Velocity and shear stress for an Oldroyd-B fluid within two cylinders

详细信息    查看全文

• 作者：Shin Min Kang ; Waqas Nazeer ; Muhammad Athar…
• 关键词：Oldroyd ; B fluid ; velocity field ; shear stress ; rotational oscillatory flow ; Laplace and Hankel transforms
• 刊名：Boundary Value Problems
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,433 KB
• 参考文献：1. Stokes, GG: On the Effect of the Rotation of Cylinders and Spheres About Their Axes in Increasing the Logarithmic Decrement of the Arc of Vibration. Cambridge University Press, Cambridge (1886)
  2. Casarella, MJ, Laura, PA: Drag on oscillating rod with longitudinal and torsional motion. J. Hydronaut. 3, 180-183 (1969) CrossRef
  3. Rajagopal, KR: Longitudinal and torsional oscillations of a rod in a non-Newtonian fluid. Acta Mech. 49, 281-285 (1983) CrossRef MATH
  4. Rajagopal, KR, Bhatnagar, RK: Exact solutions for some simple flows of an Oldroyd-B fluid. Acta Mech. 113, 233-239 (1995) CrossRef MathSciNet MATH
  5. Erdogan, ME: A note on an unsteady flow of a viscous fluid due to an oscillating plane wall. Int. J. Non-Linear Mech. 35, 1-6 (2000) CrossRef MathSciNet MATH
  6. Fetecau, C, Vieru, D, Fetecau, C: A note on the second problem of Stokes for Newtonian fluids. Int. J. Non-Linear Mech. 43, 451-457 (2008) CrossRef MATH
  7. Fetecau, C, Fetecau, C: Starting solutions for some unsteady unidirectional flows of a second grade fluid. Int. J. Eng. Sci. 43, 781-789 (2005) CrossRef MathSciNet MATH
  8. Fetecau, C, Fetecau, C: Starting solutions for the motion of a second grade fluid due to longitudinal and torsional oscillations of a circular cylinder. Int. J. Eng. Sci. 44, 788-796 (2006) CrossRef MathSciNet MATH
  9. Vieru, D, Akhtar, W, Fetecau, C, Fetecau, C: Starting solutions for the oscillating motion of a Maxwell fluid in cylindrical domains. Meccanica 42, 573-583 (2007) CrossRef MATH
  10. Hayat, T, Siddiqui, AM, Asghar, S: Some simple flows of an Oldroyd-B fluid. Int. J. Eng. Sci. 39, 135-147 (2001) CrossRef
  11. Hayat, T, Mumtaz, S, Ellahi, R: MHD unsteady flows due to non-coaxial rotations of a disk and a fluid at infinity. Acta Mech. Sin. 19, 235-240 (2003) CrossRef
  12. Hayat, T, Ellahi, R, Asghar, S, Siddiqui, AM: Flow induced by non-coaxial rotation of a porous disk executing non-torsional oscillating and second grade fluid rotating at infinity. Appl. Math. Model. 28, 591-605 (2004) CrossRef
  13. Hayat, T, Ellahi, R, Asghar, S: Unsteady periodic flows of a magnetohydrodynamic fluid due to non-coaxial rotations of a porous disk and fluid at infinity. Math. Comput. Model. 40, 173-179 (2004) CrossRef MathSciNet MATH
  14. Aksel, N, Fetecau, C, Scholle, M: Starting solutions for some unsteady unidirectional flows of Oldroyd-B fluids. Z. Angew. Math. Phys. 57, 815-831 (2006) CrossRef MathSciNet MATH
  15. Khan, M, Ellahi, R, Hayat, T: Exact solution for oscillating flows of generalized Oldroyd-B fluid through porous medium in a rotating frame. J. Porous Media 12, 777-788 (2009) CrossRef
  
• 作者单位：Shin Min Kang (1)
  Waqas Nazeer (2)
  Muhammad Athar (2)
  Muhammad Danial Hisham (2)
  Young Chel Kwun (3)
  
  1. Department of Mathematics and RINS, Gyeongsang National University, Jinju, 660-701, Korea
  2. Division of Science and Technology, University of Education, Township, Lahore, Pakistan
  3. Department of Mathematics, Dong-A University, Busan, 604-714, Korea
  
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

This paper aims to explore the possible solutions for the movement of an Oldroyd-B fluid placed under certain conditions, i.e. the fluid is present within two cylinders, which are coaxial and oscillating within. Having said that the governing model will be an Oldroyd-B fluid, we wish to achieve our goal of finding the velocity and shear stress by using some common transformations, namely the Laplace transformation and the Hankel transformation. The final results, for the sake of simplicity, will be expressed in the form of generalized G-function and they satisfy all imposed initial and boundary conditions. Keywords Oldroyd-B fluid velocity field shear stress rotational oscillatory flow Laplace and Hankel transforms