微流道內非牛頓流體熱傳之黏性耗散效應

Heat Transfer of Non-Newtonian Fluid Flow in a Microchannel with Viscous Dissipation.

溫瑞安(Ruei-An Wen)

指導教授 ： 陳建信

國立虎尾科技大學/工程學院/機械設計工程研究所/碩士(2013年)

摘要

近年來有關微流道內流體熱傳現象之文獻大多數係探討牛頓流體的流動行為分析，然而生醫檢測、化學分析等無法視流體為牛頓流體。 本文主要目的在於探討平行板微流道內冪律流體受電滲與壓力驅動之熱全展熱傳特性，研究發現本問題有五個統御參數，包括：流動特性指數、長度尺度比 (德拜長度與流道半高之比)、無因次化壓力梯度、焦耳熱參數 (焦耳熱與壁面熱通量之比) 以及布林克曼數。本研究直接對電位場、速度場與溫度分佈之解析表示式進行數值積分求解，並進而獲得各項流動與熱傳參數之解答。 研究結果顯示，流動特性指數增加則溫度分佈會增加，在流體加熱情況下，布林克曼數與焦耳熱增加則溫度隨之減少，而長度尺度比減少則溫度隨之減少。 考慮壓力梯度下則溫度變化範圍減少。在流體冷卻情況下，布林克曼數與焦耳熱減少則溫度隨之增加並導致流道中心溫度高於壁面溫度。 在流體加熱情況下，流動特性與焦耳熱增加則紐塞爾數減少，考慮黏性散逸，長度尺度比減少則紐塞爾數隨之減少，壓力梯度與流動特性指數增加則紐塞爾數隨之減少。在流體冷卻情況下，布林克曼數與焦耳熱減少則紐塞爾數隨之增加，而有奇異點。

關鍵字

微流道 ； 電滲 ； 冪律流體 ； 焦耳熱 ； 黏性耗散

並列摘要

Most of the studies pertinent to microchannel flows were concerned with Newtonian fluids in recent years. However, microfluidic devices are usually used to biomedical diagnosis, chemical analysis which may not be treated as Newtonian fluids. An analysis is performed to investigate the heat transfer charateristics of thermally fully-developed, combined electroosmotic and pressure driven flow of non-Newtonian power-law fluids in a parallel plate microchannel. The present problem is found to be governed by five parameters, namely, the flow behavior index, the length scale ratio (ratio of Debye length to half channel height), the dimensionless pressure gradient, the Joule heating parameter (ratio of Joule heating to surface heat flux), and the Brinkman number. The solutions for flow and heat transfer parameters are obtained by numerical integrations of the analytical expressions. The results show that temperature variation can be increased by increasing the flow behavior index. In fluid heating case, the Brinkman number and the Joule heating increases with decreasing the temperature. However, the length scale ratio increases with decreasing the temperature. The dimensionless pressure gradient increases with decreasing temperature variation. In fluid cooling case, the Brinkman number and the Joule heating decreases with increasing temperature, leading to the temperature of channel centerline is higher than surface channel. In fluid heating case, the flow behavior index and the Joule heating increases with decreasing the Nusselt number. To take account of viscous dissipation, the Nusselt number decreases with decreasing the length scale ratio, the Nusselt number decreases with increasing the dimensionless pressure gradient and the flow behavior index. In fluid cooling case, increasing the Nusselt number by decreasing the Brinkman number and the Joule heating while it have singularities.

並列關鍵字

Microchannel flow ； Electroosmosis ； Power-law fluids ； Joule heating ； Viscous dissipation

參考文獻

[1] S. J. Kim and D. Kim, ”Forced Convection in Microstructures for Electronic Equipment Cooling”, ASME J. Heat Transfer, 121,pp.639-645, (1999).

[2] H. Y. Zhang, D. Pinjala , T. N. Wong , K. C. Toh , and Y. K Joshi, ”Single-Phase Liquid Cooled Microchannel Heat Sink for Electronic Packages”, Appl. Therm. Eng., 25, pp.1472-1487, (2005).

[3] G. L. Morini and , M. Spiga , ”The Role of the Viscous Disspation in Heated Microchannel”, ASME J. Heat Transfer, 129, pp308-318, (2007).

[4] C. H. Chen”Forced Convection Heat Transfer in Microchannel Heat Sinks”, Int. J. Heat Mass Transfer, 50, pp.2182-2189, (2007).

ation of an electrostatic micropump for drug-delivery applications, J. Micromech. Microeng 7, 186-188, (1997).