本研究通過實驗的方式探究截面尺寸為500 μm × 100 μm的微流道之側壁加熱熱傳現象。實驗中採用微粒子影像測速技術(Micro-Particle Image Velocimetry, Micro-PIV)測量雷諾數為20時流場的跨向速度分佈，藉由溫度螢光感測塗料(Temperature Sensitive Paint, TSP)測量螢光溶液的溫度分佈，通過加熱方向的溫度梯度計算壁面的熱通量，並最終得到沿流動方向的紐塞數分佈。實驗結果表明除靠近加熱源一側外，流道遠離加熱源一側壁面也存在溫度梯度分佈，有熱量輸入流道，存在共軛熱傳現象。
本研究在數值模擬利用Ansys Fluent軟體，仿照實驗台進構建計算區域，使用與實驗相同的邊界條件進行共軛熱傳數值計算，模擬結果與實驗結果吻合，證明了共軛熱傳模型的可靠度。共軛熱傳對流場的影響主要為各壁面熱量分佈不均，在基礎案例（雷諾數Re=20且相對熱傳導係數kb/kf=1.79）中，若僅考慮加熱源總熱量從靠近加熱源壁面傳入流體之熱量，紐塞數Nu=0.87，考慮四個壁面傳入流體之熱量，紐塞數Nu=4.55，忽略共軛熱傳將嚴重低估流道的熱傳性能。本研究分析流道下壁面kb/kf在0.21~6.48範圍內對共軛熱傳現象之影響，結果顯示，當kb/kf增加，流道下壁面吸收的熱量占流道吸收總熱量比率由37%提升至90%，紐塞數Nu由3.07提升至5.75，但流體吸收的總熱量卻先上升後下降，在kb/kf=1.79時存在極大值。本研究亦分析了Re在10-320範圍內對共軛熱傳行為之影響，結果表明Re越大，流道吸收熱量越多，下壁面發生的軸向熱傳現象程度降低。流體Nu達到完全熱發展的距離隨之增加。本研究觀察到了前人文獻中的出口效應，出口效應的程度與影響長度Lend隨kb/kf增加而增加，在0.21<kb/kf<1.11範圍前人的經驗公式不再適用，此時須使用三位共軛熱傳模擬計算出口效應長度。

In this study, the heat transfer in microchannel under sidewall heating condition is investigated experimentally. The microchannel has a width of 500 μm and a depth of 100 μm. Micro-Particle Image Velocimetry (Micro-PIV) and Temperature Sensitive Paint (TSP) are applied to measure the velocity and temperature field distributions while Reynolds number is 20. The heat flux is determined via deriving the temperature gradient and is used to calculate Nusselt number with fluid bulk temperature and near-wall temperature. The experiment data demonstrate that the temperature gradient exists in the regions close to the heat source as well as those away from the heat source. It means that conjugate heat transfer occurs in microchannel.
Ansys Fluent is used for numerical analysis. The numerical domain is a simplified model of the experimental test section with the same boundary conditions. Comparisons between numerical and experimental results show the reliability of the numerical conjugate heat transfer model. The fully developed Nusselt number is 0.87 if only heat from the nearest wall to heater is considered and it will be 4.56 if all four wall is considered. The effect of channel wall thermal conductivity ratio on the conjugate heat transfer is numerically investigated from 0.21 to 6.48. The results show that heat percentage through bottom wall will increase from 37% to 90% with the rising wall thermal conductivity ratio, which makes the bottom wall the mainly heating wall. Consequently, the average Nusselt number increase from 3.07 to 5.75. However, the total heat absorbed by fluid reveals a single peak trend with the highest value occurring at wall thermal conductivity ratio equal to 1.79. The effect of Reynolds number on conjugate heat transfer is also numerically explored at the range of 10 to 320. It is found that the axial heat transfer is significantly affected in the bottom solid wall. The thermal entrance length and total heat absorbed by fluid show a positive correlation to Reynolds number. In addition, this study captures the end region effect spotted by the previous researcher. The end region effect and length have positive correlation with thermal conductivity ratio. Meanwhile, the empirical formula between axial conduction number and end region length is not suitable if thermal conductivity ratio within 0.21 to 1.11. An three dimension conjugate heat transfer model should be applied to do further research.

[1] H. Sutter, “The Free Lunch Is Over: A Fundamental Turn Toward Concurrency in Software,” http://www.gotw.ca/publications/concurrency-ddj.htm, 2009.
[2] Military Handbook: Reliabillity Prediction of Electronic Equipment. United States Department of Defence, 1990.
[3] G.L. Morini, “Single-phase convective heat transfer in microchannels: a review of experimental results,” International Journal of Thermal Sciences, vol. 43, pp. 631-651, 2004.
[4] A. Bejan, Convection Heat Transfer, 4thed.: John Wiley&Sons, 2013.
[5] R.K. Shah, A.L. London, Laminar Flow Forced Convection in Ducts.: Academic Press, 1978.
[6] H. Herwig, O.Hausner, “Critical view on new results in micro-fluid mechanics an example,” International Journal of Heat and Mass Transfer, vol. 46, pp. 935-937, 2001.
[7] C.P. Tso, S.P. Mahulikar, “Experimental verication of the role of Brinkman number in microchannels using local parameters,” International Journal of Heat and Mass Transfer, vol. 43, pp. 1837-1849, 1999.
[8] A.G. Fedorov, R. Viskanta, “Three-dimensional conjugate heat transfer in the microchannel heat sink for electronic packaging,” International Journal of Heat and Mass Transfer, vol. 43, pp. 399-415, 1999.
[9] M.K. Moharana, G. Agarawal, S. Khandekar, “Axial conduction in single-phase simultaneously developing flow in a rectangular mini-channel array,” International Journal of Thermal Sciences, vol. 50, no. 6, pp. 1001-1012, 2011.
[10] T.Y. Lin, S.G. Kandlikar, “A theoretical model for axial heat conduction effects during single-phase flow in microchannels,” Journal of Heat Transfer, vol. 134, pp. 020902, 2011.
[11] Y. Kabar, R. Bessaih, M. Rebay, “Conjugate heat transfer with rarefaction in parallel plates microchannel,” Superlattices and Microstructures, vol. 60, pp. 370-388, 2013.
[12] G. Maranzana, I. Perry, D. Maillet, “Mini- and micro-channels: influence of axial conduction,” International Journal of Heat and Mass Transfer, vol. 47, pp. 3993-4004, 2003.
[13] C. Nonino, S. Savino, S.D. Giudice, L. Mansutti, “Conjugate forced convection and heat conduction in circular microchannels,” International Journal of Heat and Fluid Flow, vol. 30, pp. 823-830, 2009.
[14] Z. Li, Y.L. He, G.H. Tang, W.Q. Tao, “Experimental and numerical studies of liquid flow and heat transfer in microtubes,” International Journal of Heat and Mass Transfer, vol. 50, pp. 3447-3460, 2007.
[15] D. Lelea, S. Nishio, K. Takano, “The experimental research on microtube heat transfer and fluid flow of distilled water,” International Journal of Heat and Mass Transfer, vol. 47, pp.2817-2830, 2004.
[16] P.S. Lee, S.V. Garimella, D. Liu, “Investigation of heat transfer in rectangular microchannels,” International Journal of Heat and Mass Transfer, vol. 48, pp. 1688-1704, 2005.
[17] I. Tiselj, G. Hetsroni, B. Mavko, A. Mosyak, E. Pogrebnyak, Z. Segal, “Effect of axial conduction on the heat transfer in micro-channels,” International Journal of Heat and Mass Transfer, vol. 47, pp.2551-2565, 2004.
[18] G. Hetsroni, M. Gurevich, A. Mosyak, R. Rozenblit, “Drag reduction and heat transfer of surfactants flowing in a capillary tube,” International Journal of Heat and Mass Transfer, vol. 47, pp.3797-3809, 2004.
[19] G. Hetsroni, A. Mosyak, E. Pogrebnyak, L.P. Yarin, “Heat transfer in micro-channels: Comparison of experiments with theory and numerical results,” International Journal of Heat and Mass Transfer, vol. 48, pp.5580-5601, 2005.
[20] C.Y. Huang, C.M. Wu, Y.N. Chen, T.M. Liou, “The experimental investigation of axial heat conduction effect on the heat transfer analysis in microchannel flow,” International Journal of Heat and Mass Transfer, vol. 70, pp.169-173, 2014.
[21] W. Qu, I. Mudawar, “Analysis of three-dimensional heat transfer in micro-channel heat sinks,” International Journal of Heat and Mass Transfer, vol. 45, pp.3973-3985, 2002.
[22] S.X. Zhang, Y.L. He, G. Lauriat, W.Q. Tao, “Numerical studies of simultaneously developing laminar flow and heat transfer in microtubes with thick wall and constant outside wall temperature,” International Journal of Heat and Mass Transfer, vol. 53, pp.3977-3989, 2010.
[23] M.K. Moharana, P.K. Singh, S. Khandekar, “Optimum Nusselt Number for Simultaneously Developing Internal Flow Under Conjugate Conditions in a Square Microchannel,” Journal of Heat Transfer, vol. 134, pp. 071703, 2012.
[24] M. Avci, O. Aydin, M.E. Arici, “Conjugate heat transfer with viscous dissipation in a microtube,” International Journal of Heat and Mass Transfer, vol. 55, pp.5302-5308, 2012.
[25] M. Rahimi, R. Mehryar, “Numerical study of axial heat conduction effects on the local nusselt number at the entrace and ending regions of a cicular microchannel,” International Journal of Thermal Sciences, vol. 59, pp.87-94, 2012.
[26] R.J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annual Review of Fluid Mechanics, vol. 23, pp. 261-304, 1991.
[27] Z.C. Liu, C. Landerth, R.J. Adrian, T.J. Hanratty, “High resolution measurement of turbulent structure in a channel with particle image velocimetry,” Experiments in Fluids, vol. 10, pp. 301-312, 1991.
[28] J.G. Santiago, S.T. Wereley, C.D. Meinhart, D.J. Beebe, R.J. Adrian, “A particle image velocimetry system for microfluidics,” Experiments in Fluids, vol. 25, pp. 316-319, 1998.
[29] C.D. Meinhart, S.T. Wereley, J.G. Santiago, “PIV measurements of a microchannel flow,” Experiments in Fluids, vol. 27, pp. 414-419, 1999.
[30] T. Liu, “Pressure-and Tempereature-Sensitive Paints,” Encyclopedia of Aerospace Engineering, 2010.
[31] R. Samy, T. Glawdel, C.L. Ren, “Method for microfluidic whole-chip temperature measurement using thin-film poly(dimethylsiloxane)/rhodamine B,” Analytical Chemistry, vol. 80, pp. 369-375, 2008.
[32] R. Risius, W.H. Beck, C. Klein, U.Henne, A. Wagner, “Determination of heat transfer into a wedge model in a hypersonic fow using temperature‑sensitive paint,” Experiments in Fluids, vol. 58, pp. 117, 2017.
[33] C.Y. Huang, C.A. Lin, H.Y, Wang, T.M. Liou, “The application of temperature-sensitive paints for surface and fluid temperature measurements in both thermal developing and fully developed regions of a microchannel,” International Journal of Thermal Sciences, vol. 23, no. 3, pp. 037001, February 2013.
[34] 吳政旻, “應用溫度感測螢光技術探討定熱通量下矩形微直管流體與壁面熱傳特性,” 清華大學動力機械工程學系學位論文, 2013.
[35] C.D. Meinhart, S.T. Wereley, J.G. Santiago, “A PIV Algorithm for Estimating Time-Averaged Velocity Fields,” Journal of Fluids Engineering, vol. 122, pp. 285-289, 2000.
[36] T. Liu, J.P. Sullivan, “Pressure and Temperature Sensitive Paints,” Springer Science & Business Media, 2004.
[37] Y.H. Tennico, M.T. Koesdjojo, S. Kondo, “Surface modification-assisted bonding of polymer-based microfluidic devices,” Sensors and Actuators B: Chemical, vol. 143, pp. 799-804, 2010.
[38] Microchem, “SU-8 2000 Permanent Epoxy Negative Photoresist,” http://www.micro-resist.de/daten/mcc/su_8_2000_5_2015.pdf.
[39] V. A, “Experimental investigation of the influence of flow structure on compound angled film cooling performance,” ETH Zurich PhD thesis, 2009.
[40] K.W. Lee, J.D. Slinker, A.A. Gorodetsky, S.F. Torres, H.D. Abruna, P.L. Houston, G.G. Malliaras, “Photophysical properties of tris(bipyridyl)ruthenium(II) thin films and devices,” Physical Chemistry Chemical Physics, vol. 5 , pp. 2706-2709, 2003.
[41] S.N. Shoghl, J. Jamali, M.K. Moraveji, “Electrical conductivity, viscosity, and density of different nanofluids: An experimental study,” Experimental Thermal and Fluid Science, vol. 74, pp. 339-346, 2016.
[42] R. Guo, X. Sun, S. Yao, “Semi‐Liquid‐Metal‐(Ni‐EGaIn)‐Based Ultraconformable Electronic Tattoo,” Advanced Materials Technologies, vol. 4, pp. 1900183, 2019.
[43] Alfa Aesar, “Safety Data Sheet,” https://www.alfa.com/en/msds/?language=EN&
subformat=AGHS&sku=12478
[44] 張銘翔, “以實驗方法探討微流道傾斜式結構誘導聲流的流暢與熱傳增益,” 清華大學動力機械工程學系學位論文, 2018.
[45] C.Y. Huang, C.M. Lai, J.S. Li, “Applications of pixel-by-pixel calibration method in microscale measurements with pressure-sensitive paint,” Journal of Microelectromechanical Systems, vol. 21, pp. 1090-1097, 2012.
[46] R.A. Lima, S. Wada, K. Tsubota, “Confocal micro-PIV measurements of three-dimensional profiles of cell suspension flow in a square microchannel,” Measurement Science and Technology, vol. 17, pp. 797-808, 2006.
[47] G. Ferreira, A. Sucena, L.L. Ferras, F.T. Pinho, A.M. Afonso, “Hydrodynamic entrance lengths for incompressible laminar flow in rectangular ducts,” Fluids, vol.6, pp. 240, 2021.