Effect of Viscous Dissipation and Heat Source on Flow and Heat Transfer of a Dusty Fluid Over an Unsteady Stretching Sheet
-
摘要: 研究含尘流体在不稳定伸展面上,作水动力学边界层流动及其热交换问题.研究中计及摩擦生热(粘性耗散)和内部发热或吸热的影响.应用适当的相似变换,将控制流动和热交换的基本方程组,变成一组非线性的常微分方程.利用Runge-Kutta-Fehlberg-45格式对变换后的方程进行数值求解.按发热进程分两种不同情况分析:VWT(变壁面温度)和VHF(变热通量).物理参数,如像磁场参数、流(体)-固(体微粒)的相互作用参数、不稳定参数、Prandtl数、Eckert数、含尘微粒的数量密度以及热源/汇参数,分别绘出这些物理参数变化时的速度和温度分布曲线;同时,列表和讨论了对壁面温度梯度函数和壁面温度函数的影响.Abstract: The problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface was investigated.The study considered the effects of frictional heating (viscous dissipation) and internal heat generation or absorption. The basic equations governing the flow and heat transfer were reduced to a set of nonlinear ordinary differential equations by applying suitable similarity transformations. The transformed equations were solved numerically by Runge-Kutta-Fehlberg-45 order method. An analysis was carried out for two different cases of heating processes, namely Variable Wall Temperature (VWT) and Variable Heat Flux (VHF). The effects of various physical parameters such as magnetic parameter, fluid-particle interaction parameter, unsteady parameter, Prandtl number, Eckert number, number density of dust particles and heat source/sink parameter on velocity and temperature profiles were shown in several plots and the effect of wall temperature gradient function and wall temperature function were tabulated and discussed.
-
[1] Sakiadis B C. Boundary layer behavior on continuous solid surface—Ⅰ: boundary layer equations for two dimensional and axisymmetric flow[J]. AIChE Journal, 1961, 7(1): 26-28. [2] Sakiadis B C. Boundary layer behavior on continuous solid surfaces—Ⅱ: boundary layer behavior on continuous flat surface[J]. AIChE Journal,1961,7(1): 221-225. [3] Crane L J. Flow past a stretching plate[J]. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 1970, 21(4): 645-647. [4] Grubka L J, Bobba K M. Heat transfer characteristics of a continuous stretching surface with variable temperature[J]. Journal of Heat Transfer, 1985, 107(1): 248-250. [5] Chen C H. Laminar mixed convection adjacent to vertical, continuously stretching sheets[J]. Heat and Mass Transfer, 1998, 33(5/6): 471-476. [6] Elbashbeshy E M A, Bazid M A A. Heat transfer over an unsteady stretching surface[J]. Heat and Mass Transfer, 2004, 41(1): 1-4. [7] Sharidan S, Mahmood T, Pop I. Similarity solutions for the unsteady boundary layer flow and heat transfer due to a stretching sheet[J]. International Journal of Applied Mechanics and Engineering, 2006, 11(3): 647-654. [8] Tsai R, Huang K H, Huang J S. Flow and heat transfer over an unsteady stretching surface with a non-uniform heat source[J]. International Communications in Heat and Mass Transfer, 2008, 35(10): 1340-1343. [9] Ishak A, Nazar R, Pop I. Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet[J].Heat and Mass Transfer, 2008, 44(8): 921-927. [10] Aziz A. A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(4): 1064-1068. [11] Vajravelu K, Roper T. Flow and heat transfer in a second grade fluid over a stretching sheet[J]. International Journal of Non-Linear Mechanics, 1999, 34(6): 1031-1036. [12] Chen C H. Combined heat and mass transfer in MHD free convection from a vertical surface with ohmic heating and viscous dissipation[J]. International Journal of Engineering Science, 2004, 42(7): 699-713. [13] Dulal Pal, Hiremath P S. Computational modelling of heat transfer over an unsteady stretching surface embedded in a porous medium[J]. Meccanica, 2010, 45(3): 415-424. [14] Vajravelu K, Hadjinicolaou A. Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation[J]. International Communications in Heat and Mass Transfer, 1993, 20(3): 417-430. [15] Veena P H, Subhash Abel M, Rajagopal K, Pravin V K. Heat transfer in a visco-elastic fluid past a stretching sheet with viscous dissipation and internal heat generation[J]. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 2006, 57(3): 447-463. [16] Saffman P G. On the stability of laminar flow of a dusty gas[J]. Journal of Fluid Mechanics, 1962, 13(1): 120-128. [17] Datta N, Mishra S K. Boundary layer flow of a dusty fluid over a semi-infinite flat plate[J]. Acta Mechanica, 1982, 42(1/2): 71-83. [18] Agranat V M. Effect of pressure gradient of friction and heat transfer in a dusty boundary layer[J]. Fluid Dynamics, 1988, 23(5): 729-732. [19] Vajravelu K, Nayfeh J. Hydromagnetic flow of a dusty fluid over a stretching sheet[J].International Journal of Non-Linear Mechanics, 1992, 27(6): 937-945. [20] XIE Ming-liang, LIN Jian-zhong, XING Fu-tang. On the hydrodynamic stability of a particle-laden flow in growing flat plate boundary layer[J].Journal of Zhejiang University, Science A, 2007, 8(2): 275-284. [21] Palani G, Ganesan P. Heat transfer effects on dusty gas flow past a semi-infinite inclined plate[J]. Forsch Ingenieurwes, 2007, 71(3/4): 223-230. [22] Gireesha B J, Ramesh G K, Subhas Abel M, Bagewadi C S. Boundary layer flow and heat transfer of a dusty fluid flow over a stretching sheet with non-uniform heat source/sink[J]. International Journal of Multiphase Flow, 2011, 37(8): 977-982. [23] Schlichting H. Boundary Layer Theory[M]. New York: McGraw-Hill, 1968. [24] Shercliff J A. A Text Book of Magneto-Hydromagnetics[M]. London: Pergamon Press, 1965.
点击查看大图
计量
- 文章访问数: 1757
- HTML全文浏览量: 141
- PDF下载量: 635
- 被引次数: 0