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New approximate formula for the generalized temperature integral
Author(s) -
Chen Haixiang,
Liu Naian
Publication year - 2009
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.11775
Subject(s) - kinetic energy , exponential integral , mathematics , exponential function , integral equation , mathematical analysis , volume integral , physics , classical mechanics
The generalized temperature integral $ \int\nolimits_0^T {T^m \,\exp ( - E/RT)dT} $ frequently occurs in nonisothermal kinetic analysis. This article has proposed a new approximate formula for the generalized temperature integral, which is in the following form:$$ h_m = x^{(0.11168 + 0.04426m)} e^{( - 0.00150 - 0.00055m)x - (0.39922 + 0.16360m)}. $$For commonly used values of m in kinetic analysis, the deviation of the new approximation from the numerical values of the integral is within 0.4%. More importantly, the new formula represents the exponential approximation, which is not found earlier, and it can result in a new and very accurate integral method in kinetic analysis. © 2009 American Institute of Chemical Engineers AIChE J, 2009