Review and evaluation of the approximations to the temperature integral

The kinetics of processes involving solids may be determined from experiments under non-isothermal conditions. On analyzing data by integral methods, it is necessary to calculate the temperature integral, which does not have an analytical solution. Instead of performing the numerical integration, mo...

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Bibliographic Details
Published in:AIChE journal 2007-11, Vol.53 (11), p.2905-2915
Main Author: ORFAO, José J. M
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
approximations
Chemical engineering
Exact sciences and technology
Kinetics
Mathematical functions
non-isothermal
Temperature
temperature integral
thermal analysis
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Summary:The kinetics of processes involving solids may be determined from experiments under non-isothermal conditions. On analyzing data by integral methods, it is necessary to calculate the temperature integral, which does not have an analytical solution. Instead of performing the numerical integration, most of the researchers prefer to circumvent the problem by using approximate expressions, not always adequate. The widespread use of inaccurate approximations does not contribute to a coherent growth of scientific knowledge. In the present article, a critical review of the known approximations is carried out and a clear ranking is established. Moreover, the deviations of the calculated activation energies relatively to the numerical solution are discussed, and some recommendations are proposed. Namely, it is shown that a "novel" expression, previously presented in another form in the well known "Handbook of Mathematical Functions", approximates very accurately the temperature integral and allows to obtain correct values of the activation energy. © 2007 American Institute of Chemical Engineers AIChE J, 2007
ISSN:0001-1541
1547-5905
DOI:10.1002/aic.11296