Journals Information
Universal Journal of Applied Mathematics Vol. 1(1), pp. 7 - 13
DOI: 10.13189/ujam.2013.010102
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The Approximation of the Chemical Reaction Rate by Solving the Integral Equation
D.L. Tsyganov1,2,*
1 Instituto de Plasmas de Fusao Nuclear, Laboratorio Associado
2 Instituto Superior Tecnic, Av. Rovisco Pais, 1049-001, Lisboa, Portugal
ABSTRACT
The paper discusses possible methods of approximation of the chemical reaction rate constant for the range of values that lie outside of the experimental temperature range: direct approximation of chemical reaction rate constants obtained by processing experimental values; approximation based on an analytical model of dependence of the integrated process cross-section on energy; and approximation based on the direct solution of the chemical reaction rate constant equation with arbitrary dependence of the integrated process cross-section on energy. The second-order reactions CH4+²Ñ→C±á3+H+M, CH3+²Ñ→C±á2+H+M, CH3+²Ñ→C±á+H2+M were explored. To solve the integrated equation, the variational Tikhonov's regularization method was used. It was shown that this method allowed both estimating the threshold energy value and re-establishing the cross-section form. By using the calculated cross-section we can obtain estimated chemical reaction rate constants over a wide temperature range. The data obtained can be used in various calculations in applied fields, in particular, in hypersonic gas dynamics problems, as well as for filling information system databases.
KEYWORDS
Tikhonov's regularization, Chemical reaction rate constant, Cross-section, Integral equation
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] D.L. Tsyganov , "The Approximation of the Chemical Reaction Rate by Solving the Integral Equation," Universal Journal of Applied Mathematics, Vol. 1, No. 1, pp. 7 - 13, 2013. DOI: 10.13189/ujam.2013.010102.
(b). APA Format:
D.L. Tsyganov (2013). The Approximation of the Chemical Reaction Rate by Solving the Integral Equation. Universal Journal of Applied Mathematics, 1(1), 7 - 13. DOI: 10.13189/ujam.2013.010102.