Algebraic Evaluation of Temperatures and Heat Transfer Rates in Simple Bodies with a 1-D Composite Lumped Model. Its Connection to the Heisler/Gröber Charts

Abstract

Calculations of temperature histories and heat transfer rates in simple bodies (infinite plate, infinite cylinder and sphere) have been traditionally explained in courses on heat transfer by way of the popular Heisler/Gröber charts, which are applicable to dimensionless times, τ, greater than 0.2. This imposing restriction comes from the ‘one-term series solutions' used in their construction. The central goal of this educational paper is to predict mean, surface and centre temperatures, as well as heat transfer rates of simple bodies, by implementing a 1-D composite lumped analysis. This effortless analysis brings about a handful of algebraic equations that can be easily evaluated with a pocket-size calculator. Even more important, the same algebraic equations can be extended into the sensible subregions described by dimensionless times less than 0.2; these subregions are ignored by the Heisler/Gröber charts.

Keywords

unsteady temperatures heat transfer simple bodies lumped model

Get full access to this article

View all access options for this article.

References

Hagen

K. D.

, Heat Transfer with Applications, Prentice Hall, Englewood Cliffs, NJ, 1999.

Cengel

Y. A.

, Heat Transfer, McGraw-Hill, New York, 1997.

Holman

J. P.

, Heat Transfer, 8th edn, McGraw-Hill, New York, 1997.

Kreith

, and Bohn

M. S.

, Principles of Heat Transfer, 6th edn, West, St. Paul, MN, 1996.

Incropera

F. P.

, and De Witt

D. P.

, Fundamentals of Heat Transfer, 3rd edn, John Wiley, New York, 1996.

Suryanarayana

N. V.

, Engineering Heat Transfer, West, St. Paul, MN, 1995.

Bejan

, Heat Transfer, John Wiley, New York, 1993.

Thomas

L. C.

, Heat Transfer, 2nd edn, Prentice Hall, Englewood Cliffs, NJ, 1992.

White

F. M.

, Heat Transfer, Addison Wesley, Reading, MA, 1988.

10.

Lienhard

J. H.

, A Heat Transfer Textbook, 2nd edn, Prentice Hall, Englewood Cliffs, NJ, 1987.

11.

Chapman

A. J.

, Fundamental of Heat Transfer, 3rd edn, MacMillan, New York, 1987.

12.

Ozisik

M. N.

, Basic Heat Transfer, McGraw-Hill, New York, 1985.

13.

Sucec

, Heat Transfer, Brown, Dubuque, IA, 1985.

14.

Welty

J. R.

, Engineering Heat Transfer, John Wiley, New York, 1974.

15.

Heisler

M. P.

, Temperature charts for induction and constant temperature heating, Trans. ASME., 69, 227–236 (1947).

16.

Gurney

H. P.

, and Lurie

, Charts for estimating temperature distributions in heating and cooling of solid shapes, Industrial Engineering and Chemistry, 15, 1170–1172 (1923).

17.

Boelter

L. M. K.

Cherry

V. H.

Johnson

H. A.

, and Martinelli

R. C.

, Heat Transfer Notes, University of California Publications, Berkeley, CA, 1945. Also published by McGraw-Hill, New York, NY, 1965.

18.

Campo

, and Salazar

, Matching solutions for unsteady conduction in simple bodies with surface heat fluxes, AIAA J. Thermophysics and Heat Transfer, 10, 699–701 (1996).

19.

Gröber

Erk

, and Grigull

, Fundamentals of Heat Transfer, McGraw-Hill, New York, 1961.

20.

Arpaci

, Conduction Heat Transfer, Addison-Wesley, Reading, MA, 1966.