混合微通道中不稳定的广义Couette流

M·L·考兰吉尼; B·K·贾

doi:10.3879/j.issn.1000-0887.2011.01.003

混合微通道中不稳定的广义Couette流

doi: 10.3879/j.issn.1000-0887.2011.01.003

M·L·考兰吉尼¹,
B·K·贾²

1.
卡诺科技大学数学系,乌地尔,尼日利亚;2.艾哈迈杜〖KG-*4〗·〖KG-*4〗贝洛大学数学系,扎里亚, 尼日利亚

详细信息

中图分类号: O357.3
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出版历程
- 收稿日期: 2010-08-30
- 修回日期: 2010-11-22
- 刊出日期: 2011-01-15

Unsteady Generalized Couette Flow in Composite Microchannel

M. L. Kaurangini¹,
Basant K. Jha²

1.
Department of Mathematical Sciences, Kano University of Science and Technology, Wudil-Nigeria;

摘要

摘要: 在一个平行板通道中，部分充满了均匀的多孔介质，部分为纯流体的流动区，对其微通道中完全发展的不稳定层流进行了数值分析，流动由其中一块板的运动和压力梯度所引起．多孔介质区域的流动，采用扩展的Brinkman模型，即Darcy模型，纯净流动区域的流动，采用Stokes方程．还对稳定的完全发展流进行了理论分析，给出了分界面速度、边界板处的速度和表面摩擦的闭式解．通过数值计算发现，稳定完全发展流的闭式解，和不稳定流动的数值解，在所有时间点上得到很好地吻合．
- 不稳定 /
- 混合 /
- 微通道
Abstract: A numerical study was reported to investigate the unsteady fully developed laminar fluid flow in microchannel parallel-plates partially filled with uniform porous medium and partially with a clear fluid. The flow was induced by the movement of one of the plates and pressure gradient.Brinkman-Extended Darcy model was utilized to model the flow in porous region while Stokes equation was used in the clear fluid region.A theoretical analysis was also presented for the steady fully developed flow to find the closed form expressions for interfacial velocity,the velocity and skin frictions at the bounding plates.During the course of numerical computations,it is observed that there is an excellent agreement between the closed form solutions for steady fully developed flow with numerical solution of unsteady flow at large values of time.
- unsteady /
- composite /
- microchannel

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参考文献(33)

[1]	Beavers G S, Joseph D D. Boundary conditions at a naturally permeable wall[J]. Journal of Fluid Mechanics, 1967, 30(1): 197-207. doi: 10.1017/S0022112067001375
[2]	Larson R E, Higdon J J L. Microscopic flow near the surface of two-dimensional porous media—Ⅰ axial flow[J]. Journal of Fluid Mechanics, 1987, 166: 449-472.
[3]	Larson R E, Higdon J J L. Microscopic flow near the surface of two-dimensional porous media—Ⅱ tranverse flow[J].Journal of Fluid Mechanics, 1987, 178: 119-136. doi: 10.1017/S0022112087001149
[4]	Sahraoui M, Kaviany M. Slip and no-slip velocity boundary conditions at interface of porous, plain media[J].International Journal of Heat Mass Transfer, 1992, 35(4): 927-943. doi: 10.1016/0017-9310(92)90258-T
[5]	Nield D A, Bejan A. Convection in Porous Media[M]. New York: Springer-Verlag, 1992.
[6]	Nield D A, Bejan A. Convection in Porous Media[M]. 3rd edition. New York: Springer-Verlag, 2006.
[7]	Kaviany M. Principles of Heat Transfer in Porous Media[M]. New York: Springer-Verlag, 1991.
[8]	Poulikakos D, Kazmierczak M. Forced convection in a duct partially filled with a porous material[J]. ASME Journal of Heat Transfer, 1987, 109(3): 653-662. doi: 10.1115/1.3248138
[9]	Kuznetsov A V. Analytical investigation of Couette flow in a composite channels partially filled with a clear fluid[J]. International Journal of Heat Mass Transfer, 1998, 41(16): 2556-2560. doi: 10.1016/S0017-9310(97)00296-2
[10]	Pantokratoras A. Fully developed Couette flow of three fluids with variable thermo physical properties flowing through a porous medium channel heated asymmetrically with large temperature differences[J]. Journal of Heat Transfer, 2007, 129(12): 1742-1747. doi: 10.1115/1.2768103
[11]	Jaballah S, Bennacer R, Sammouda H, Belghith A. Numerical simulation of mixed convection in a channel irregularly heated and partially filled with a porous medium[J]. Journal of Porous Media, 2008, 11(3): 247-257.
[12]	Siddiqui A M, Zeb A, Ghori Q K. Some exact solutions of 2D steady flow of an incompressible viscous fluid through a porous medium[J].Journal of Porous Media, 2006, 9(6): 491-502. doi: 10.1615/JPorMedia.v9.i6.10
[13]	Jain N C, Gupta P, Sharma B. Three dimensional Couette flow with transpiration cooling through porous medium in slip flow regime[J].Modeling, Measurement and Control B, 2006, 75(5): 33-52.
[14]	Ochoa-Tapia J A, Whitaker S. Momentum transfer at the boundary between a porous medium and a homogeneous fluid—Ⅰ theoretical development experiment[J]. International Journal Heat Mass Transfer, 1995, 38(14): 2635-2646. doi: 10.1016/0017-9310(94)00346-W
[15]	Ochoa-Tapia J A, Whitaker S. Momentum transfer at the boundary between a porous medium and a homogeneous fluid—Ⅱ comparison with experiment[J]. International Journal of Heat Mass Transfer, 1995, 38(14): 2647-2655. doi: 10.1016/0017-9310(94)00347-X
[16]	Nield D A. The limitations of the Brinkman-Forchheimer equation in modeling flow in a saturated porous medium and at an interface[J]. International Journal of Heat and Fluid Flow, 1991, 12(3): 269-272. doi: 10.1016/0142-727X(91)90062-Z
[17]	Alazmi B, Vafai K. Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer[J]. International Journal of Heat and Mass Transfer, 2001, 44(9): 1735-1749. doi: 10.1016/S0017-9310(00)00217-9
[18]	Kuznetsov A V. Analytical investigation of the fluid flow in the interface region between a porous medium and a clear fluid in channels partially filled with a porous medium[J]. Application of Science Research, 1996, 56(1): 53-67. doi: 10.1007/BF02282922
[19]	Kuznetsov A V. Fluid mechanics and heat transfer in the interface region between a porous medium and a fluid layer: a boundary layer solution[J].Journal of Porous Media, 1999, 2(3): 309-321.
[20]	Kuznetsov A V. Fluid flow and heat transfer analysis of Couette flow in a composite duct[J]. Acta Mechanica, 2000,140(3): 163-170. doi: 10.1007/BF01182508
[21]	Oliveski R D C, Marczak L D F. Natural convection in a cavity filled with a porous medium with variable porosity and Darcy number[J].Journal of Porous Media, 2008, 11(7): 655-667. doi: 10.1615/JPorMedia.v11.i7.40
[22]	Zahi N, Boughamoura A, Dhahri H, Nasrallah S B. Flow and heat transfer in a cylinder with a porous medium insert along the compression stroke[J].Journal of Porous Media, 2008, 11(6): 525-540. doi: 10.1615/JPorMedia.v11.i6.20
[23]	Gorla R S R. Heat transfer between two vertical parallel walls partially filled with a porous medium: use of a brinkman-extended Darcy model[J].Journal of Porous Media, 2008, 11(5): 457-466. doi: 10.1615/JPorMedia.v11.i5.30
[24]	Arkilic E B, Breuer K S, Schmitt M A. Gaseous flow in microchannels[C]Application of Microfabrication to Fluid Mechanics, Chicago, 1994, 56-66.
[25]	Beskok A, Karniadakis G E. Simulation of heat and momentum transfer in complex microgeometries[J].Journal of Thermophysics and Heat Transfer, 1994, 8(4): 647-755. doi: 10.2514/3.594
[26]	Choi S B, Barron R F, Warrington R O. Fluid flow and heat transfer in microtubes[C]Micromechanical Sensors, Actuators and Systems, ASME, 1991, 123-134.
[27]	Khaled A R A, Vafai A. The effect of the slip condition on Stokes and Couette flows due to an oscillating wall: exact solutions[J].International Journal of Non-Linear Mechanics, 2004, 39(5): 795-809. doi: 10.1016/S0020-7462(03)00043-X
[28]	Aydin O, Avei M. Heat and fluid flow characteristics of gases in micro pipes[J].International Journal of Heat Mass Transfer, 2006, 49(9/10): 1723-1730. doi: 10.1016/j.ijheatmasstransfer.2005.10.020
[29]	Chen C K, Weng H C. Natural convection in a vertical microchannel[J]. ASME Journal of Heat Transfer, 2005, 127(9):1053-1056. doi: 10.1115/1.1999651
[30]	Khadrawi A F, Othman A, Al-Nimr M A. Transient free convection fluid flow in a vertical microchannel as described by the hyperbolic heat conduction model[J].International Journal of Thermophysics, 2005, 26(3): 905-918. doi: 10.1007/s10765-005-5586-2
[31]	Haddad O M, Abuzaid M M, Al-Nimr M A. Developing free convection gas flow in a vertical open-ended microchannel filled with porous media[J]. Numerical Heat Transfer, Part A, 2005, 48(7): 693-710. doi: 10.1080/10407780590968006
[32]	Gad-el-Hak M. The MEMS Handbook[M]. New York: CRC Press, 2001.
[33]	Ross S L. Differential Equations[M]. 3rd edition. John Wiley & Sons Inc, 2004.