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https://elib.bsu.by/handle/123456789/304284| Title: | Лучистая теплопроводность в телах с переменной во времени температурой поверхности |
| Other Titles: | Radiative thermal conductivity of bodies with time-variable surface temperature / V.А. Kot |
| Authors: | Кот, В. А. |
| Keywords: | ЭБ БГУ::ЕСТЕСТВЕННЫЕ И ТОЧНЫЕ НАУКИ::Физика |
| Issue Date: | 2023 |
| Publisher: | Минск : БГУ |
| Citation: | Взаимодействие излучений с твердым телом : материалы 15-й Междунар. конф., Минск, Беларусь, 26-29 сент. 2023 г. / Белорус, гос. ун-т ; редкол.: В. В. Углов (гл. ред.) [и др.]. – Минск : БГУ, 2023. – С. 89-92. |
| Abstract: | Рассмотрено уравнение радиационной гидродинамики, когда внутренняя энергия и непрозрачность имеют степенные зависимости от плотности и температуры. Получены высокоточные автомодельные решения при степенном и экспоненциальном законах изменении во времени температуры поверхности. Предложен новый подход к приближенному решению задачи, когда для непрозрачности по Росселанду K имеем K = K (T0)(T/T0)-n, где n – показатель степени, задающий характер поглощения телом излучения. Метод основан на преобразовании исходного уравнения dT / dt = χdTn+4 / dx2, где χ = 16δT30 / (3(n+4)K(T0)p2Cv). При степенном законе уравнение преобразуется в следующее: d2θn+4 / dη2 + (1+k(n+3))ηdθ / dη – 2kθ = 0, где T = T0(t / t0)k θ (η), η = x / √2χTn0t(n+3)k. Решение задачи представлено в виде θ = (1+a ζ) (1- ζ)1/n+3, где ζ = η/η0. Ошибка аналитического решения по сравнению с численным составляет сотые доли процента |
| Abstract (in another language): | The equation for the radiative flow dynamics of a solid body, the dependences of whose internal energy and opacity on its density and temperature are defined by power functions, was considered. The high-accuracy self-similar solutions have been obtained for the radiation wave generated in the body by the laser radiation in the cases where the surface temperature of the body changes by the power or exponential laws. A new approach to the approximate solution of the equation for the radiative thermal conductivity of a body with a Rosseland opacity KR characterized by the power dependence on the temperature KR = KR (T0)(T/T0)-n, where n is the component determining the character of absorption of radiation by the body, has been proposed. The method developed is based on the transformation of the initial equation for the radiative thermal conductivity of a body dT / dt = χdTn+4 / dx2, where χ = 16δT30 / (3(n+4)K(T0)p2Cv) is the coefficient characterizing the heat flow in the body. In particular, in the case where the surface temperature of the body changes by the power law, this equation is transformed into the differential equation d2θn+4 / dη2 + (1+k(n+3))ηdθ / dη – 2kθ = 0, where T = T0(t / t0)k θ (η), η = x / √2χTn0t(n+3)k. The solution of the problem was sought for in the form of the polynomial θ = (1+a ζ) (1- ζ)1/n+3, where ζ = η/η0. The coefficient a was determined with the use of the relation dV(1) / dζ = -(n+3)(n+4)-1(1+k(n+3))η20, and then the integral relation 2(1+k(n+4))∫10θζdζ = η-20 was used. The solutions of the problem with high approximation accuracies have been obtained. The errors of the calculations performed for the two variants of the law of change in the surface temperature of the body, as compared to those of the numerical solutions, comprised hundredths of a percent |
| Description: | Секция 1. Процессы взаимодействия излучения и плазмы с твердым телом = Section 1. Processes of radiation and plasma interaction with solids |
| URI: | https://elib.bsu.by/handle/123456789/304284 |
| ISSN: | 2663-9939 (Print) 2706-9060 (Online) |
| Licence: | info:eu-repo/semantics/openAccess |
| Appears in Collections: | 2023. Взаимодействие излучений с твердым телом |
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