數值模擬外橢球體與內球體間之層流自然對流熱傳

Numerical simulation of free convection heat transfer between outer ellipsoid and inner sphere

陳玟瑞(Wen Ruey Chen)

液壓半徑比與軸比 ； hydraulic radius ratio and axis ratio

冷凍空調&能源科技

119期（2020 / 01 / 10）

36 - 46

繁體中文;英文

數值模擬液壓半徑比與軸比效應之牛頓流體在等溫邊界條件介於外橢球體與內球體間之自然對流熱傳現象。在一穩定溫度變化之等溫邊界條件為內球面為等溫熱面同時外橢球為等溫冷面。有系統的模擬計算完成幾個不同的普郎多數和某一範圍的萊利數，在流場和溫度場上的幾何比參數（Ω和R）之效應解出平均紐賽數。控制方程式分別為渦旋、流線函數、能量方程式在球極座標系統表示之。參數探討所引導的結果更進一步展現熱流場主要是以固定的普朗多數0.7，萊利數範圍從10^3到10^5，和參數（ln Ω）從-0.8到8.0的範圍。針對以上，平均熱傳率傳遞穿越過不同複合幾何環間的熱對流結構詳述有一重要效應。

The effects of hydraulic radius ratio and axis ratio with a Newtonain fluid have been investigated numerically to determine heat transfer by natural convection between the sphere and ellipsoid with isothermal boundary conditions. The inner sphere and outer ellipsoid were heated and cooled in a steady change of temperature. Calculations were carried out systematically for a range of the Rayleigh numbers to determine the average Nusselt numbers which are affected by the geometric ratio parameters (Ω and R) on the flow and temperature fields. The governing equations, in terms of vorticity, stream function and temperature are expressed in a spherical polar coordinate system. Results of the parametric study conducted further reveal that the heat and flow fields are primarily dependent on the Rayleigh number, hydraulic radius ratio, and axis ratio, for a fixed Prandtl number of 0.7, with the Rayleigh number ranging from 10^3 to 10^5 , and the parameters (ln Ω) varying from -0.8 to 8.0. Above all, the specification of different convective configurations has a significant effect on the average heat transfer rate across the composite annulus gap.

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