臺灣博碩士論文加值系統

本文係利用數值方法,針對在波浪形微渠道中的電滲透流與熱傳，做ㄧ探討，並將電動效應和波浪表面的振幅列入考慮。運用簡單的坐標轉換方法將一個複雜的波浪形微管轉換成一個規則的、容易計算的平滑圓管。其統御方程式，包括Poisson - Boltzmann方程式、修正的Navier- Stokes方程式、能量方程式及其相對應的邊界條件也同時轉化至計算區域，然後應用有限差分方法來求解。文中探討在不同的波長振幅比 和電動參數 下，電滲流體流場和溫度場的分布。結果顯示，在波形微管中，表面摩擦係數和局部紐塞數是沿著波浪形微管的流向方向振盪。隨著電動參數 和波長比 的增加，局部紐塞數振盪幅度也隨之增加，但表面摩擦係數相對的減少。在較大的電動參數 和波長比 之下，的確能強化傳熱效果。而在波形平板渠道中，我們將探討在邊界速度滑移和溫度跳躍下的情況下，努森數、艾柯數、熱源G及電位比 對流場及溫度場的影響。結果顯示，表面摩擦係數及局部紐塞數沿著流動的方向，在波長比 的情況下，呈現震盪現象， 其中，隨著努森數及波長比 的增加，紐塞數的振幅也隨之變大，而艾柯數和熱源G 變大，也有相同的效果，但是表面摩擦係數的振幅，卻隨著努森數的增加而變小，因此，較大的努森數及波長比 ，對熱傳效應的改善，是顯著而有效的。此外，當上下板面在不同的電位時，在速度方面，正電位對速度有加速作用，而負電位則有減速作用，甚至會形成逆流。在溫度方面，正電位對有散熱降溫效果，而負電位則會阻礙熱量散失。表面摩擦係數和紐塞數是沿著波浪形微管的流向方向振盪。隨著電位比的增加，局部紐塞數及表面摩擦係數振盪幅度也隨之增加。

This study numerically investigates the electroosmotic flow and heat transfer in a wavy surface of the micro-channels. For the case of wavy micro-tube, the solution takes the electrokinetic effect and the amplitude of the wavy surface into consideration. A simple coordinate transformation method is used to transform a complex wavy micro-tube into a regular, circular tube. The governing equations, including the Poisson-Boltzmann equation, the modified Navier-Stokes equations, and the energy equation with their corresponding boundary conditions are also transformed into the computational domain and then solved by the finite difference method. In chapter 2 , the main objective is to investigate the difference of fluid flow and temperature fields for various wavelength ratio and the electrokinetic parameter .
In chapter 3 and chapter 4, we want to research how the fluid flow and temperature fields are dominated by kinds of wavelength ratio 、Knudsen number、Eckert number、heat generation G and potential ratio. Results show that the distributions of the skin-friction coefficient and the local Nusselt number are oscillatory along the stream-wise direction for the wavy micro-tube . The amplitude of the oscillated local Nusselt number increases with an increase in the electrokinetic parameter and wavelength ratio , but that of the skin-friction coefficient decreases with an increase in the electrokinetic parameter . The heat transfer enhancement is significant for larger electrokinetic parameter and wavelength ratio .The distributions of the local Nusselt number and skin-friction coefficient domenstrate that are oscillatory along the stream-wise direction for the wavy micro-tube .
The oscillated local Nusselt number amplitude increase with an increase in the Knudsen number, heat generation G, Eckert number and wavelength ratio , but skin-friction coefficient amplitude decreases as the Knudsen number increases.
The positive potential increases the velocity, and the negative potential decreases the velocity, even creates back flow,. In wall temperature, the positive potential enhances the heat transfer effects than negative potential does. The amplitude of local Nusselt number and skin-friction coefficient increases as an increase of the potential ratio.

中文摘要………………………………………………………………I
Abstract ………………………………………………………………III
目錄……………………………………………………………………V
圖目錄…………………………………………………………………VII
表目錄…………………………………………………………………VII
符號說明………………………………………………………………X
第一章、緒論
1-1研究目的與背景 ……………………………………………………1
1-2文獻回顧 ……………………………………………………………2
1-3研究方法 ……………………………………………………………4
1-4本文架構 ……………………………………………………………5
第二章、電滲透流在波浪形微管中的熱傳研究
2-1前言與文獻提要 ……………………………………………………6
2-2統御方程式及邊界條件 ……………………………………………8
2-3結果與討論 …………………………………………………………21
第三章、考慮邊界速度滑移及熱源效應下之電滲透流
在水平波形微渠道中的熱傳分析
3-1前言與文獻提要 ……………………………………………………34
3-2統御方程式及邊界條件 ……………………………………………37
3-3結果與討論 …………………………………………………………44

第四章、相異電位對電滲透流在水平波形微渠道中的熱傳研究
4-1前言與文獻提要 ……………………………………………………66
4-2統御方程式及邊界條件 ……………………………………………68
4-3結果與討論 …………………………………………………………74
第五章、結論與展望
5-1 結論 …………………………………………………………………94
5-2 建議與展望 …………………………………………………………97
參考文獻 ………………………………………………………………98
附錄一……………………………………………………………………107
附錄二……………………………………………………………………109

[1]D. Burgreen and F.R. Nakache, Electrokinetic Flow in Ultrafine Capillary Silts, Journal of Physical Chemistry, Vol.68 (1964)pp. 1084-1091.

[2] C.L. Rice, R. Whitehead, Electrokinetic Flow in a Narrow Cylindrical Capillary, Journal of Physical Chemistry, Vol.69 (1965)pp. 4017–4024.

[3]S. Levine, J.R. Marriott, G. Neale, N. Epstein, Theory of Electrokinetic Flow
in Fine Cylindrical Capillaries at High Zeta Potentials, Journal of Colloid and Interface Science ,Vol.52 (1975) pp.136–149.

[4]L.P. Hsu, C.Y. Kao, S.J. Tseng, Electrokinetic Flow Through an Elliptical Microchannel: Effects of Aspect Ratio and Electrical Boundary Conditions, Journal of Colloid and Interface Science, Vol.248 (2002)pp. 176–184.

[5]J. Yang, A. Bhattacharrya, J.H. Masliyah, D.Y. Kwok, Oscillating Laminar Electrokinetic Flow in Infinitely Extended Rectangular Microchannels, Journal of Colloid and Interface Science ,Vol.261 (2003) pp.21–31.

[6]S. Arulanandam, D. Li, Liquid Transport in Rectangular Microchannels by Electroosmotic Pumping, Colloids and Surfaces, Vol.161 (2000)pp. 89–102.

[7]C. Yang, D. Li, Analysis of Electrokinetic Effects on Liquid Flow in Rectangular Microchannels, Journal of Colloid and Interface Science ,Vol.143 (1998) pp.339-353.
[8]R. J. Yang, L. M. Fu, C. C. Hwang, Electroosmotic Entry Flow in a Microchannels, Journal of Colloid and Interface Science, Vol.244 (2001) pp.173-179.

[9]C.Yang, D.Li, J.H.Masliyah, Modeling Forced Liquid Convection in Rectangular Microchannels with Electrokinetic Effects, International Journal of Heat and Mass Transfer, Vol.41 (1998) pp.4229-4249.

[10]D. Maynes, B.W. Webb, Fully-Developed Electro-osmotic Heat Transfer in Microchannels, International Journal of Heat and Mass Transfer,Vol.46 (2003) pp.1359–1369.

[11]D. Maynes, B.W. Webb, The Effect of Viscous Dissipation in Thermally Fully Developed Electro-osmotic Heat Transfer in Microchannels, International Journal of Heat and Mass Transfer,Vol. 47 (2004) pp.987–999.

[12]P. Dutta, A. Beskok, T. C. Warburton, Numerical Simulation of Mixed Electroosmotic/Pressure Driven Microflows, Numerical Heat and Transfer, Part A. Vol.41 (2002)pp. 131-148.

[13]Z. Yang, X.F. Peng, B.X. Wang, Fully Developed Electroosmotically and Hydrodynamically Induced Convection between Two Parallel Plates, Numerical Heat and Transfer, Part A. Vol.50 (2006)pp. 905-926.



[14]P. Dutta, K. Horiuchi, H.M.Yin, Thermal Characteristics of Mixed Electroosmotic and Pressure-Driven Microflows, Computers and Mathematics with Application ,Vol.52 (2006) pp.651–670.

[15]M.I. Char, W.J. Hsu, Heat Transfer of Mixed Electroosmotic and Pressure-Driven Flows in Microtubes with Isothermal Boundary Conditions, International Communications in Heat and Mass Transfer,Vol. 36 (2009) pp.498-502.

[16]J. C. Burns, T. Parks, Peristaltic Motion, Journal of Fluid Mechanics, Vol.29 (1967)pp.731-743.

[17]J.L. Goldstein, E.M. Sparrow, Heat/mass Transfer Characteristics for Flow in a Corrugated Wall Channel, ASME Journal of Heat Transfer, Vol.99 (1977) pp.187-195.

[18]C. C. Wang, C. K. Chen, Forced Convection in a Wavy-wall Channel, International Journal of Heat Mass Transfer ,Vol.45 (2002)pp. 2587-2595.

[19]D. Yang and Y. Liu, Numerical Simulation of Electroosmotic Flow in Microchannels with Sinusoidal Roughness, Colloids and Surface A: Physicochemical and Engineering Aspects Vol.328 (2008) pp.28-33.




[20]J. M. Molho,A. E. Herr, M. Desphande, J. R. Gilbert, M. G. Garguilo, P. H. Paul, P. M. John, T. M. Woudenberg, and C. Connel, Fluid Tranport Mechanisms in Micro Fluidic Devices, in Proc. 1998 ASME Micro-Electro-Mechanical-Systems(MEMS), Los Angeles, CA,（1998） pp. 69-75.

[21] P . H. Paul, M. G. Graguilo, and D. J. Rakestraw, Imaging of Pressure and Electro-kinetically Driven Flows Through Open Capillaries, Analytical Chemistry, Vol. 70,（1998）pp.2459-2467.

[22] E. B. Cummings, S. K. Griffiths, R. H. Nilson, and P. H. Paul, Tissue
Fluids in Microchannel Subjected to an Externally Applied Electric
Potential, Conditions for Similitude Chemistry, Vol. 72,（2000）pp.
2526-2532.

[23] A. E. Herr, J. I. Molho, J. G. Santiago, M. G. Mungal, T. W. Kenny, and M.
G. Gar-guilo, Electroosmotic Capillary Flow with Non Uniform Zeta
Potenital, Analytical Chemistry, Vol. 72,（2000）pp. 1053-1057.

[24] S. C. Jacobson, T. E. McKnight, and J. M. Ramsey, Microfluidic Devices
for Electro-Kinetically Driven Parallel and Serial Mixing, Analytical
Chemistry, Vol. 71,（1999）pp.4455-4459.



[25] N. A. Polson and M. A. Hayes, Electroosmotic Flow Control of Fluids on a Capillary Electrophoresis Microdevice Using an Applied External Voltage, Analytical Chemistry, Vol. 72, no. 10,（2000）pp. 1088-1092.

[26] N. A. Patankar and H. H. Hu, Numerical Simulation of Electroosmotic
Flow, Analytical Chemistry, Vol. 72,（1998）pp. 1870-1881.

[27] S. V. Ermakov, S. C. Jacobson, and J. C. Tamsey, Computer Simulation of Electro-kinetic Transport in Micro Fabricated Channel Structures, Analytical Chemistry, Vol. 70,（1998）pp. 4494-4504.

[28] F. Bianchi, R. Ferriagno, and H. H. Girault, Finite Element Simulation of
an Electro- osmotic-Driven Flow Division at a T-junction of Microscale
Dimension, Analytical Chemistry, Vol. 72,（2000）pp. 1987-1993.

[29] G. M. Mala, D. Li and J. D. Dale, Heat Transfer and Fluid Flow in
Microchannesl, International Journal of Heat Mass Transfer, Vol.40,
（1997）pp. 3079-3088.


[30]P.H. Paul, M.G. Garguilo, D.J. Rakestraw, Imaging of Pressure and
Electrokinetically Driven Flows through Open Capillaries, Analytical
Chemistry ,Vol.70(1998) pp.2459-2467.



[31]S. Zeng, C.G. Chen, J.C. Mikkelsen, J.G. Santiago, Fabrication and
Characterization of Electroosmaotic Micro-pumps, Sensor. Actuator. B Chemistry, Vol.79 (2001)pp. 107-114.

[32]S. Zeng, C.H. Chen, J.G. Santiago, J.R. Chen, R.N. Zare,J.A. Tripp, F. Svec,
J.M.J. Frechet, Electroosmotic Flow Pumps with Polymer Frits, Sensor.
Actuator. B Chemistry, Vol.79 (2001)pp. 209-212.

[33]G. Wang, P. Vanka, Convective Heat Transfer in Periodic Wavy
Passages, International Journal of Heat Mass Transfer, Vol.38 (1995)
pp.3219.

[34]Keisuke Horiuchi, P. Dutta , Joule Heating Effects in Electroosmoticaaly Driven Microchannel Flows, International Journal of Heat and Mass Transfer,Vol.47（2004）pp.3085-3095.

[35] E.M. Sparrow, J.L. Novotny, S.H. Lin, Laminar Flow of a Heat-generating
Fluid in a Parallel-Plate Channel, AICHE Journal ,Vol.9 (1963)pp.
797-804.

[36] D. Maynes, B.W. Webb, Fully Developed Electro-osmotic Heat Transfer in
Microchannels, International Journal of Heat Mass Transfer ,Vol.46 (2003)
pp. 1359-1369.



[37] P. Dutta and A. Beskok , Analytical Solution of Combined
Electroosmotic/Pressure Driven Flows in Two-Dimensional Straight
Channels:Finite Debye Layer Effect, Analytical Chemistry,Vol.73
(2001), pp.1979-1986.

[38]Mohamed Gad-el-Hak, The Fluid Mechanics of Microdevices-The Freeman Scholar Lecture, Journal of Fluids Engineering, Vol.121(1999), pp5-33.

[39] S. Blancher, R. Creff, L.L. Quere, Mixed Convective Flow of Immiscible Viscous Fluids, International Journal of Heat Fluid Flow, Vol.19(1998), pp.39-48.

[40] S. Selvarajan, E.G. Tulapurkara, V.V. Ram, A Numerical Study of Flow through Wavy-walled Channels, International Journal of Numerical Mechanical Fluids ,Vol.26 (1998) , pp.519-531.

[41] M. Greiner, R.F. Chen, R.A. Wirtz, Enhanced Heat transfer/Pressure
Drop Measured from a Flat Surface in a Grooved Channels,
ASME Journal of Heat Transfer, Vol.113(1991), pp.498-500.

[42]R.A. Wirtz, F. Huang, M. Greiner, Correlation of Fully Developed Heat Transfer and Pressure Drop in a Symmetrically Grooved Channel, ASME Journal of Heat Transfer, Vol.121 (1999), pp.236-239.




[43]E.B. Arkilic, Mass Flow and Tangential Momentum Accommodation in Silicon Micro machined Channels, Journal of Fluid Mechanics,Vol.437,（2001）,pp.29-43

[44]Yu S. and Ameel T. A., Slip Flow Heat Transfer in Rectangular
Microchannels, International Journal of Heat and Mass Transfer,
Vol.44(2001), pp.4225-4234.

[45]R.J. Yang, L.M. Fu, Y.C. Lin, Electroosmotic Flow in Microchannels, Journal of Colloid Interface Science, Vol. 239 (2001), pp. 98-105.

[46]R,J. Yang, L.M. Fu, C.C. Hwang, Electroosmotic Entry Flow in a Microchannel, Journal of Colloid Interface Science, Vol.244 (2001), pp. 173-179.
[47]L. Ren, D. Li, Electroosmotic Flow in Getrogeneous Microchannels, Journal of Colloid Interface Science, Vol.243 (2001), pp. 255-261.

[48]N.A. Patankar, H.H. Hu, Numerical Simulation of Elecrtroosmotic Flow, Analytical Chemistry, Vol.70 (1998), pp. 1870-1881.

[49]P. Dutta, A. Beskok, T.C. Warburton, Electroosmotic Flow Control in
Complex Microgeometries, Journal of Microelectromech. Systems
Vol.11(2002), pp.36-44.

[50]C.Y. Yang, D. Li,J.H. Masliyah, Modeling Forced Liquid Convection in Rectangular Microchannels with Electrokinetic Effects, International Journal of Heat Mass Transfer ,Vol.41 (1998) , pp.4229-4249.

[51]D. Maynes, B.W. Webb, Fully Developed Electro-osmotic Heat Transfer in
Microchannels, International Journal of Heat Mass Transfer,
Vol.46(2003), pp.36-44.

[52]D. Maynes, B.W. Webb, Fully Developed Thermal Transport in Combined
Pressure and Electro-osmotically Driven Flow in Microchannels, Journal of
Heat Transfer, Vol.125(2003), pp.889-895.

[53]D, Maynes, B.W. Webbm The Effect of Viscous Dissipation in Thermally Fully Developed Electro-osmotic Heat Transfer in Microchannels, International Journal of Heat Mass Transfer ,Vol.47 (2004), pp. 987-999.


[54]X.Y. Chen, K.C. Toh, C. Yang, J.C. Chai, Numerical Computation of
Hydrodynamically and Thermally Developing Liquid Flow in
Microchannels with Electrokinetic Effects, Journal of Heat Transfer, Vol.126(2004), pp.70-75

[55]S. Chakraborty, Analytical Solutions of Nusselt Number for Thermally
Fully Developed Flow in Microtubes under a Combined Action of
Electroosmaotic Forces and Imposed Pressure Gradients, International
Journal of Heat Mass Transfer, Vol.49 (2006), pp.810-813.




[56]A,Q, Zade,M.T.Manzari, S.K. Hannani, An Analytical Solution for
Thermally Fully Developed Combined Pressure-Electroosmotically Driven Flow in Microchannels, International Journal of Heat Mass Transfer, Vol.50(2007), pp.1087-1096.

[57]C.Y. Soong, S.H. Wang, Theoretical Analysis of Electrokinetic Flow and Heat Transfer in a Microchannel under Asymmetric Boundary Conditions, Journal of Colloid Interface Science, Vol.265(2003), pp. 202-213.