Transport phenomena in bispherical coordinates
Transport phenomena in bispherical coordinates
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双球坐标中的传输现象
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
A. J. Giacomin
中科院分区：
文献类型：
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作者：
P. Gilbert;A. J. Giacomin
输运现象的实践传统上局限于笛卡尔柱面、柱面、球面和双极柱面。对于连续性和运动方程，迪克斯曼增加了环面坐标。我们最近的工作扩展了可用于解决运输问题的几何，将偏心圆柱包括在内。然而，这一简短的可用坐标系不能描述交通现象中遇到的许多几何形状。在这里，我们通过将双球坐标添加到已为其建立变化方程的不断增长的坐标系列表中来解决对传输现象的可用几何的限制。双球坐标使我们能够解决偏心球或角之间的运输问题，而球坐标无法处理这些问题。因此，我们建立了这个坐标系的变方程，并提供了三个实例，展示了如何获得动量、热量和质量传递问题的新的精确解。传统上，输运现象的实践仅限于笛卡尔、柱面、球面和双极柱面。对于连续性和运动方程，迪克斯曼增加了环面坐标。我们最近的工作扩展了可用于解决运输问题的几何，将偏心圆柱包括在内。然而，这一简短的可用坐标系不能描述交通现象中遇到的许多几何形状。在这里，我们通过将双球坐标添加到已为其建立变化方程的不断增长的坐标系列表中来解决对传输现象的可用几何的限制。双球坐标使我们能够解决偏心球或角之间的运输问题，而球坐标无法处理这些问题。因此，我们建立了这个坐标系的变方程，并提供了三个实例，说明如何获得动量、热量和质量传递问题的新的精确解。
The practice of transport phenomena has traditionally been confined to Cartesian, cylindrical, spherical, and bipolar cylindrical. For just the equations of continuity and motion, Dijksman added toroidal coordinates. Our recent work expanded the geometries available for solving transport problems to include eccentric cylindrical. However, this short list of available coordinate systems cannot describe many geometries encountered in transport phenomena. Here, we address this restriction on available geometries for transport phenomena by adding bispherical coordinates to the growing list of coordinate systems for which the equations of change have been developed. Bispherical coordinates allow us to solve transport problems between eccentric spheres or horns, which spherical coordinates cannot handle. We thus develop the equations of change for this coordinate system and provide three worked examples showing how to get new exact solutions to momentum, heat, and mass transfer problems.The practice of transport phenomena has traditionally been confined to Cartesian, cylindrical, spherical, and bipolar cylindrical. For just the equations of continuity and motion, Dijksman added toroidal coordinates. Our recent work expanded the geometries available for solving transport problems to include eccentric cylindrical. However, this short list of available coordinate systems cannot describe many geometries encountered in transport phenomena. Here, we address this restriction on available geometries for transport phenomena by adding bispherical coordinates to the growing list of coordinate systems for which the equations of change have been developed. Bispherical coordinates allow us to solve transport problems between eccentric spheres or horns, which spherical coordinates cannot handle. We thus develop the equations of change for this coordinate system and provide three worked examples showing how to get new exact solutions to momentum, heat, and mass transfer problems.