Flow on Oscillating Rectangular Duct for Maxwell Fluid
-
摘要: 分析了不可压缩Maxwell流体在震荡矩形截面管道中的非稳定流动问题.利用Fourier变换和Laplace变换作为数学工具,提出了问题的解,该解可以看成稳态解和暂态解之和.大倍数时,暂态消失,解可以表示为稳态解.在极限情况的案例中给出了Newton流体的解.当震荡频率不存在时,得到了Maxwell流体在震荡矩形截面管道中流动问题的解.最后,以图形形式给出不同参数时,矩形管道正弦震荡达到稳态所需要的时间.同时,分别描绘了x和y变化时的速度曲线.Abstract: An analysis for the unsteady flow of an incompressible Maxwell fluid in an oscillating rectangular cross section was presented. Using the Fourier and Laplace transforms as mathematical tool, the solutions were presented as sum of steady-state and transient solutions. For large times, when the transients disappear, the solution was represented by the steady-state solution. Solutions for Newtonian fluids appear as limiting cases of the solutions obtained here. In the absence of frequency of oscillation, the problem for flow of Maxwell fluid in a duct of rectangular cross-section moving parallel to its length was obtained. Finally, the required time to reach the steady-state for sine oscillations of the rectangular duct is obtained by graphical illustrations for different parameters. Moreover, the graphs are sketched for velocity for the variations of x and y.
-
Key words:
- Maxwell fluid /
- oscillating rectangular duct /
- velocity field
-
[1] Vieru D, Nazar M, Fetecau Corina, Fetecau C. New exact solutions corresponding to the first problem of Stokes for Oldroyd-B fluids[J]. Int J Computers and Mathematics With Appl, 2008, 55(8): 1644-1652. [2] Fetecau C, Fetecau Corina. Decay of a potential vortex in a Maxwell fluid[J]. Int J Non-Linear Mech, 2003, 38(7): 985-990. [3] Fetecau C, Fetecau Corina. A new exact solution for the flow of a Maxwell fluid past an infinite plate[J]. Int J Non-Linear Mech, 2003, 38(3): 423-427. [4] Fetecau C, Fetecau Corina. The Rayleigh-Stokes-Problem for a fluid of Maxwellian type[J]. Int J Non-Linear Mech, 2003, 38(4): 603-607. [5] Nadeem S, Asghar S, Hayat T, Hussain Mazhar. The Rayleigh Stokes problem for rectangular pipe in Maxwell and second grade fluid[J]. Meccanica, 2008, 43(5): 495-504. [6] Chen C K, Chen C I, Yang Y T. Unsteady unidirectional flow of a Maxwell fluid in a circular duct with different given volume flow rate conditions[J]. J Mechanical Engineering Science, 2002, 216(5): 583-590. [7] Broer L J F. On the hydrodynamics of viscoelastic fluids[J]. Appl Sci Res A, 1956, 6(2/3): 226-236. [8] Thurston G R. Theory of oscillation of a viscoelastic medium between parallel planes[J]. J Appl Phys, 1959, 30(12): 1855-1860. [9] Thurston G R. Theory of oscillation of a viscoelastic fluid in a circular tube[J]. JASA, 1960, 32(2): 210-213. [10] Jones J R, Walters T S. Flow of elastico-viscous liquids in channels under the influence of a periodic pressure gradient—part Ⅰ[J]. Rheol Acta , 1967, 6(3): 240-245. [11] Jones J R, Walters T S. Flow of elastico-viscous liquids in channels under the influence of a periodic pressure gradient—part Ⅱ[J]. Rheol Acta, 1967, 6(4): 330-338. [12] Peev G, Elenkov D, Kunev I. On the problem of oscillatory laminar flow of elastico-viscous liquids in channels[J]. Rheol Acta, 1970, 9(4): 506-508. [13] Bhatnagar R K. Flow of an Oldroyd fluid in a circular pipe with time dependent pressure gradient[J]. Appl Sci Res, 1975, 30(4): 241-267. [14] Ramkissoon H, Eswaran C V, Majumdar S R. Unsteady flow of an elastico-viscous fluid in tubes of uniform cross-section[J]. Int J Non-Linear Mech, 1989, 24(6): 585-597. [15] Rahaman K D, Ramkissoon H. Unsteady axial viscoelastic pipe flows[J]. J Non-Newtonian Fluid Mech, 1995, 57(1): 27-38. [16] Walitza E, Maisch E, Chmiel H, Andrade I. Experimental and numerical analysis of oscillatory tube flow of viscoelastic fluids represented at the example of human blood[J]. Rheol Acta, 1979, 18(1): 116-121. [17] Bohme G. Stromungsmechanik Nicht-Newtonscher Fluid[M]. Stuttgart: B G Teubner, 1981. [18] Wood W P. Transient viscoelastic helical flows in pipes of circular and annular cross-section[J]. J Non-Newtonian Fluid Mech, 2001, 100(1/3): 115-126. [19] Nazar M, Zulqarnain M, Saeed Akram M, Asif M. Flow through an oscillating rectangular duct for generalized Maxwell fluid with fractional derivatives[J]. Communications in Nonlinear Science and Numerical Simulation, 2012, 17(8): 3219-3234.
点击查看大图
计量
- 文章访问数: 1189
- HTML全文浏览量: 80
- PDF下载量: 1086
- 被引次数: 0