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Abstract
The general method of evaluating the temperature integral for temperature dependent frequency factors have been considered. The values of the temperature integral as evaluated by the present method are in excellent agreement with those obtained numerically.
Approximations for the temperature integral
Their underlying relationship
Abstract
The temperature integral cannot be analytically integrated and many simple closed-form expressions have been proposed to use in the integral methods. This paper first reviews two types of simple approximation expressions for temperature integral in literature, i.e. the rational approximations and exponential approximations. Then the relationship of the two types of approximations is revealed by the aid of a new equation concerning the 1st derivative of the temperature integral. It is found that the exponential approximations are essentially one kind of rational approximations with the form of h(x)=[x/(Ax+k)]. That is, they share the same assumptions that the temperature integral h(x) can be approximated by x/Ax+k). It is also found that only two of the three parameters in the general formula of exponential approximations are needed to be determined and the other one is a constant in theory. Though both types of the approximations have close relationship, the integral methods derived from the exponential approximations are recommended in kinetic analysis.
Abstract
Three rational fraction approximations for the temperature integral have been proposed using the pattern search method. The validity of the new approximations has been tested by some numerical analyses. Compared with several published approximating formulas, the new approximations is more accurate than all approximations except the approximations proposed by Senum and Yang in the range of 5≤E/RT≤100. For low values of E/RT, the new approximations are superior to Senum-Yang approximations as solutions of the temperature integral.
Abstract
Abstract
A new approximate formula for temperature integral is proposed. The linear dependence of the new fomula on x has been established. Combining this linear dependence and integration-by-parts, new equation for the evaluation of kinetic parameters has been obtained from the above dependence. The validity of this equation has been tested with data from numerical calculating. And its deviation from the values calculated by Simpson's numerical integrating was discussed. Compared with several published approximate formulae, this new one is much superior to all other approximations and is the most suitable solution for the evaluation of kinetic parameters from TG experiments.
Abstract
Abstract
Abstract
The accuracy and scope of application of previously reported approximations of the temperature integral were evaluated. The
exact solution was obtained independently by solving the temperature integral numerically be Simpson's rule, the trapezoidal
rule and the Gaussian rule.
Two new approximations have been proposed: