Lie Group Analysis for the Effect of Temperature-Dependent Fluid Viscosity and Thermophoresis Particle Deposition on Free Convective Heat and Mass Transfer in the Presence of Variable Stream Conditions
-
摘要: 研究二维稳定不可压缩流体在竖向延伸平面上的流动.流体黏性假设为与温度相关的线性函数.对控制方程进行伸缩群变换,由于变换参数之间的关系让方程解保持不变.在找到3个绝对不变量后,推导对应动量方程的一个三阶一般微分方程和两个对应能量方程和扩散方程的二阶一般微分方程.求出具有边界条件方程的数值解,发现随着平面延伸距离增加,随温度变化的流体黏性降低让流速变慢.在平面的某个特定点处,随着黏性减少流速变慢但温度增加.热泳微粒沉积在浓度边界层起着关键作用.最后对计算结果进行讨论并给出图例.
-
关键词:
- Lie群分析 /
- 随温度变化的流体黏性 /
- 热辐射 /
- 热泳微粒沉积
Abstract: A steady two-dmiensional flow of incompressible fluid over a vertical stretching sheet was studied. The fluid viscosity was assumed to vary as a linear function of temperature. A scaling group of transformations was applied to the governing equations. The system remained invariant due to some relations among the parameters of the transformations. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equations corresponding to energy and diffusion equations were derived. The equations along with the boundary conditions were solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases with the decreasing viscosity while the temperature increases in this case. The impact of thermophoresis particle deposition plays an miportant role on the concen tration boundary layer. The results thus obtained are presented graphically and discussed. -
[1] Oberlack M. Similarity in non-rotating and rotating turbulent pipe flows[J]. J Fluid Mechanics, 1999, 379(1): 1-22. doi: 10.1017/S0022112098001542 [2] Bluman G W, Kumei S. Symmetries and Differential Equations[M]. New York: Springer-Verlag,1989. [3] Pakdemirli M, Yurusoy M. Similarity transformations for partial differential equations[J]. SIAM Rev, 1998, 40(1): 96-101. doi: 10.1137/S003614459631001X [4] Crane L J. Flow past a stretching plate[J]. Z Angew Math Phys, 1970, 21(4): 645-647. doi: 10.1007/BF01587695 [5] Sakiadis B C. Boundary-layer behavior on continuous solid surface─Ⅰ:the boundary-layer equations for two-dimensional and asymmetric flow[J]. AIChE J, 1961, 7(2): 26-28. doi: 10.1002/aic.690070108 [6] Sakiadis B C. Boundary-layer behavior on continuous solid surface─Ⅱ:the boundary-layer on a continuous flat surface[J]. AIChE J, 1961,7(2): 221-225. doi: 10.1002/aic.690070211 [7] Gupta P S, Gupta A S. Heat and mass transfer on a stretching sheet with suction and blowing[J]. Can J Chem Eng, 1977, 55(6): 744-746. doi: 10.1002/cjce.5450550619 [8] Abel M S, Khan S K, Prasad K V. Study of visco-elastic fluid flow and heat transfer over a stretching sheet with variable viscosity[J]. Int J Non-Linear Mech, 2002,37(1): 81-88. [9] Epstein M, Hauser G M, Henry R E. Thermophoretic deposition of particles in natural convection flow from vertical plate[J]. ASME J Heat Trans, 1985, 107(2): 272-276. doi: 10.1115/1.3247410 [10] Goren S L. Thermophoresis of aerosol particles in laminar boundary layer on a flat plate[J]. J Colloid Interface Sci, 1977, 61(1): 77-85. doi: 10.1016/0021-9797(77)90416-7 [11] Garg V K, Jayaraj S. Thermophoresis of aerosol particles in laminar flow over inclined plates[J]. Int J Heat Mass Transf, 1988,31(4): 875-890. doi: 10.1016/0017-9310(88)90144-5 [12] Jayaraj S, Dinesh K K, Pillai K L. Thermophoresis in natural convection with variable properties[J]. Int J Heat Mass Transf, 1999, 34(3): 469-475. doi: 10.1007/s002310050284 [13] Selim A, Hossain M A, Rees D A S. The effect of surface mass transfer on mixed convection flow past a heated vertical flat permeable plate with thermophoresis[J]. International Journal of Thermal Science, 2003, 42(6): 973-981. doi: 10.1016/S1290-0729(03)00075-9 [14] Wang C C. Combined effects of inertia and thermophoresis on particle deposition onto a wafer with wavy surface[J]. Int J Heat Mass Transf, 2006, 49(8): 1395-1402. doi: 10.1016/j.ijheatmasstransfer.2005.09.036 [15] Wang C C, Chen C K. Thermophoresis deposition of particles from a boundary layer flow onto a continuously moving wavy surface[J]. Acta Mech, 2006, 181(1): 139-151. doi: 10.1007/s00707-005-0297-0 [16] Chamka A, Pop I. Effect of thermophoresis particle deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium[J]. Int Comm Heat Mass Trans, 2004, 31(3): 421-430. doi: 10.1016/j.icheatmasstransfer.2004.02.012 [17] Chamka A, Jaradat M, Pop I. Thermophoresis free convection from a vertical cylinder embedded in a porous medium[J]. Int J Appl Mech Eng, 2004, 9(4): 471-481. [18] Nield D A, Bejan A. Convection in Porous Media[M]. 2nd ed. New York: Springer, 1999. [19] Ingham D, Pop I. Transport Phenomena in Porous Media Ⅰ[M].Pergamon: Oxford,1998. [20] Ingham D, Pop I. Transport Phenomena in Porous Media Ⅱ[M].Pergamon: Oxford,2002. [21] CHEN Chieh-li, CHAN Kun-chieh. Combined effects of thermophoresis and electrophoresis on particle deposition onto a wavy surface disk[J]. Int J Heat Mass Transfer, 2008, 51(7): 2657-2664. doi: 10.1016/j.ijheatmasstransfer.2007.09.035 [22] WANG Chi-chang. Combined effects of inertia and thermophoresis on particle deposition onto a wafer with wavy surface[J]. Int J Heat Mass Transfer, 2008, 51(7): 1395-1402. [23] Gary J, Kassoy D R, Tadjeran H, et al. The effects of significant viscosity variation on convective heat transport in water saturated porous medium[J]. J Fluid Mech, 1982, 117(2): 233-241. doi: 10.1017/S0022112082001608 [24] Mehta K N. Sood S. Transient free convection flow with temperature-dependent viscosity in a fluid saturated porous medium[J]. Int J Engg Sci, 1992, 30(5): 1083-1087. doi: 10.1016/0020-7225(92)90032-C [25] Mukhopadhyay S, Layek G C, Samad S A. Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity[J]. Int J Heat Mass Transfer, 2005, 48 (7): 4460-4466. doi: 10.1016/j.ijheatmasstransfer.2005.05.027 [26] Mukhopadhyay S, Layek G C. Effects of thermal radiation and variable fluid viscosity on free convective flow and heat transfer past a porous stretching surface[J]. Int J Heat Mass Transfer, 2008, 51(6): 2167-2178. doi: 10.1016/j.ijheatmasstransfer.2007.11.038 [27] Brewster M Q. Thermal Radiative Transfer Properties[M]. New York: John Wiley and Sons, 1992. [28] Batchelor G K. An Introduction to Fluid Dynamics[M]. London: Cambridge University Press, 1987. [29] Ling J X, Dybbs A. Forced convection over a flat plate submersed in a porous medium: variable viscosity case[R]. Paper 87-WA/HT-23, American Society of Mechanical Engineers, N Y, 1987. [30] Gill S. A process for the step-by-step integration of differential equations in an automatic digital computing machine[J]. Proceedings of the Cambridge Phil Society, 1951,47(1): 96-108. doi: 10.1017/S0305004100026414 [31] Hossain M A, Khanafer K, Vafai K. The effect of radiation on free convection flow of fluid with variable viscosity from a porous vertical plate[J]. Int J Thermal Sci, 2001, 40(2): 115-124. doi: 10.1016/S1290-0729(00)01200-X
点击查看大图
计量
- 文章访问数: 1165
- HTML全文浏览量: 68
- PDF下载量: 831
- 被引次数: 0