A dilution refrigerator is an essential apparatus for achieving sub-Kelvin temperatures. Porous-media heat exchangers used inside dilution refrigerators at temperatures below 100 mK are crucial components that determine their optimal performance. In this study, a numerical model of a porous-media heat exchanger is developed. The local thermal non-equilibrium heat transfer model captures the Kapitza heat transfer between solid and fluid components, whereas the coupled Brinkman-Forchheimer and Navier-Stokes equations describe fluid flows in porous media. Results indicate that a liquid gap can enhance the thermal conduction between the flow channel and porous media, thus improving the heat-exchange efficiency of the porous media. For a constant-volume and -thickness porous media, the most suitable length-to-width ratio is 5. The concentrated phase exhibits a lower outlet temperature, whereas the dilute phase exhibits an appropriate pressure drop. For a constant-volume and -length porous media, the optimal width-to-thickness ratio is 10, which provides the best thermal and hydrodynamic performances. For a full-width liquid gap, increasing its thickness enhances both the thermal and hydrodynamic performances but also increases the usage of 3He. Under a constant volume of liquid gap, a partial-width liquid gap can improve the heat-exchange efficiency, thus achieving better thermal and hydrodynamic performances than the conventional full-width one.

中文翻译：

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几何结构对亚开尔文多孔介质换热器的影响

稀释制冷机是实现亚开尔文温度的重要设备。温度低于 100 mK 的稀释制冷机内使用的多孔介质热交换器是决定其最佳性能的关键组件。在这项研究中，开发了多孔介质换热器的数值模型。局部热非平衡传热模型捕获固体和流体成分之间的卡皮查传热，而耦合的 Brinkman-Forchheimer 和 Navier-Stokes 方程则描述多孔介质中的流体流动。结果表明，液体间隙可以增强流道与多孔介质之间的热传导，从而提高多孔介质的换热效率。对于恒定体积和厚度的多孔介质，最合适的长宽比为5。浓相表现出较低的出口温度，而稀相表现出适当的压降。对于恒定体积和长度的多孔介质，最佳宽厚比为 10，这可提供最佳的热性能和流体动力性能。对于全宽液体间隙，增加其厚度不仅可以增强热性能和流体动力性能，而且还可以增加 3He 的使用量。在液隙体积恒定的情况下，部分宽度液隙可以提高换热效率，从而获得比传统全宽度液隙更好的热性能和流体动力性能。