本文利用有限元素法的數值模擬，分析微管道中電滲驅動混合壓力驅動的作用下之流場與熱傳現象。其方程式包含描述電滲流動的統御方程式：（1）Poisson-Boltzmann方程式，用以描述微渠道內電雙層電位勢分佈；（2）Laplace 方程式，用以描述外加電場電位勢分佈；（3）具電驅動力之Navier-Stokes方程式，用以描述微渠道內速度場分佈。(4)具有焦耳熱效應的能量方程式，以描述熱傳現象。
考慮不具有焦耳熱效應時的流場現象及具有焦耳熱效應時的熱傳現象，並利用不同物理參數探討其變化。在管道設計上，探討不同尺寸的管道長度對於流場與熱傳的效應，進一步探討一組管道具有中間障礙物時的影響。
選擇不同外加電場強度，發現外加電場強度越大時壁面臨近流體速度越快，該速度隨著不同流道長度增加而增加，外加電場強度對溫度及紐賽數的效應也有相同趨勢的變化。固定外加電場強度，改變雷諾數時，隨著雷諾數的增加，壁面效應較小。在具有障礙物的管道中，因受限低雷諾數的影響，並不會產生分離流及迴流區。

This study uses the numerical simulation by the Finite Element Method(FEM) to analyze the flow field and heat transfer in electroosmotic flow mixed pressure driven flow. The governing equations used to describe electroosmotic flow include: (1)Poisson-Boltzmann equation for the electric field of electric double layer(EDL),(2)Laplace equation for the applied electric field (3)Navier-Stokes equation with electriokinetic body force for the velocity field, and(4)Energy equation with Joule heating for heat transfer.
The flow field is analyzed when Joule heating effect does not exist, and the heat transfer is analyzed when Joule effect exists. Using different physical parameters discusses different variations. This paper investigates how the different channel lengths affect the flow field and heat transfer. In addition, the channel with a block is also studied in the medium.
The velocity fluid increases near the wall when the applied electric field is stronger. Velocity, temperature and Nusselt number distribution have increased with an increase in the channel lengths. The wall effect decreases with increasing Reynolds number when the applied electric field is fixed. When the channels has a block, flow field did not produce the separation and recirculation flow because of very low Reynolds

[1] P. Gravesen, J. Branebjerg, and O.S. Jensen,“Microfluidics-a review”, Journal of Micromechanics And Microengineering, vol. 3, p. 168-182(1993)
[2] G. Karniadakis and A. Besko, “Microflows and Nanoflowas : fundamentals And simulation,” Academic Press, New York(2005)
[3] M. Bao and W. Wang, “Future of Micro electromechanical Systems (MEMS). ”Ssensors and Actuators A56, p. 135-141(1996).
[4] S. L. Zeng, H. Chuan, J. C. Mikkelsen and J.G. Santiago, “Fabrication and characterization of electroosmotic micropumps,” Sensors and Actuators B, vol. 79 , p. 107-114 (2001).
[5] W. Qu, G. M. Mala and D. Li, “Pressure-Driven Water Flows in Trapezoidal Silicon Microchannels,” Int. J. Heat Mass Transfer,vol. 43, p. 353-364(2000)
[6] M. M. Rahman and F. Gui,” Experimental measurements of fluid flow and heat transfer in microchannel cooling passages in a chip substrate,” ASME Adv. Electronic Packaging, vol. 4, p.685-692(1993)
[7] W. Urbanek, J. N. Zemel and H. H. Bau, “Investigation of the temperature dependence of Poiseuille numbers in microchannel flow,” J. Micromechanics and Microengineering, vol. 3, p. 206-208(1993)
[8] D. Burgreen and F. R. Nakache, “Electrokinetic flow in ultrafine capillary slits,” J. Phys. Chem., vol. 68, p. 1084(1964)
[9] C. L. Rice and R. Whitehead, “Electrokinetic flow in a narrow cylindrical capillary,” J. Phys. Chem., vol. 69, p. 4017-4024(1965)
[10] C. Yang and D. Li, “Electrokinetic effects on pressure-driven liquid flows in rectangular micro channels, ” J. Colloid Interface Sicence, vol. 194, p. 95-107(1997)
[11] C. Yang and D. Li, “Analysis of electrokinetic effects on the liquid flow in rectangular micro channels, ” Colloid and Surface A: Phyicochemical and Engineering Aspects, vol.143, p. 339-353(1998)
[12] R. J. Yang, L. M. Fu and Y. C. Lin, “Electroosmotic entry flow in Microchannels,” J. Colloid Interface Science, vol. 244, p. 173-179(2001)

[13] S. Arulanandam and D. Li, “Liquid transport in rectangular microchannels by electroosmotic pumping”, Colloids and Surfaces A: Phyicochemical and Engineering Aspects, vol. 161, p. 89-102(2000)
[14] X. Xaun, B. Xu, D. Sinton and D. Li, “Electroosmosis flow with joule heating effects,” Lab Chip, vol. 4, p. 230–236.(2004)
[15] W. B. Reuss, D. A. Saville and W. R. Schowalter, “Colloidal Dispersions Cambridge Monographs on Mechanics and Applied Mathematics”, Cambridge University Press, Cambridge (1989)
[16] R. J. Hunter, “ Zeta Potential in Colloid Science: Principles and Appliciations,” Academic Press, New York(1981)
[17] G. M. Mala, D. Li, C. Werner, H. J. Jacobasch and Y. B. Ning, “Flow characteristics of water through a microchannel between two parallel plates with electrokinetic effects,” Int. J. Heat and Fluid Flow, vol. 18, p. 489-496(1997)
[18] M. S. Chun and H. W. Kwak, “Electrokinetic flow and electroviscous effect in a charged slit-like microfluidic channel with nonlinear Poisson-Boltzmann field,” Korea-Australia Rheology J , vol. 15, p. 83-90(2003)
[19] C. Yang, D. Li, Masliyah and H. Jacob, “Modeling forced liquid convection in rectangular microchannels with electrokinetic effects ,” Int. J. Heat Mass Transfer,vol. 41,p. 4229-4249(1998)
[20] Z. W. Chen，”毛細電滲微流泵的流行與驅動”，機械工程學報，vol. 42，p. 22-26(2006)
[21] N. A. Patankar, and H. H. Hu, “ Numerical Simulation of Electroosmotic Flow,” Analytical Chemistry, vol. 70, p. 1870-188 (1998)
[22] S. V. Ermakov, S. C. Jacobson and J. M. Ramsey, “ Computer Simulations of Electrokinetic Transport in Microfabricated Channel Structures,” Analytical Chemistry, vol. 70, p. 4494-4504 (1998)
[23] S. V. Ermakov, S. C. Jacobson and J. M. Ramsey, “ Computer Simulations of Electrokinetic Injection Techniques in Microfluidic Devices ,” Analytical Chemistry, vol. 72, p. 3512-3517(2000)

[24] H. Wang, P. Ioventitti, E. Harvey, and S. Masood, “Passive Mixing in Microchannels by Applying Geometric Variations,” Proceedings of SPIE, vol. 4982, p. 282-289(2003)
[25] X. Fu, S. Liu, X. Ruan, and H. Yang, “Research on Staggered Oriented Ridges Static Micromixers,” Sensor and Actuators B, vol. 114, p. 618-624.(2006)
[26] A. M. Jacobi, “Flow and heat transfer in microchannels using a microcontinuum approach,” ASME J. Heat Transfer, vol. 111, p. 1083-1085(1989)
[27] A. Eringen, “Simple microfluids,” Int. J. Eng. Sci., vol. 2, p. 205-217(1964)
[28] G. M. Mala, D. Li, C. Werner, H. J. Jacobasch and Y.B. Ning ,“ Flow Characteristics of Water Through a Microchannel between Two Parallel Plates with Electrokinetic Effects,” Int. J. Heat and Fluid Flow, vol. 18, p. 489-496(1997)
[29] C. Yang and D. Li, “ Electrokinetic Effects on Pressure-Driven Liquid Flows in Rectangular Microchannels,” J. of Colloid and Interface Science, vol. 194, p. 95-107(1997)
[30] T. S. Zhao and Q. Liao, “Thermal effects on electro-osmotic pumping of liquids in microchannels,” J. Micromech Microeng. vol. 12, p. 962-970(2002)
[31] G. Y. Tang, C. Yang, C. J.Chai and H. Q. Gong, “Electroosmotic Flow and Capillary Electrophoresis with the Joule Heating Effect: The Nernst-Planck Equation versus the Boltzmann Distribution,” Langmuir, vol. 19, p. 10975-10984(2003)
[32] D. Maynes and B. W. Webb, “Fully-Developed Thermal Transport in Combined Pressure and Electro-Osmotically Driven Flow in Microchannels,” ASME J. Heat Transfer, vol. 125, p. 889-895(2003)
[33] G. Y. Tang, C. Yang, J. C. Chai, and H. Q. Gong, “Joule Heating Effects on Electroosmotic Flow and Mass Species Transport in a Microcapillary,” Int. J. Heat Mass Transfer, vol. 47, p. 215-227(2004)
[34] C. Yang, D. Li and J. H. Masliyah, “ Modeling Forced Liquid Convection in Rectangular Microchannels with Electrokinetic Effects,” Int. J. Heat Mass Transfer, vol. 41, p. 4229-4249(1998)
[35] C. Canuto, “Spectral Methods: Fundamentals in Single Domains,” Berlin, Springer-Verlag(2006)
[36] J. W. Thomas, “Numerical Partial Differential Equations: Finite Difference Methods,” New York, Springer(1985)
[37] W. Malalasekera, “An Introduction to Computational Fluid Dynamics: the Finite Volume Methods,” London, Longman(1995)
[38] J. N. Reddy, “An Introduction to the Finite Element Method,” New York, McGraw-Hill(1993)
[39] O. Pironneau, “Finite Element Method for Fluids,” Chichester, Wiley(1989)
[40] 王至勤，“有限元素法”，曉園出版社(1985)
[41] R. L. Burden and J. D. Faires, “Numerical Analysis,” Australia, Thomson Brooks(2005)
[42] A. J. Chorin, “Numerical Solution of Navier-Stokes Equations,” Mathematics of Computation, vol. 22, p.745-762(1968)
[43] J T. C.ue, “Numerical Analysis of Vortex Shedding behind a Porous Square Cylinder,” Int. J. Num. Methods for Heat & Fluid Flow, vol. 14, p. 649-663(2004)
[44] T. K. Yang, ”Experimental Study of Electroosmotic Flow in Microchannels with Velocity/Temperature Measurements,” MS Thesis, National Sun Yat-Sen University(2007)
[45] P. Zhang, C. C. Zuo and D. Y. Zhou, “Numerical Simulation on Joule Heating Effect of Electroomotic Flow in Rectangular Microchannels,” J. Fine Chemicals, vol. 23, p. 571-574(2006)
[46] I. T. Wang, “Simulation of Gaseous Flow in a Microchannel,” MS Thesis, National Sun Yat-Sen University( 2003)
[47] Y. C. Huang, “Passive Mixing Enhancements indifferent Geometric Microchannels with Roughened Surfaces,” MS Thesis, National Sun Yat-Sen University(2007)
[48] H. Keisuke and D. Prashanta, “Joule heating effect in electroosmotically driven microchannel flows,” Int. J. Heat Mass Transfer, vol. 47, p. 3085-3095(2004)
[49] 郭勝安，”探討焦耳熱對微流道電滲流的影響”，國立台灣大學工程科學及海洋工程學系碩士論文(2008)
[50] 張志彰，”為管道電滲流場之壓力分佈與混合機制分析”，國立成功大學工程科學系碩士論文(2003)