本文首先針對矩型封閉容器內二維奈米流體自然對流熱傳遞現象，建構其熱質傳遞數學模式。矩型容器之左右直立壁分別為高低溫之等溫面，而上下水平壁皆為絕熱面。本文模式主要考慮（一）奈米微粒與基底流體間相對速度效應；（二）奈米流體熱傳導係數隨奈米微粒濃度、顆粒微流動及流體溫度變化效應；及（三）流動剪應力導致懸浮奈米微粒遷徙現象等。利用所建構理論模式，本文以有限體積數值方法，針對方型容器內奈米微粒均勻分佈之奈米流體穩態自然對流熱傳遞現象進行數值模擬研究；所探討之無因次參數及其範圍分別為：萊利數，RaT,f = 103 ~ 106；普朗特數，Prf = 6.06；奈米微粒體積濃度，cv,i = 0.01、1、4%。數值模擬結果顯示，奈米流體之壁面平均熱傳係數均較基底流體（純水）者為高，且隨微粒濃度增加愈見顯著。另外，本文依先前研究(林建中(2004))所探討實驗條件，進行其模擬分析並發現，當方型容器熱傳壁面間溫差為2K、4K條件下，且奈米流體微粒濃度為cv,i = 0.01%或0.35%時，所預測平均紐賽數值與實驗數據頗為吻合。

In the present study heat and mass transport phenomena associated with two-dimensional natural convection in a rectangular enclosure filled with nanofluids is modeled. The enclosure is differentially heated by two isothermal vertical walls, while the remaining walls are kept adiabatic. A mixture continuum approach was adopted in modeling the problem considered, taking into account the following effects:（a）the relative velocity between the dispersed nanoparticles and the suspending base fluid; （b）the mechanisms and factors inducing thermal conductivity enhancement such as particle concentration, temperature, and micro-convection around the dispersed particles; and（c）the shear-induced particle migration in the nanofluid. Numerical simulations have then been undertaken for steady-state natural convection heat transfer in a square enclosure filled with nanofluid of homogeneous distributed nanoparticles with the relevant dimensionless parameters in the following ranges: the Rayleigh number, RaT,f = 103 ~ 106; the Prandtl number, Prf = 6.06; the volumetric fraction of the nanoparticles, cv,i = 0.01, 1, 4%. In the presence of significantly higher thermal conductivity due to the dispersed nanoparticles, numerical results clearly show that the average heat transfer rate across the enclosure filled with nanofluid can be markedly higher than that with the pure base fluid, depending on the volumetric fraction. Moreover, efforts were taken to perform corresponding simulations to the experiments conducted in the previous study (Lin, 2004). Fairly good agreement was found between the predicted and measured results for the averaged Nusselt number of the nanofluid of lower particle fractions cv,i = 0.01% and 0.35% in a square enclosure differentially heated with a temperature difference of 2 or 4 K.

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