考慮重力沉降效應的旋轉奈米流體層熱不穩定性

Abstract

本研究探討一上下兩水平無限延伸平板間充滿奈米流體並受到底部加熱與旋轉作用下的熱穩定性行為，並進行線性穩定性分析。為更準確描述奈米粒子與基底流體間的相對滑移現象，所採用的對流傳輸模型除考慮布朗運動與熱泳效應外，亦納入重力沉降機制。研究對象為氧化鋁–水基奈米流體，考量三種代表性奈米粒子粒徑（20 nm、40 nm、60 nm），以分析重力沉降對熱不穩定性的影響。結果顯示，旋轉效應（以泰勒數 Ta 表示）對系統具有穩定化作用，然而此穩定效果會隨奈米粒子體積分率的增加而逐漸減弱。當重力沉降效應增強時，系統穩定性明顯提升，且與熱泳效應的交互作用可能在低泰勒數條件下引發振盪型對流模式的出現。隨著泰勒數的增加，振盪模式逐漸受到抑制，並轉由靜態模式主導不穩定性。當泰勒數達到足夠大時，對流初始狀態將穩定地由具有較高臨界波數的靜態模式所控制。值得注意的是，所觀察到的熱不穩定性特徵與傳統旋轉一般黏性流體層系統顯著不同，顯示重力沉降所導致的奈米粒子遷移機制在調控旋轉奈米流體層對流時的穩定性過程中扮演關鍵角色。

This study focuses on the linear stability analysis of a nanofluid layer confined between two horizontal boundaries, uniformly heated from below and subjected to rotational motion. The convective transport model incorporates gravity-induced nanoparticle settling to account for interfacial slip between the dispersed phase and the base fluid, alongside conventional mechanisms such as thermophoresis and Brownian diffusion. To assess the influence of gravitational settling on flow instability, three representative nanoparticle diameters—20 nm, 40 nm, and 60 nm—are considered for an aluminum oxide–water nanofluid system. The results indicate that rotation, quantified by the Taylor number (Ta), generally stabilizes the flow. However, this stabilizing influence weakens progressively with increasing nanoparticle volume fraction. The presence of gravitational settling significantly enhances stability, and its interaction with thermophoretic effects can give rise to oscillatory modes at lower rotation rates. As Ta increases, oscillatory behavior is suppressed, and stationary modes become dominant. At sufficiently large values of Ta, the onset of instability is consistently governed by stationary modes characterized by higher critical wavenumbers. Importantly, the observed instability characteristics differ substantially from those of classical rotating viscous fluids, underscoring the pivotal role of gravity settling in shaping the onset and structure of convective instability in rotating nanofluid systems