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Technical Brief

Simple Formulas to Predict Center and Mean Temperatures and Total Heat Transfer in Regular Configurations With Surface Temperature Under Small- and Large-Time Conditions

[+] Author and Article Information
Antonio Campo

Department of Mechanical Engineering,
The University of Vermont,
Burlington, VT 05405
e-mail: campanto@yahoo.com

Yunesky Masip Macía

Escuela de Ingeniería Mecánica,
Pontificia Universidad Católica de Valparaíso,
Av. Brasil No. 2950,
Valparaíso, Chile

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received August 22, 2018; final manuscript received November 6, 2018; published online February 6, 2019. Assoc. Editor: Gerard F. Jones.

J. Thermal Sci. Eng. Appl 11(3), 034503 (Feb 06, 2019) (7 pages) Paper No: TSEA-18-1415; doi: 10.1115/1.4041938 History: Received August 22, 2018; Revised November 06, 2018

Simple formulas for the prediction of three important thermal quantities, the center temperature, the mean temperature, and the total heat transfer in regular configurations (large plane wall, long cylinder, and sphere) cooled/heated with prescribed uniform surface temperature during “small time,” are addressed in the present paper. Two immediate engineering applications deal with quenching of metals and sterilization of canned food. The simple formulas emanate from the truncated one term series of the supplementary infinite series at small time. The small time subregion has been traditionally characterized in the heat conduction literature by the dimensionless time or Fourier number τ< 0.24 in the large plane wall, τ< 0.21 in the long cylinder, and τ< 0.19 in the sphere. Excellent agreement between the obtained simple formulas and the traditional solutions (namely the exact, analytical infinite series for “all time”) are attained for the center temperature, mean temperature, and total heat transfer in the large plane wall, long cylinder, and sphere.

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