Nonstationary temperature field of a multilayer plate under the periodic action of a heat flux in the presence of self-radiation
UDC 539.3, 517.95 We construct the solution of a one-dimensional nonlinear nonstationary heat-conduction problem for a multilayer plate in the case where one of its bounding surfaces is heated by a heat flux whose intensity varies as a sinusoidal function of time, whereas the opposite surface is coo...
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| Datum: | 2026 |
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| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9886 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 539.3, 517.95
We construct the solution of a one-dimensional nonlinear nonstationary heat-conduction problem for a multilayer plate in the case where one of its bounding surfaces is heated by a heat flux whose intensity varies as a sinusoidal function of time, whereas the opposite surface is cooled down in the process of convective heat exchange with the medium whose temperature varies according to the exponential law. Moreover, we take into account the effect of thermal emission from the heated surface. The solution is constructed by using generalized functions, the appropriate Green's function for the multilayer plate, and linear splines. The exact sums of the series required to improve the rate of convergence of slowly convergent series are found. The results of numerical analyses of the temperature fields in a five-layer plate are also presented. |
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| DOI: | 10.3842/umzh.v78i5-6.9886 |