HeatTransfer-I-Section-5

2 for all values of bi if fo 02 addional terms are

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Unformatted text preview: tial Energy Content Qi = πR 2 Lρc p (Ti − T∞ ) •  Single Term Approxima/ons € –  When Fo > 0.2 we can use just one term in the summa/ons. * J0() and J1() are Bessel func/ons tabulated in your text. Transient Conduc/on •  Sphere ∞ Temperature Fourier Coefficient Eigenvalues T - T∞ Cn 2 =∑ sin ζn r R exp( −ζn FoR ) Ti - T∞ n =1 ζn ( r / R) 2[sin ζn − ζn cos ζn ] Cn = ζn − sin ζn cosζn 1 − ζn cot ζn = BiR ( ) 2 Surface Heat Flux 2 k (Ti - T∞ ) ∞ [sin ζn − ζn cosζn ] q' ' = ∑ ζ 2 − ζ sinζ cosζ exp(−ζn2FoR ) R n n n n =1 n Total Heat Flow ∞ Q 1 [sin ζn − ζn cosζn ] 2 = 1 − 6∑ 3 exp( −ζn FoR ) Qi ζn − sin ζn cosζn n =1 ζn 2 Initial Energy Content Qi = 4 3 πR 3 ρc p (Ti − T∞ ) •  Single Term Approxima/ons € –  When Fo > 0.2 we can use just one term in the summa/on. 18 19 Transient Conduc/on •  Eigenvalues: –  The first eigenvalue can be found in Table...
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This document was uploaded on 02/14/2014 for the course ENGR 6901a at Memorial University.

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