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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, USA
campanto@yahoo.com

Yunesky Masip Macia

Escuela de Ingeniería Mecánica, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile
yunesky.masip@pucv.cl

1Corresponding author.

ASME doi:10.1115/1.4041938 History: Received August 22, 2018; Revised November 06, 2018

Abstract

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 uniform surface temperature during "small time" and "large time" are addressed. 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". In the heat conduction literature, the "small time" sub-region has been described by dimensionless time or Fourier number ? < 0.24 in the large plane wall, ? < 0.21 in the long cylinder and ? < 0.19 in the sphere. Excellent agreement between the simple formulas and the traditional solutions (namely the exact, analytical infinite series for "all time") are attained for the center and mean temperatures and total heat transfer in the large plane wall, long cylinder and sphere.

Copyright (c) 2018 by ASME
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