已有許多實驗証明沿著工作流體運作擺放適當的複數磁性材料做為蓄熱器的多層結構，能夠有效地提升磁致冷機具的效能。要如何最佳化多層式AMR (Active magnetic regenerator) 是一個屬於多重物里量耦合的問題，但同時也是對室溫磁致冷很重要的課題。截至目前為止，關於多層式AMR研究並不多，但了解多層式AMR是一件迫切且重要的事。研究多層式AMR首先面臨的是熱傳與流體力學耦合的現象，其次相較於單層的AMR結構，多層式AMR要處理非常大量的參數，如磁性材料長度的選擇、組合與材料性質，並且材料可能還需額外的研究。為了解決這些複雜的問題，使用COMSOL軟體處理熱傳與流體力學，同時利用Gennes model進行磁性材料的特性計算。在本論文中使用GdxTb(1-x)合金進行二層與三層AMR結構的研究。其研究結果証實使用雙層AMR結構能夠使得致冷能力達到二倍以上，並且三層結構能夠再優化雙層AMR結構的表現。最後提出一個First-order approximation與Cooling index能夠直接經由參數估算其組合能夠達到的致冷能力。

It has been demonstrated experimentally that grading the regenerator along the flow direction with multiple magnetocaloric materials (MCMs) with varying Curie temperatures improves the performance of magnetic refrigeration significantly. The optimization of the graded active magnetic regenerator (AMR) is a multiphysics problem, which is crucial to the realization of room-temperature magnetic refrigeration. Until now, only few models have been built and further work to understand the grading effects is urgently needed. In addition to the challenges of the coupling of magnetic, heat transfer and fluid dynamic phenomena and the vast parameter space of the graded regenerator (e.g. composition and geometry), relevant material properties of the MCMs may not yet be available for modeling. To address these issues, a COMSOL model with key material properties estimated by the mean field theory and the de Gennes model has been built. In this paper, two-segment regenerators composed of GdxTb(1-x) alloys are studied first. Compared to a pure Gd regenerator, it is demonstrated that a two-segment one can achieve a >2-time increase in cooling capacity. And three-segment one can improve the performance of two-segment cases. Furthermore, the temperature of the fluid
, which can be estimates using cooling index, is found to correlate strongly with the cooling capacity, and could potentially serve as an index for performance prediction. Finally, using the first-order approximation could directly estimate the cooling capacity with parameters. The estimation using cooling index method and first-order approximation could survey vast parameters in a short time, which can save much time.

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