of Heat Transfer
Volume128
Issue number4
DOIs
StatePublished - Apr 2006

Keywords

  • Conduction
  • Fin efficiency
  • Frost
  • Heat transfer
  • Sector method

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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