科資中心編號 RA78-2629

題　　　名 自由邊界垂直平直平行板間自然與混合對流熱傳之研究

Studies in Free and Mixed Convection Heat Transfer between Vertical Parallel Plates Subject to Free Boundary.

研　究　者 黃文雄 ; 郭鴻森

HUANG,WEN-HSIUNG ; KOU,HONG-SEN

機構　名稱 大同工學院機械工程系(TTCTMEE)

經費　來源 行政院國家科學委員會(NSC)

補助　金額 247000

補助　編號 NSC77-0401-E036-02

研究開始日期 1987/08

研究結束日期 1988/07

出版　日期 1988/08

頁　冊　數 116

語　　　文 英文

建檔　日期 1998/07

原件　提供 行政院國家科學委員會(NSC) 微縮片號: NSC77-0401-E036-002 2片115幅

科資分類號 IF;IF0602

關　鍵　詞 熱傳遞 ; 垂直流道 ; 自然及混合對流

Heat transfer ; Vertical channels ; Free and mixed convection

摘　　　要

由於在電子組件散熱系統,熱交換器以及太陽能系統設計中,垂直流道是一個很常見的配置.因此,在對稱或不對稱加熱之流道中的穩流自然及混合對流問題遂成為近年來相當熱門的研究題目.在電子冷卻的應用上,成列的電路板被安置於電子系統內部而形成此垂直流道配置.而流體即在其中流動以帶走元件所產生的熱量.

本報告的主要內容由一系列對於垂直流道內的對流熱傳研究之結果所構成.第一章考慮局部完全展開流(Locally fully developed flow)之熱傳特性.如同熟知的強制對流流動,在流道內的自然對流流場亦包含進口區及完全展開區二個區域.進口區的長度可經由有限差分數值法來求得;而完全展開區內之納瑟數(Nusselt number),溫度分佈及速度分佈則可由積分動量及能量方程式來求其解析解.在用整體流場溫度(Bulk mean temperature)作為參考溫度的定義之下,三種基本熱邊界條件(即等溫-等溫,等溫-等熱流量及等熱流量-等熱流量)的納瑟數及溫度分佈皆被解出,以研究其對流場的不同影響.

第二章目的在針對垂直流道內層流混合流的熱傳特性進行數值研究.空氣自然對流由浮力效應引起,自二個次流道(Subchannel)向上流動,而在下游混合並繼續上升.速度,溫度以及壓力的分佈,經由求解拋物線型邊界層方程式而得,也因此可求出沿各壁面的局部以及平均納瑟數.在計算過程中,二平行的側板考慮為對稱等溫的情形,而中間板部份則有等溫及等熱流量二種邊界條件.此外,由計算結果可以進一步探討混合的現象,而且中間板的幾何條件對二側板間熱傳性能的影響也可一併求出.

第三章目的在於以數值方法探討處於無限外界之下,二等溫且長度及厚度皆為有限值之垂直平行板間的層流自然對流問題.由求解橢圓型統制方程式及利用自由邊界處理方法(Free boundary),來計算整個流場的速度,溫度和壓力分布,以及在板面上之局部納瑟數.葛拉修數(Grashof number)的計算範圍為10²-10⁶,且包括對稱及不對稱加熱二種情形,尤其是二板溫差比 .gamma. /sub T/對流場的影響方面.最後可以針對各個物理配置,計算其平均納瑟數與葛拉修數之間的關係.

本報告最後部份將前各章的結論同列於第四章,以做綜合比較.現及未來進行之研究題目及方向亦在此部份提及. 在此,作者感謝中華民國國家科學委員會的支持,本研究方得以完成.同時亦感謝大同公司CAD/CAM中心在數值模擬方面給予的協助.

The problems of laminar free/mixed convection flows within symmetrically or asymmetrically heated, vertical channels have recently been the topics of interest because they are frequently encountered in cooling of electronic equipment as well as designing of solar collector systems, trombe wall channels, and even heat exchangers. In the electronic cooling application, an array of circuit cards, on which electronic components are mounted, is positioned vertically in a cabinet to form such channels through which the cold fluids pass.

The major parts of this report just stem from a series of studies on the convection heat transfer between vertical parallel plates. In chapter one, the work is to sutdy the thermal characteristics of free convection in the locally fully developed flows within asymmetrically heated vertical channels. Similar to that in the well known forced convection internal flow, the flow field may include entrance region and fully developed region simultaneously as channel is long enough. The thermal entrance length in the developing region for air is calculated numerically through the finite difference method with the model of boundary layer equations. For the fully developed region, the Nusselt number and generalized temperature profiles in terms of bulk mean temperature, as well as velocity distribution are carried out analytically by means of the integrations on the momentum and energy equations. Results for three different combinations of thermal boundary conditions on the respective wall surfaces (i.e. isothermal-isothermal, isoflux-isothermal, and isoflux- isoflux) are provided to illustrate their distinctly substantial influences with rather clear expressions.

Chapter two is concerned with the numerical study of the heat transfer characteristics of the laminar mixing flow within a vertical channel. Free convection flows are induced by buoyant force from the sub-channels and mix upward in the downstream main channel. The parabolic boundary layer equations are solved to obtain the velocity, temperature, and pressure distributions for the whole flow field, as well as Nusselt numbers along the plate walls. In the computation, the parallel side walls are considered isothermal and symmetric heating. Results for both isothermal and isoflux central plate cases are presented. The mixing phenomena are investigated. and the influence of the central plate on the heat transfer performance is also evaluated.

Chapter three is concerned with the numerical investigation of the laminar free convection flow between two isothermal, vertical parallel plates which are located in the infinite environment and have finite thicknesses and lengths. The elliptic type governing equations, subject to free boundary conditions, have been solved to sutdy the velocity, temperature, and pressure distributions throughout, as well as local Nusselt numbers from 10/sup 2/ to 10/sup 6/ are presented for both symmetric and asymmetric heating cases, and the influence of wall temperature difference ratio, r'/sub T/ on the flow pattern is also considered. For each case, the relationship between average Nusselt number and Grashof number is obtained after computation.

At the end of this report, a summary of the conclusions obtained from the above researches is given in chapter four.

Finally, the authors wish to acknowledge the National Science Council, R.O.C., for supporting the present research under Grant number: NSC77-0401- E036-02. Appreciation is also expressed to the CAD/CAM CENTER of TATUNG COMPANY for the valuable help in numerical simulation.