雙重擴散對流與共軛熱傳的數值模擬與弱非線性穩定性分析

Abstract

本研究探討了雙重擴散對流的弱非線性穩定性分析，以及奈米流體的三維雙重擴散對流和共軛熱傳的數值模擬。 在穩定性分析方面，本研究的創新在於用弱非線性穩定分析探討在不穩定開始時，各種參數(路易斯數、普朗特數和溶質瑞利數)對熱傳和質傳的影響。 在奈米流體的雙重擴散對流和共軛熱傳的數值模擬方面，本研究的創新在於: (1) 探討在三維空間中，非均勻溫度和非均勻濃度的邊界條件對奈米流體熱傳和質傳的影響。 (2) 探討在三維空間中，多層固體中各層的材料組成與排列方式對奈米流體共軛熱傳的影響。研究結果顯示相較於均勻溫度和均勻濃度邊界條件，非均勻溫度和非均勻濃度邊界條件能加強對流，進而顯著提升熱傳率。透過改變多層固體中各層的排列方式，能顯著提升熱傳率。這些發現對提高傳熱與傳質效率具有重要指導意義，在傳熱與傳質系統的設計與優化上具有很大的應用潛力。 為了加速數值模擬，本研究開發了求解奈米流體瞬態三維雙重擴散對流和共軛熱傳的多重網格法。此方法可以研究各種形狀、尺寸和位置的多個熱和質量源/匯。多重網格方法可將計算速度提高數百倍。隨著解析度（網格點數）的增加，可以實現更大的加速。這些優點使其在實際工業和工程應用中非常有用。

This study investigates the weakly nonlinear stability of double-diffusive convection, as well as the numerical simulations of three-dimensional double-diffusive convection and conjugate heat transfer involving nanofluids. In the stability analysis, the innovation of this study lies in using weakly nonlinear stability analysis to investigate the effects of various parameters (the Lewis number, Prandtl number and solutal Rayleigh number) on heat and mass transfer at the onset of instability. In the numerical simulations of double-diffusive convection and conjugate heat transfer involving nanofluids, the innovations of this study are: (1) The effects of non-uniform temperature and concentration boundary conditions on three-dimensional heat and mass transfer in nanofluids are investigated. (2) The effects of the composition and arrangement of layers in multilayer solids on three-dimensional conjugate heat transfer involving a nanofluid are explored. The results show that, compared with uniform temperature and concentration boundary conditions, non-uniform temperature and concentration boundary conditions enhance convection and thus significantly improve the heat transfer rate. By changing the arrangement of layers in a multilayer solid, the heat transfer rate can be significantly improved. These findings provide important guidance for improving heat and mass transfer efficiency and have great potential for application in the design and optimization of heat and mass transfer systems. To accelerate numerical simulations, a multigrid method for solving the transient three-dimensional double-diffusive convection and conjugate heat transfer involving nanofluids is developed. The developed methodology allows the investigation of multiple heat and mass sources/sinks of various shapes, sizes, and positions. The multigrid method can accelerate computation by several hundred times. With increasing resolution (number of grid points), a greater speedup can be achieved. These advantages make it very useful in practical industrial and engineering applications.