基于二阶滑移边界的MHD在可渗透延伸壁面上的驻点流研究

许晓勤; 陈淑梅

doi:10.21656/1000-0887.370032

基于二阶滑移边界的MHD在可渗透延伸壁面上的驻点流研究

doi: 10.21656/1000-0887.370032

许晓勤^1,2,
陈淑梅²

¹福建船政交通职业学院汽车运用工程系, 福州 350007;²福州大学机械工程及自动化学院, 福州 350116

基金项目: 2012年度中央财政支持地方高校发展专项资金（闽教财\[2012\]788号）

详细信息

作者简介:
许晓勤（1981—），女，讲师，博士生（通讯作者. E-mail: m140210004@fzu.edu.cn);陈淑梅（1960—），女，教授，博士生导师.

中图分类号: O351.2
计量
- 文章访问数: 1085
- HTML全文浏览量: 152
- PDF下载量: 571
- 被引次数: 0
出版历程
- 收稿日期: 2016-01-22
- 修回日期: 2016-02-15
- 刊出日期: 2016-08-15

Study on MHD Stagnation-Point Flow Over Permeable Stretching Sheets With 2nd-Order Slip Boundaries

XU Xiao-qin^1,2,
CHEN Shu-mei²

¹Automobile Application Engineering Dept., Fujian Chuanzheng Communications College, Fuzhou 350007, P.R.China;²School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, P.R.China

摘要

摘要: 研究了多孔介质中带二阶滑移边界的不可压缩MHD粘性流体在可渗透指数延伸壁面上的驻点流问题.通过相似变换将描述驻点流的控制方程转换为非线性常微分方程，并利用MATLAB的bvp5c函数求解非线性问题.分析并讨论了一、二阶滑移参数，抽吸/喷注参数以及渗透参数对速度分布和壁面剪切力的影响.结果显示在多孔介质中当壁面延伸速度小于外界主流速度时，随着一阶滑移参数、二阶滑移参数绝对值、抽吸/喷注参数以及渗透参数的增大，速度增大，壁面剪切力减小且均为正数；而当壁面延伸速度大于外界主流速度时形成一个反边界层，速度减小，壁面剪切力绝对值也减小且均为负数；二阶滑移参数对速度剖面和壁面剪切力的影响略大于一阶滑移参数的影响，抽吸/喷注参数对速度剖面和壁面剪切力的影响明显大于渗透参数或磁场参数的影响.
- 可渗透延伸壁面 /
- 二阶滑移 /
- MHD /
- 驻点流 /
- 边界层
Abstract: The incompressible MHD viscous flow with 2nd-order slip about stagnation points over permeable exponentially stretching sheets in porous media was studied. The governing equations describing the stagnation point flow were reduced to nonlinear differential equations through the similarity transformations. Then the bvp5c function in MATLAB was employed to solve the nonlinear problem. Finally, the effects of the 1st- and 2nd-order slip parameters, the suction/injection parameter and the permeability parameter on the velocity and the skin friction were analyzed and discussed. The results show that the velocity increases but the skin friction decreases and is positive with the 1st-order slip parameter and the absolute value of the 2nd-order slip parameter, the suction/injection parameter and the permeability parameter, when the sheet’s stretching velocity is smaller than the external mainstream velocity; however, an anti-boundary layer forms, the velocity decreases and the absolute value of the skin friction also decreases but is negative, when the sheet’s stretching velocity is larger than the external mainstream velocity. The effect of the 2nd-order slip parameter is slightly greater than that of the 1st-order slip parameter on the velocity and the skin friction, and the effect of the suction/injection parameter is significantly greater than that of the permeability parameter.
- permeable stretching sheet /
- 2nd-order slip /
- MHD /
- stagnation-point flow /
- boundary layer

HTML全文

参考文献(29)

[1]	Crane L J. Flow past a stretching plate[J]. Zeitschrift für Angewandte Mathematik und Physik ZAMP,1970,21(4): 645-647.
[2]	Andersson H I. MHD flow of a viscoelastic fluid past a stretching surface[J]. Acta Mechanica,1992,95(1): 227-230.
[3]	Ariel P D. On computation of the three-dimensional flow past a stretching sheet[J]. Applied Mathematics and Computation,2007,188(2): 1244-1250.
[4]	Khan Y, Wu Q B, Faraz N, Yildirim A. The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet[J]. Computers and Mathematics With Applications,2011,61(11): 3391-3399.
[5]	A·艾哈迈德, S·阿司哈. 双曲拉伸面上的流动及其热交换[J]. 应用数学和力学, 2012,33(4): 425-433.(Ahmad A, Asghar S. Flow and heat transfer over a hyperbolic stretching sheet[J]. Applied Mathematics and Mechanics,2012,33(4): 425-433.(in Chinese))
[6]	Sparrow E M, Beavers G S, Hung L Y. Flow about a porous-surfaced rotating disk[J]. International Journal of Heat and Mass Transfer,1971,14(7): 993-996.
[7]	Sparrow E M, Beavers G S, Hung L Y. Channel and tube flows with surface mass transfer and velocity slip[J]. Physics of Fluids,1971,14(7): 1312-1319.
[8]	Wang C Y. Stagnation flows with slip: exact solution of the Navier-Stokes equations[J]. Zeitschrift für Angewandte Mathematik und Physik ZAMP,2003,54(1): 184-189.
[9]	Wang C Y. Flow due to a stretching boundary with partial slip—an exact solution of the Navier-Stokes equations[J]. Chemical Engineering Science,2002,57(17): 3745-3747.
[10]	Ariel P D. Axisymmetric flow due to stretching sheet with partial slip[J]. Computers & Mathematics With Applications,2007,54(7/8): 1169-1183.
[11]	ZHANG Tian-tian, JIA Li, WANG Zhi-cheng. Validation of Navier-Stokes equation for the slip flow analysis within transition region[J]. International Journal of Heat and Mass Transfer,2008,51(25/26): 6323-6327.
[12]	Pereira G G. Effect of variable slip boundary conditions on the flows of pressure driven non-Newtonian fluids[J].Journal of Non-Newtonian Fluid Mechanics,2009,157(3): 197-206.
[13]	FANG Tie-gang, YAO Shan-shan, ZHANG Ji, Aziz A. Viscous flow over a shrinking sheet with a second order slip flow model[J]. Communications in Nonlinear Science and Numerical Simulation,2010,15(7): 1831-1842.
[14]	Sahoo B, Poncet S. Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition[J]. International Journal of Heat and Mass Transfer,2011,54(23/24): 5010-5019.
[15]	B·萨胡. 二阶流体通过径向延伸平面时滑移、黏性耗散、焦耳热对MHD流动的影响[J]. 应用数学和力学, 2010,31(2): 150-162.(Sahoo B. Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet[J]. Applied Mathematics and Mechanics,2010,31(2): 150-162.(in Chinese))
[16]	Mahmood T, Shah S M, Abbas G. Magnetohydrodynamic viscous flow over a shrinking sheet with second order slip flow model[J].Heat Transfer Research,2014,46(8):725-734. doi: 10.1615/HeatTransRes.2015007512.
[17]	王克用, 王大中, 李培超. 多孔介质平板通道传热模型的两种求解方法[J]. 应用数学和力学, 2015,36(5): 494-504.(WANG Ke-yong, WANG Da-zhong, LI Pei-chao. Two decoupling methods for the heat transfer model of a plate channel filled with a porous medium[J]. Applied Mathematics and Mechanics,2015,36(5): 494-504.(in Chinese))
[18]	Rosali H, Ishak A. Stagnation-point flow over a stretching/shrinking sheet in a porous medium[C]//The 2013 UKM FST Postgraduate Colloquium.Selangor, Malaysia, 2013: 949-955. doi: 10.1063/1.4858776.
[19]	FANG Tie-guang, ZHANG Ji, YAO Shan-shan. Viscous flow over an unsteady shrinking sheet with mass transfer[J].Chinese Physics Letters,2009,26(1): 014703.
[20]	苏晓红, 郑连存, 张欣欣. DTM-BF方法和可渗透收缩壁面上带滑移速度的非稳态磁流体力学流动[J]. 应用数学和力学, 2012,33(12): 1451-1464.(SU Xiao-hong, ZHENG Lian-cun, ZHANG Xin-xin. On DTM-BF method and dual solutions for an unsteady MHD flow over a permeable shrinking sheet with velocity slip[J]. Applied Mathematics and Mechanics,2012,33(12): 1451-1464.(in Chinese))
[21]	Singh V, Agarwal S. MHD flow and heat transfer for Maxwell fluid over an exponentially stretching sheet with variable thermal conductivity in porous medium[J]. Thermal Science,2014,18(S2): S599-S615.
[22]	LIN Yan-hai, ZHENG Lian-cun, ZHANG Xin-xin. Magnetohydrodynamics thermocapillary Marangoni convection heat transfer of power-law fluids driven by temperature gradient[J]. Journal of Heat Transfer,2013,135(5): 051702.
[23]	Ranjan R, DasGupta S, De S. Mass transfer coefficient with suction for turbulent non-Newtonian flow in application to membrane separations[J]. Journal of Food Engineering,2004,65(4): 533-541.
[24]	Ranjan R, DasGupta S, De S. Mass transfer coefficient with suction for laminar non-Newtonian flow in application to membrane separations[J].Journal of Food Engineering,2004,64(1): 53-61.
[25]	Rahman M M, Rosca A V, Pop I. Boundary layer flow of a nanofluid past a permeable exponentially shrinking/stretching surface with second order slip using Buongiorno’s model[J].International Journal of Heat and Mass Transfer,2015,25(2): 299-319.
[26]	Wang C Y. Stagnation flow towards a shrinking sheet[J].International Journal of Non-Linear Mechanics,2008,43(5): 377-382.
[27]	LIN Yan-hai, ZHENG Lian-cun, ZHANG Xin-xin, MA Lian-xi, Chen G. MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation[J].International Journal of Heat and Mass Transfer,2015,84: 903-911.
[28]	Nandeppanavar M M, Vajravelu K, Abel M S, Siddalingappa M N. Second order slip flow and heat transfer over a stretching sheet with non-linear Navier boundary condition[J]. International Journal of Thermal Sciences,2012,58: 143-150.
[29]	薛定宇, 陈阳泉. 高等应用数学问题的MATLAB求解[M]. 北京: 清华大学出版社, 2013: 277-280.(XUE Ding-yu, CHEN Yang-quan.Advanced Applied Mathematical Problem Solutions With MATLAB[M]. Beijing: Tsinghua University Press, 2013: 277-280.(in Chinese))

施引文献

资源附件(0)

访问统计

点击查看大图

计量

文章访问数: 1085
HTML全文浏览量: 152
PDF下载量: 571
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

基于二阶滑移边界的MHD在可渗透延伸壁面上的驻点流研究

doi: 10.21656/1000-0887.370032

作者简介:
许晓勤（1981—），女，讲师，博士生（通讯作者. E-mail: m140210004@fzu.edu.cn);陈淑梅（1960—），女，教授，博士生导师.

计量

Study on MHD Stagnation-Point Flow Over Permeable Stretching Sheets With 2nd-Order Slip Boundaries

计量

目录

留言板

基于二阶滑移边界的MHD在可渗透延伸壁面上的驻点流研究

doi: 10.21656/1000-0887.370032

作者简介: 许晓勤（1981—），女，讲师，博士生（通讯作者. E-mail: m140210004@fzu.edu.cn);陈淑梅（1960—），女，教授，博士生导师.

计量

出版历程

Study on MHD Stagnation-Point Flow Over Permeable Stretching Sheets With 2nd-Order Slip Boundaries

计量

出版历程

目录

作者简介:
许晓勤（1981—），女，讲师，博士生（通讯作者. E-mail: m140210004@fzu.edu.cn);陈淑梅（1960—），女，教授，博士生导师.