Elemental approximate analytic procedure for the annular fin of hyperbolic profile amenable to a heat transfer course

Abstract

Straight or longitudinal fins of variable profile are explained in most textbooks on heat transfer, but unfortunately annular or circular fins of variable profile are not. Owing to this limitation, the present article addresses an elemental approximate analytic solution for treating the governing quasi 1-D heat equation descriptive of an annular fin of hyperbolic profile. To solve this equation approximately, usage of the mean radius of the annular fin is made. The transformed ordinary differential equation with constant coefficients is equivalent to the quasi 1-D heat equation for the straight fin of uniform profile that appears in all heat transfer textbooks. Within the framework of engineering analysis and design, the estimates of approximate temperatures and companion heat transfer rates for the annular fin of hyperbolic profile owing realistic values of the parameters give evidence of good quality and minimal errors. The transformation procedure is carried out in a step-by-step manner and can be readily comprehended by undergraduate students in mechanical engineering programs.

Keywords

Annular fin of hyperbolic profile mean radius equivalent straight fin of uniform profile temperature distribution heat transfer rate fin efficiency

Get full access to this article

View all access options for this article.

References

Kraus

Aziz

Welty

. Extended surface heat transfer, New York: Wiley, 2001.

Wolf

. Heat transfer, New York: Harper & Row Limited, 1983.

White

. Heat transfer, Reading: Addison Wesley, 1984.

Becker

. Heat transfer: a modern approach, Berlin: Kluwer Academic Publications. Part of Springer-Verlag, 1986.

Chapman

. Fundamentals of heat transfer, 5th ed. New York: MacMillan, 1987.

Bayazitoglu

Özişik

. Elements of heat transfer, New York: McGraw-Hill, 1988.

Bejan

. Heat transfer, New York: John Wiley, 1993.

Suryanarayana

. Engineering heat transfer, New York: West Publishing Co., 1995.

Mills

. Basic heat transfer, 2nd ed. Upper Saddle River: Prentice-Hall, 1999.

10.

Thomas

. Heat transfer, 2nd ed. Tulsa: Capstone Co., 2000.

11.

Arpaci

Selamet

. Introduction to heat transfer, Upper Saddle River: Prentice-Hall, 2000.

12.

Kreith

Bohn

. Principles of heat transfer, 6th ed. Pacific Grove: Brooks/Cole, 2001.

13.

Kaviany

. Principles of heat transfer, New York: John Wiley, 2001.

14.

Çengel

. Heat transfer, 2nd ed. New York: McGraw-Hill, 2003.

15.

Lienhard

IV Lienhard

V . A heat transfer textbook, Cambridge, MA: Phlogiston Press, 2003.

16.

Kubie

. Heat transfer: a problem solving approach, New York: Taylor & Francis, 2003.

17.

Jiji

. Heat transfer essentials, Redding: Begell House, 2004.

18.

Incropera

DeWitt

Bergman

. Introduction to heat transfer, 5th ed. New York: John Wiley, 2006.

19.

Janna

. Engineering heat transfer, Boca Raton: CRC Press, 2008.

20.

Nellis

Klein

. Heat transfer, New York: Cambridge University Press, 2008.

21.

Holman

. Heat transfer, 10th ed. New York: McGraw-Hill, 2008.

22.

Faghri

Zhang

Howell

. Advanced heat and mass transfer, Columbia: Global Digital Press, 2010.

23.

Han

J-C

. Analytical heat transfer, Boca Raton: CRC Press, 2012.

24.

Schneider

. Conduction heat transfer, Reading: Addison-Wesley, 1955.

25.

Abramowitz

Stegun

. Handbook of mathematical functions, Washington, DC: United States Government Printing Office, 1964, pp. 446.

26.

Gardner

. Efficiency of extended surfaces. ASME (trans.) 1945; 65: 621–631.

27.

Arpaci

. Conduction heat transfer, Reading: Addison-Wesley, 1966.