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Explicit equations for transient heat conduction in finite solids for Bi 2推荐
Heat Mass Transfer (2009) 45:375–380
DOI 10.1007/s00231-008-0438-9
ORIGINAL
Explicit equations for transient heat conduction in finite solids
for Bi 2
A. G. Ostrogorsky Æ B. B. Mikic
Received: 21 January 2008 / Accepted: 28 August 2008 / Published online: 17 September 2008
Springer-Verlag 2008
Abstract A set of correlations is developed for transient
oh hL
heat conduction in finite solids (plates, cylinders and ¼ ðTS T1 Þ BihS ð2Þ
on k
S
spheres) exposed to high Biot number convection boundary
conditions. For Bi C 3, the error of the approximate solu- where h(W/m2 K) is heat transfer coefficient and Bi is the
tions is well below 1% of the initial temperature difference Biot number,
driving the transient. hL
Bi ¼ : ð3Þ
k
The Fourier’s infinite series solution for transient heat
conduction in finite plates, cylinders and spheres are known
1 Introduction
since 1822 [3]. The exponential terms in the Fourier series
decay rapidly with time [4–9], so
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