滑移垂直壁面驻点附近的混合对流边界层流动

F·阿曼; A·艾萨克; I·伯普

doi:10.3879/j.issn.1000-0887.2011.12.009

滑移垂直壁面驻点附近的混合对流边界层流动

doi: 10.3879/j.issn.1000-0887.2011.12.009

敦胡先翁工艺大学遗产与艺术科学系,巴力拉惹 86400,峇株巴辖,柔佛,马来西亚;
马来西亚国民大学数学科学学院科学技术系,万宜新UKM 43600,雪兰莪,马来西亚;

基金项目: 马来西亚国民大学的财政资助(UKM-GUP-2011-202)

详细信息

中图分类号: O357.4⁺¹;O357.1
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出版历程
- 收稿日期: 2010-01-17
- 修回日期: 2011-09-21
- 刊出日期: 2011-12-15

Mixed Convection Boundary Layer Flow Near the Stagnation Point on a Vertical Surface With Slip

Faculty of Science, Arts and Heritage, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Johor, Malaysia;
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia;
Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romania

摘要

摘要: 就粘性不可压缩流体，研究垂直壁面的滑移，对壁面驻点附近稳定混合对流边界层流动的影响．假定表面温度和外部流动速度与到驻点的距离呈线性变化．首先，将偏微分的控制方程，转变为常微分方程组，然后应用打靶法进行数值求解．对不同数值的控制参数，按分顺流和逆流两种情况，分析和讨论了流动特性和热传导特征．结果表明，逆流时，在浮力参数的某一范围内出现双解；顺流时，解是唯一的．一般而言，速度滑移导致壁面热传导率增大，而热滑移使之减小．
- 双解 /
- 传热 /
- 混合对流 /
- 驻点 /
- 滑移
Abstract: A steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation point on a vertical surface with slip effect at the boundary was considered. The temperature of the sheet and the velocity of the external flow were assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations were first transformed into a system of ordinary differential equations, which was then solved numerically by a shooting method. The features of the flow and heat transfer characteristics for different values of the governing parameters were analyzed and discussed. Both assisting and opposing flows were considered. The results indicate that for the opposing flow, dual solutions exist for a certain range of the buoyancy parameter, while for the assisting flow, the solution is unique. In general, the velocity slip increases the heat transfer rate at the surface, while the thermal slip decreases it.
- dual solutions /
- heat transfer /
- mixed convection /
- stagnation point /
- slip

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参考文献(20)

[1]	Ishak A, Nazar R, Pop I. Mixed convection on the stagnation point flow toward a vertical, continuously stretching sheet[J]. J Heat Trans T ASME, 2007, 129(8):1087-1090. doi: 10.1115/1.2737482
[2]	Ramachandran N, Chen T S, Armaly B F. Mixed convection in stagnation flows adjacent to vertical surfaces[J]. J Heat Trans T ASME, 1988, 110(2): 373-377. doi: 10.1115/1.3250494
[3]	Devi C D S, Takhar H S, Nath G. Unsteady mixed convection flow in stagnation region adjacent to a vertical surface[J]. Heat Mass Transf, 1991, 26(2): 71-79.
[4]	Nazar R, Amin N, Filip D, Pop I. Stagnation point flow of a micropolar fluid towards a stretching sheet[J]. Int J Non-Linear Mech, 2004, 39(7): 1227-1235. doi: 10.1016/j.ijnonlinmec.2003.08.007
[5]	朱婧，郑连存，张欣欣. 具有延伸表面的驻点流动和传热问题的级数解[J]. 应用数学和力学, 2009, 30(4): 432-442.（ZHU Jing, ZHENG Lian-cun, ZHANG Xin-xin. Analytical solution to stagnation-point flow and heat transfer over a stretching sheet based on homotopy analysis[J]. Applied Mathematics and Mechanics(English Edition), 2009, 30(4): 463-474.）
[6]	Hassanien I A, Gorla R S R. Combined forced and free convection in stagnation flows of micropolar fluids over vertical non-isothermal surfaces[J]. Int J Eng Sci, 1990, 28(8): 783-792. doi: 10.1016/0020-7225(90)90023-C
[7]	Lok Y Y, Amin N, Pop I. Unsteady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface[J]. Int J Thermal Sci, 2006, 45(12): 1149-1157. doi: 10.1016/j.ijthermalsci.2006.01.015
[8]	Ishak A, Nazar R, Bachok N, Pop I. MHD mixed convection flow near the stagnation-point on a vertical permeable surface[J]. Physica A, 2010, 389(1): 40-46. doi: 10.1016/j.physa.2009.09.008
[9]	Wang C Y. Stagnation flows with slip: exact solutions of the Navier-Stokes equations[J]. Z Angew Math Phys, 2003, 54(1): 184-189. doi: 10.1007/PL00012632
[10]	Wang C Y. Stagnation slip flow and heat transfer on a moving plate[J]. Chem Eng Sci, 2006, 61(23): 7668 -7672. doi: 10.1016/j.ces.2006.09.003
[11]	Ariel P D. Two dimensional stagnation point flow of an elastic-viscous fluid with partial slip[J]. Z Angew Math Mech, 2008, 88(4): 320-324. doi: 10.1002/zamm.200700041
[12]	Labropulu F, Li D. Stagnation-point flow of a second-grade fluid with slip[J]. Int J Non-Linear Mech, 2008, 43(9): 941-947. doi: 10.1016/j.ijnonlinmec.2008.07.004
[13]	朱婧，郑连存，张志刚. 幂律速度运动表面上磁流体在驻点附件的滑移流动[J] 应用数学和力学, 2010, 31(4): 411-419.(ZHU Jing, ZHENG Lian-cun, ZHANG Zhi-gang. The effect of the slip condition on the MHD stagnation-point over a power-law stretching sheet[J]. Applied Mathematics and Mechanics(English Edition), 2010, 31(4): 439-448.) doi: 10.1007/s10483-010-0404-z
[14]	Cao K, Baker J. Slip effects on mixed convective flow and heat transfer from a vertical plate[J]. Int J Heat Mass Transfer, 2009, 52(15/16): 3829-3841. doi: 10.1016/j.ijheatmasstransfer.2009.02.013
[15]	Fang T, Yao S, Zhang J, Aziz A. Viscous flow over a shrinking sheet with a second order slip flow model[J]. Commun Nonlinear Sci Numer Simulat, 2010, 15(7): 1831-1842. doi: 10.1016/j.cnsns.2009.07.017
[16]	Fang T, Zhang J. Thermal boundary layers over a shrinking sheet: an analytical solution[J]. Acta Mech, 2010, 209(3/4): 325-343. doi: 10.1007/s00707-009-0183-2
[17]	Andersson H I. Slip flow past a stretching surface[J]. Acta Mech, 2002, 158(1/2): 121-125. doi: 10.1007/BF01463174
[18]	Mukhopadhyay S. Effects of slip on unsteady mixed convective flow and heat transfer past a porous stretching surface[J]. Nucl Eng Des, 2011, 241: 2660-2665. doi: 10.1016/j.nucengdes.2011.05.007
[19]	Ishak A, Nazar R, Pop I. Mixed convection stagnation point flow of a micropolar fluid towards a stretching sheet[J]. Meccanica, 2008, 43(4): 411-418. doi: 10.1007/s11012-007-9103-5
[20]	Zheng L C, Liang C, Zhang X X. A numerical method for solving the boundary layer equations of laminar natural convection about a vertical plate[J]. J Univ Sci Technol Beijing, 2007, 14(1): 33-35. doi: 10.1016/S1005-8850(07)60007-3