Mathematical Analysis of Maxwell Fluid Flow through a Porous Plate Channel Induced by a Constantly Accelerating or Oscillating Wall

被引:25
|
作者
Fetecau, Constantin [1 ]
Ellahi, Rahmat [2 ,3 ]
Sait, Sadiq M. [4 ]
机构
[1] Acad Romanian Scientists, Sect Math, Bucharest 050094, Romania
[2] Int Islamic Univ, Fac Basic & Appl Sci, Dept Math & Stat, Islamabad 44000, Pakistan
[3] Univ Calif Riverside, Dept Mech Engn, Riverside, CA 92521 USA
[4] King Fahd Univ Petr & Minerals, Ctr Commun & IT Res, Res Inst, Dhahran 31261, Saudi Arabia
关键词
Maxwell fluid; porous plate channel; unsteady motions; finite Fourier sine transform; exact solutions; UNSTEADY UNIDIRECTIONAL FLOWS; VISCOELASTIC FLUID; MODEL;
D O I
10.3390/math9010090
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Exact expressions for dimensionless velocity and shear stress fields corresponding to two unsteady motions of incompressible upper-convected Maxwell (UCM) fluids through a plate channel are analytically established. The porous effects are taken into consideration. The fluid motion is generated by one of the plates which is moving in its plane and the obtained solutions satisfy all imposed initial and boundary conditions. The starting solutions corresponding to the oscillatory motion are presented as sum of their steady-state and transient components. They can be useful for those who want to eliminate the transients from their experiments. For a check of the obtained results, their steady-state components are presented in different forms whose equivalence is graphically illustrated. Analytical solutions for the incompressible Newtonian fluids performing the same motions are recovered as limiting cases of the presented results. The influence of physical parameters on the fluid motion is graphically shown and discussed. It is found that the Maxwell fluids flow slower as compared to Newtonian fluids. The required time to reach the steady-state is also presented. It is found that the presence of porous medium delays the appearance of the steady-state.
引用
收藏
页码:1 / 13
页数:13
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