含异物电子器件元件温度场的数学模型

V.I. Havrysh
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引用次数: 0

摘要

已经开发了用于确定温度场的线性和非线性数学模型,并随后用于分析具有半透明外来夹杂物的各向同性介质中的温度状态,这些介质也受到外部热负荷的影响。为了解决非线性边值问题,引入线性化函数,利用线性化函数对原非线性热传导方程和非线性边界条件进行线性化,得到了相对于线性化函数和部分线性化边界条件具有偏导数、不连续系数和奇异系数的部分线性化二阶微分方程。对于部分线性化的微分方程和边界条件的最终线性化,采用分段常数函数根据夹杂物边界表面上的一个空间坐标逼近温度。对得到的线性边值问题,采用Hankel积分变换方法求解,得到了解析解,并确定了引入的线性化函数。为了对外部热负荷引起的温度行为和热交换过程进行数值分析,开发了软件工具,用于创建依赖于空间坐标的温度分布的几何图像。所得结果表明,所建立的非均质介质外加热换热过程的数学模型与实际物理过程相符合。所得结果表明,所建立的非均质介质外加热换热过程的数学模型与实际物理过程相符合。所建立的模型可以分析外部热负荷下具有外来元素的环境的热阻。因此,可以增加它并保护它免受过热,这不仅会导致单个元件的破坏,而且会导致整个结构的破坏。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mathematical Models of the Temperature Field in Elements of Electronic Devices with Foreign Inclusion
Linear and non-linear mathematical models for the determination of the temperature field, and subsequently for the analysis of temperature regimes in isotropic media with semi-transparent foreign inclusions that are also subject to external heat load, have been developed. To solve the nonlinear boundary-value problem, a linearizing function was introduced, using which the original nonlinear heat conduction equation and nonlinear boundary conditions were linearized, and as a result, a partially linearized second-order differential equation with partial derivatives and discontinuous and singular coefficients relative to the linearizing function and partially linearized boundary conditions was obtained. For the final linearization of the partially linearized differential equation and boundary conditions, the approximation of the temperature according to one of the spatial coordinates on the boundary surfaces of the inclusion was performed by piecewise constant functions. To solve the obtained linear boundary value problem, the Hankel integral transformation method was used, as a result of which an analytical solution was obtained, which determines the introduced linearizing function. For the numerical analysis of temperature behavior and heat exchange processes caused by external heat load, software tools have been developed, which are used to create a geometric image of temperature distribution depending on spatial coordinates. The obtained results indicate the correspondence of the developed mathematical models of the analysis of heat exchange processes in heterogeneous media with external heating to a real physical process. The obtained results indicate the correspondence of the developed mathematical models of the analysis of heat exchange processes in heterogeneous media with external heating to a real physical process. The developed models make it possible to analyze environments with foreign elements under external thermal loads regarding their thermal resistance. As a result, it becomes possible to increase it and protect it from overheating, which can cause the destruction of not only individual elements, but also the entire structure.
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