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ONE MATHEMATICAL MODEL OF HEAT AND MASS TRANSFER IN MICROGRAVITY CONDITION

机译：微重力条件下传热传质的一种数学模型

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Constantly growing interest to space exploration and fast development of space technologies during last two decades require a development of mathematical models and calculation methods for quantitative analysis of physical and chemical processes in space, in particular, heat and mass transfer in micrograviry conditions. There are a lot of specific features of heat and mass transfer in microgravity condition, for example, an absence (or, at least smallness) of the natural convection and forced convection is assumed in the present work. By these reasons the heat and mass transfer process is mainly determined by heat conduction phenomena, but influence of several other effects can be sufficient too, including of diffusion, thermodiffusion and coupled diffusion (for multicomponent systems) must be taken into account too. From the mathematical point of view the problem is described by Onsager's equation system for temperature and concentrations in domain with possibly moving boundary (phase transition with Stefan condition and segregation condition on the moving boundary). Generally speaking, Onsager's equation system can be obtained as a first approximation in asymptotic expansion of usual heat and mass transfer equation system for slow fluid flow, that is with respect to small Reynolds number (fluid flow in such case is described by Stokes equation system). Beside of that, possible heat and mass sources, as a result of chemical reactions and phase transitions, together with small convective terms can be added to Onsager's equation system, created a generalized Onsager's equation system. Methods of analytical and numerical solution of Onsager's equation system and generalized Onsager's equation system arc developed in the present work. Because of smallness of non-diagonal elements of Onsager's matrix, it is proposed to use preliminary transformation of Onsager's equation system to heat conduction equation system. The last system can be solved by any relevant numerical method usually using for solution of heat conduction equation. The similar algorithm is developed for generalized Onsager's equation system. Computational potential theory is better for numerical calculation of the considered class of boundary-value problems, than finite difference or finite element method, because the problem is linear, it is formulated in domain of complex shape and there are possible moving boundaries. Then boundary integral equation method with following numerical solution by boundary element method is applied to the transformed system.
机译：在过去的二十年中，对空间探索和空间技术的快速发展的兴趣不断增长，需要开发数学模型和计算方法来定量分析空间中的物理和化学过程，特别是在微重力条件下的传热和传质。在微重力条件下，传热和传质有许多特定的特征，例如，在本工作中假设不存在（或至少很小）自然对流和强制对流。由于这些原因，传热和传质过程主要由热传导现象决定，但是其他一些影响的影响也就足够了，包括扩散，热扩散和耦合扩散（对于多组分系统）也必须考虑在内。从数学的角度来看，问题是由Onsager方程系统描述的，温度和浓度在可能具有运动边界的区域（具有Stefan条件的相变和运动边界上的偏析条件）。一般而言，对于缓慢的流体流动，即对于较小的雷诺数，Onsager方程组可以作为通常的传热和传质方程组的渐近展开的一阶近似值（在这种情况下，流体流动由Stokes方程组描述） 。除此之外，由于化学反应和相变而产生的可能的热源和质量源，再加上小的对流项，都可以添加到Onsager方程组中，从而创建了广义的Onsager方程组。本工作开发了Onsager方程组和广义Onsager方程组的解析和数值解方法。由于Onsager矩阵的非对角元素很小，因此建议将Onsager方程组的初步变换转换为热传导方程组。最后一个系统可以通过任何相关的数值方法求解，通常用于求解热传导方程。针对广义的Onsager方程系统开发了类似的算法。计算势理论比有限差分法或有限元方法更好地用于所考虑的一类边值问题的数值计算，因为该问题是线性的，它是在复杂形状的域中制定的，并且可能存在移动边界。然后将边界积分法和边界元法通过以下数值解法应用于变换后的系统。

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