Аналитическое исследование температурных полей и термических напряжений при нагреве простых тел одновременно конвекцией и излучением. Сообщение 1
Journal Title: Математичне моделювання - Year 2016, Vol 1, Issue 2
Abstract
ANALYTICAL STUDY OF TEMPERATURE FIELDS AND THERMAL STRESSES WHEN HEATING SIMPLE BODIES SIMULTANEOUSLY BY CONVECTION AND RADIATION. MESSAGE 1. Gorbunov A.D. Ukleina S.V. Abstract Relevance. To date, there is a large number of engineering techniques for calculating the joint radiant- convective heating of bodies. However, the solutions obtained are rather complicated and cumbersome even in a simplified formulation for the model of thermally thin bodies. The purpose of this paper is to obtain simpler dependencies. In addition, in these articles there are no formulas for calculating thermal stresses. The main task is to develop a simple and effective technique for calculating the temperature and thermal stress fields for convective radiation heating of bodies of simple geometric shapes. Conclusions 1. On the basis of linearizing substitution, a simple and effective engineering method for calculating the heating by radiation and convection of bodies of simple geometric shapes in the form of a plate, a cylinder, and a ball is developed for any Fourier numbers. 2. The method of dividing the heating process into two characteristic cases is used, when the number of Bio is greater than the Stark radiation number and vice versa, which made it possible to reduce the number of variables and present the solution of the problem in tabular and graphical types of execution. 3. For the thermally thin body model, a solution is obtained in a simplified form. 4 The region of linear variation with time of the temperature field is found similar to the regular regime with purely convective heating. 5. A simple formula is obtained for calculating the time of heating the body to a given temperature, which makes it possible to quickly determine the most efficient heating option. 6. Formulas for calculation of axial thermal stresses at any point of the body, on the surface and at the center are obtained. 7. Comparison of the methods with the numerical solution showed that the error in determining the temperatures does not exceed 10% and it can be considered acceptable for engineering calculations. Prospects: These studies will make it possible to contribute to the development of methods for approximate analytical solutions in nonlinear nonstationary heat conduction problems. References [1]. Kavaderov A.V., Samoilovich Yu. A. Nagrev tonkix tel odnovremenno convekciey I izlycheniem [Heating of thin objects simultaneously by radiation and convection] EPJ 1959. т. 2. no. 7. pp. 110–113. (in Russian). [2]. Vidin YU.V. Neustanovivsheyesya temperaturnoye pole v plite pri sovmestnom deystvii teplovogo izlucheniya i konvektsii [Unsteady temperature field in the plate under the combined (simultaneous?) impact of thermal radiation and convection]. EPJ 1967. т. 12. no. 5. pp. 669–671. (in Russian). [3]. Vidin YU.V., Ivanov V.V. Raschet temperaturnykh poley v tverdykh telakh, progrevayemykh konvektsiyey i radiatsiyey odnovremenno. [Calculation of temperature fields in solids heated by convection and radiation simultaneously.] – Krasnoyarsk: KPI. 1965. 144 p. (in Russian). [4]. Ivanov V.V. Teploprovodnost' tverdykh tel, progrevayemykh konvektsiyey radiatsiyey odnovremenno [Thermal conductivity of solids heated by radiation convection simultaneously]. Izvestiya Vuzov. Power engineering. 1967. no. 3. – pp.144–147. (in Russian). [5]. Postnik Yu.S. Temperaturnyy rezhim plastiny i tsilindra, nagrevayemykh odnovremenno izlucheniyem i konvektsiyey [The temperature regime of a plate and a cylinder, heated simultaneously by radiation and convection]. IFZh. 1969. T.XI. no.6. pp. 1082–1086. (in Russian). [6]. Salomatov V.V. Temperaturnyy rezhim tverdykh tel pri sovmestnom vozdeystvii radiatsii i konvektsii. [The temperature regime of solids under the combined effect of radiation and convection]. Izv. AN SSSR, Energy and Transport. no. 4. 1969. pp. 91–97. (in Russian). [7]. Furman A.V., Fuks G. Analiticheskiy raschet nagreva tel odnovremenno izlucheniyem i konvektsiyey. [Analytic calculation of heating of objects (agents?) simultaneously by radiation and convection], Izv. Universities. Ferrous metallurgy. 1967. No. 6. pp. 139–142. (in Russian). [8]. Gorbunov A.D., Ukleina S.V. Analiticheskoye issledovaniye nagreva tverdykh tel radiatsiyey. Soobshcheniye 3 [Analytical study of the heating of solids by radiation. Message 3]. Mathematical modeling. Dneprodzerzhinsk: DGTU, 2015. no 2 (33). pp. 65–68. (in Russian). [9]. Gradshtein I.S, Ryzhik I.M. Tablitsy integralov, summ, ryadov i proizvedeniy [Tables of integrals, sums, series and products]. Moscow: Science. Fizmatlit, 1971. 1108 p. (in Russian). [10]. Gorbunov, A. D. K analiticheskomu raschetu termicheskikh napryazheniy pri konvektivnom nagreve tel prostoy formy [On the analytical calculation of thermal stresses in the convective heating of simple form objects]. Mathematical modeling. Dneprodzerzhinsk: DGTU, 2011. No.1 (26). – pp.39–45. (in Russian). [11]. Gorbunov A.D., Uklein S.V. Inzhenernaya metodika rascheta poley temperatur i termicheskikh napryazheniy na nachal'noy stadii radiatsionno- konvektivnogo nagreva (okhlazhdeniya) tel pri peremennykh koeffitsiyentakh teploobmena i temperature sredy [Engineering Methods for temperature and thermal stresses fields calculation in the initial stage of convective and radiative heating (cooling) of objects within variable coefficients of heat transfer and temperature]. PROBLEMELE ENERGETICII REGIONALE TERMOENERGETICĂ. Moldova. 2016. no 2 (31) – pp. 69–76. (in Russian).
Authors and Affiliations
А. Д. Горбунов, С. В. Уклеина
Keywords
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