本論文以元素疊代（Element-by-Element）為基礎的投射有限元素流體解析法（projection finite element fluid analysis）為主，對於均勻紊流流過三維強制對流通道之三維散熱片的暫態流動及其傳熱現象進行分析。以EBE-PCG投射有限元素法取代以往有限元素法解之Navier-Stokes Equation及能量方程式，處理散熱片內部及表面（不含底面）之熱傳導現象時，考慮無速度及壓力變化。並且運用Large Eddy Simulation的紊流模式來模擬紊流流場，以前置處理之共軛梯度法（preconditioned conjugate gradient method）加以疊代而解出流體的速度場，壓力場和溫度場及散熱片的溫度場。
本文提供一套EBE-PCG數值模擬三維風道內強制對流之三維散熱片。目的在不同葉片密度及不同雷諾數下，求得通道流場中的速度場、壓力場及溫度場。研究結果顯示:
（1）紐賽數Nu值會隨著雷諾數增加而變大。
（2）低片密度在低雷諾數下紐賽數Nu值要比高片密度好。隨雷諾數增加，兩者的紐賽數Nu值會越來越接近。

This paper used Element-by-Element projection finite element for a uniform turbulent flow in a three-dimensional forced convection channel with heat sinks. Using Element-by-Element finite element preconditioned conjugate gradient method replaces the traditional finite element method for the Navier-Stokes equation and energy equation, when we treat with the surface and internal parts of fin, considering them with no velocity and pressure variations. Using large eddy simulation method turbulent model simulates turbulent flow with preconditioned conjugate gradient method for iterating process to obtain velocity field, pressure filed, and temperature field.

This paper offered a set of EBE-PCG numerical simulation method to simulate three-dimensional heat sinks in a forced convection channel. The main purpose of this study is to find velocity field, pressure filed, and temperature field of fluid and temperature field of fin under different fin densities and different Reynolds numbers. The results show:

（1） The Nusselt number will increase with increasing Reynolds number.

（2） The Nusselt number at a low fin density is better than a high fin density under the low Reynolds number, and both of the Nusselt number will be getting close with increasing Reynolds number.

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