Regression models construction for describing the thermal system state of two flat bodies in cyclic contact

V. V. Stulin

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2012), pp. 125-135.

Résumé

Sophisticated analytical solutions of cyclic contact heat transfer problems in the form of integral equations were reduced to criteria form and converted into polynomial models based on the application of experiment planning methodology with economical numerical analysis. Approximation of the desired functions was performed by discrete points using Bonnet formulas, calculations showed quite rapid convergence of approximations and in practical calculations the number of iterations was 7–11. Thirteen criteria equations of regression type were received; the equations contain the most important and diverse in composition and formation structure characteristics of quasi-steady stage of cyclic contact heat exchange. The evaluation of the adequacy of models was made using multiple correlation coefficient.

Détail

Keywords: cyclic contact heat exchange, system of integral equations, numerical experiment planning, models of the regression type.

Bibliographie

[1] Evdokimov M. A., Stulin V. V., “Analytic solution to cyclic contact heat exchange problems for a system of two flat bodies”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2008, no. 1(16), 119–129 | DOI

[2] Stulin V. V., Krupko E. A., “Approximate analytical evaluation of the thermal regime for two flat bodies in any cycle of heat contact”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Mat., 2009, no. 2(10), 65–70

[3] Stulin V. V., “Renewal of the temperature and power of heat sources on the bodies boundary in the space of Laplace transforms”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Mat., 2007, no. 2(6), 94–103 | Zbl

[4] Samarskiy A. A., Vabishchevich P. N., Computational Heat Transfer, Editorial URSS, Moscow, 2003, 784 pp.

[5] Nalimov V. V., Chernova N. A., Statistical Methods of Planning Extreme Experiments, Nauka, Moscow, 1965, 340 pp.

[6] Adler Yu. P., Markova E. V., Granovsky Yu. V., The design of experiments to find optimal conditions, Nauka, Moscow, 1976, 280 pp. | MR

[7] Akhnazarova S. L., Kafarov V. V., Experiment Optimization in Chemistry and Chemical Engineering, Vyssh. shk., Moscow, 1985, 327 pp.

[8] Kafarov V. V., Cybernetic Methods in Chemistry and Chemical Technology, Khimiya, Moscow, 1976, 464 pp.

[9] Hartmann K., Lezki E., Schëafer W., Statistische Versuchsplanung und -auswertung in der Stoffwirtschaft, VEB Deutscher Verlag für Grundstoffindustrie, Leipzig, 1974, 444 pp.; Khartman K., Letskii E., Shefer V., Planirovanie eksperimenta v issledovanii tekhnologicheskikh protsessov, Mir, M., 1977, 552 pp.

[10] Fikhtengolz G. M., A Course on the Differential and Integral Calculus, v. 2, Fizmatgiz, Moscow, 1962, 808 pp.

[11] Poznyak A. L., Skrynchenko Yu. M., Tishaev S. I., Die steels, Metallurgiya, Moscow, 1980, 244 pp.

[12] Storoghev M. V., Popov E. A., Theory of Metal Forming, Mashinostroenie, Moscow, 1977, 423 pp.

[13] Tylkin M. A. Vasiliev D. I., Rogalev A. M. Shkatov A. P., Bel'skiy E. I., Stamps for hot deformation of metals, ed. M. A. Tylkin, Vyssh. shk., Moscow, 1977, 496 pp.