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Technical Brief

# Unsteady Conduction in a Horizontal Solid Cylinder Cooled by Natural Convection: Alternate Lumped Criterion in Terms of the Solid Material

[+] Author and Article Information
Antonio Campo

Department of Mechanical Engineering,
The University of Texas at San Antonio,
San Antonio, TX 78249

Jaime Sieres

Área de Máquinas y Motores Térmicos,
Escuela de Ingeniería Industrial,
Campus Lagoas-Marcosende,
Vigo 36310, Spain
e-mail: jsieres@uvigo.es

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 22, 2013; final manuscript received April 1, 2014; published online April 23, 2014. Assoc. Editor: Jose L. Lage.

J. Heat Transfer 136(8), 084501 (Apr 23, 2014) (4 pages) Paper No: HT-13-1254; doi: 10.1115/1.4027354 History: Received May 22, 2013; Revised April 01, 2014

## Abstract

Within the framework of the potent lumped model, unsteady heat conduction takes place in a solid body whose space–mean temperature varies with time. Conceptually, the lumped model subscribes to the notion that the external convective resistance at the body surface dominates the internal conductive resistance inside the body. For forced convection heat exchange between a solid body and a neighboring fluid, the criterion entails to the lumped Biot number $Bil=(h¯/ks)(V/A)<0.1$, in which the mean convective coefficient $h¯$ depends on the impressed fluid velocity. However, for natural convection heat exchange between a solid body and a fluid, the mean convective coefficient $h¯$ depends on the solid-to-fluid temperature difference. As a consequence, the lumped Biot number must be modified to read $Bil=(h¯max/ks)(V/A)<0.1$, wherein $h¯max$ occurs at the initial temperature Ti for cooling or at a future temperature Tfut for heating. In this paper, the equivalence of the lumped Biot number criterion is deduced from the standpoint of the solid thermal conductivity through the solid-to-fluid thermal conductivity ratio.

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## References

Bejan, A., 1993, Heat Transfer, John Wiley, New York.
Incropera, F. P., and DeWitt, D. P., 2001, Introduction to Heat Transfer, 4th ed., John Wiley, New York.
Kreith, F., and Bohn, M. S., 2001, Principles of Heat Transfer, 6th ed., Brooks/Cole, Pacific Grove, CA.
Holman, J. P., 2002, Heat Transfer, 9th ed., McGraw–Hill, New York.
Çengel, Y. A., 2003, Heat Transfer, 2nd ed., McGraw–Hill, New York.
Lienhard, IV, J. H., and Lienhard, V. J. H., 2003, A Heat Transfer Textbook, 2nd ed., Phlogiston Press, Cambridge, MA.
McAdams, W. H., 1954, Heat Transmission, 3rd ed., McGraw–Hill, New York.

## Figures

Fig. 1

A horizontal solid cylinder immersed in a fluid at rest

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