Thermal State of a Region with a Thermally Insulated Moving Boundary

IF 1 4区 物理与天体物理 Q4 PHYSICS, APPLIED
E. M. Kartashov
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引用次数: 0

Abstract

Mathematical model representations of the temperature effect in regions with a thermally insulated moving boundary are developed. The boundary conditions for thermal insulation of a moving boundary are formulated both for locally equilibrium heat transfer processes within the classical Fourier phenomenology and for more complex locally nonequilibrium processes within the Maxwell–Cattaneo–Lykov–Vernott phenomenology, taking into account the finite speed of heat propagation. The applied problem of heat conductance and the theory of thermal shock for a region with a moving thermally insulated boundary, free from external and internal influences, is considered. An exact analytical solution of the formulated mathematical models for equations of the hyperbolic type is obtained. Methods and theorems of operational calculus and Riemann–Mellin contour integrals are used to calculate the originals of complex images with two branch points. A mathematical apparatus for the equivalence of functional structures for the originals of the obtained operational solutions is proposed. It is shown that the presence of a thermally insulated moving boundary leads to the appearance of a temperature gradient in the region and, consequently, to the appearance in the region of a temperature field and corresponding thermoelastic stresses of a wave nature. A numerical experiment is presented and the possibility of transition from one form of analytical solution of the temperature problem to another equivalent form is shown. The described effect manifests itself both for equations of the parabolic type based on classical Fourier phenomenology and for equations of hyperbolic type based on the generalized phenomenology of Maxwell–Cattaneo–Lykov–Vernott.

Abstract Image

热绝缘移动边界区域的热状态
摘要 建立了热绝缘移动边界区域温度效应的数学模型表示法。考虑到有限的热传播速度,在经典傅立叶现象学中为局部平衡传热过程和在 Maxwell-Cattaneo-Lykov-Vernott 现象学中为更复杂的局部非平衡传热过程提出了运动边界隔热的边界条件。研究考虑了热传导和热冲击理论的应用问题,该理论适用于具有移动热绝缘边界的区域,不受外部和内部影响。获得了双曲型方程数学模型的精确解析解。运算微积分和黎曼-梅林等值线积分的方法和定理被用于计算具有两个分支点的复数图像的原点。提出了一种数学装置,用于等效所获运算解原点的函数结构。结果表明,热绝缘运动边界的存在会导致该区域出现温度梯度,进而在该区域出现温度场和相应的热弹性应力波。本文介绍了一个数值实验,并说明了从温度问题的一种分析解法过渡到另一种等效解法的可能性。所述效应既适用于基于经典傅立叶现象学的抛物型方程,也适用于基于 Maxwell-Cattaneo-Lykov-Vernott 广义现象学的双曲型方程。
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来源期刊
High Temperature
High Temperature 物理-物理:应用
CiteScore
1.50
自引率
40.00%
发文量
0
审稿时长
4-8 weeks
期刊介绍: High Temperature is an international peer reviewed journal that publishes original papers and reviews written by theoretical and experimental researchers. The journal deals with properties and processes in low-temperature plasma; thermophysical properties of substances including pure materials, mixtures and alloys; the properties in the vicinity of the critical point, equations of state; phase equilibrium; heat and mass transfer phenomena, in particular, by forced and free convections; processes of boiling and condensation, radiation, and complex heat transfer; experimental methods and apparatuses; high-temperature facilities for power engineering applications, etc. The journal reflects the current trends in thermophysical research. It presents the results of present-day experimental and theoretical studies in the processes of complex heat transfer, thermal, gas dynamic processes, and processes of heat and mass transfer, as well as the latest advances in the theoretical description of the properties of high-temperature media.
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