Unsteady Incompressible Flow of a Generalised Oldroyed-B Fluid between Two Infinite Parallel Plates

ABSTRACT

This paper presents a study of visco-elastic flow of an
incompressible generalized Oldroyd-B fluid between two infinite parallel plates
in which the constitutive equation involves fractional order time derivative.
The solutions of field equations are being obtained for the motion of the said
fluid between two parallel plates where the lower plate starts to move with
steady velocity and the upper plate remains fixed in the first problem and the
upper plate oscillates with constant frequency and the other being at rest in
the second problem. The exact solutions for the velocity field are obtained by
using the

Cite this paper

D. Bose and U. Basu, "Unsteady Incompressible Flow of a Generalised Oldroyed-B Fluid between Two Infinite Parallel Plates,"*World Journal of Mechanics*, Vol. 3 No. 2, 2013, pp. 146-151. doi: 10.4236/wjm.2013.32012.

D. Bose and U. Basu, "Unsteady Incompressible Flow of a Generalised Oldroyed-B Fluid between Two Infinite Parallel Plates,"

References

[1] K. R. Rajagopal and A. S. Gupta, “On a Class of Exact Solutions to the Equations of Motion of a Second Grade Fluid,” International Journal of Engineering Science, Vol. 19, No. 7, 1981, pp. 1009-1014. doi:10.1016/0020-7225(81)90135-X

[2] W. C. Tan and M. Y. Xu, “The Impulsive Motion of at Plate in a General Second Grade Fluid,” Mechanics Research Communications, Vol. 29, No. 1, 2002, pp. 3-9. doi:10.1016/S0093-6413(02)00223-9

[3] M. Khan, T. Hayat and S. Asgar, “Exact Solution for MHD Flow of a Generalised Oldroyed-B Fluid with Modified Darcy’s Law,” International Journal of Engineering Science, Vol. 44, No. 5-6, 2006, pp. 333-339. doi:10.1016/j.ijengsci.2005.12.004

[4] W. C. Tan and T. Masuoka, “Stokes First Problem for an Oldroyd-B Fluid in a Porous Half-Space,” Physics of Fluids, Vol. 17, No. 2, 2005, 7 p. doi:10.1063/1.1850409

[5] H. T. Qi and M. Y. Xu, “Stokes First Problem for a Viscoelastic Fluid with the Generalized Oldroyd-B Model,” Acta Mechanica Sinica, Vol. 23, No. 5, 2007, pp. 463-469. doi:10.1007/s10409-007-0093-2

[6] C. Fetecau, M. Khan, C. Fetecau and H. Qi, “Exact Solutions for the Flow of a Generalised Oldroyed-B Fluid Induced by a Suddenly Moved Plate between Two Side Walls Perpendicular to the Plate,” Proceedings of the Romanian Academy, Series A, Vol. 11, 2010, pp. 3-10.

[7] Y. Liu, L. Zheng, X. Zhang and F. Zong, “The Oscillating Flows and Heat Transfer of a Generalized Oldroyed-B Fluid in Magnetic Field,” International Journal of Applied Mathematics, Vol. 40, 2010, p. 4.

[1] K. R. Rajagopal and A. S. Gupta, “On a Class of Exact Solutions to the Equations of Motion of a Second Grade Fluid,” International Journal of Engineering Science, Vol. 19, No. 7, 1981, pp. 1009-1014. doi:10.1016/0020-7225(81)90135-X

[2] W. C. Tan and M. Y. Xu, “The Impulsive Motion of at Plate in a General Second Grade Fluid,” Mechanics Research Communications, Vol. 29, No. 1, 2002, pp. 3-9. doi:10.1016/S0093-6413(02)00223-9

[3] M. Khan, T. Hayat and S. Asgar, “Exact Solution for MHD Flow of a Generalised Oldroyed-B Fluid with Modified Darcy’s Law,” International Journal of Engineering Science, Vol. 44, No. 5-6, 2006, pp. 333-339. doi:10.1016/j.ijengsci.2005.12.004

[4] W. C. Tan and T. Masuoka, “Stokes First Problem for an Oldroyd-B Fluid in a Porous Half-Space,” Physics of Fluids, Vol. 17, No. 2, 2005, 7 p. doi:10.1063/1.1850409

[5] H. T. Qi and M. Y. Xu, “Stokes First Problem for a Viscoelastic Fluid with the Generalized Oldroyd-B Model,” Acta Mechanica Sinica, Vol. 23, No. 5, 2007, pp. 463-469. doi:10.1007/s10409-007-0093-2

[6] C. Fetecau, M. Khan, C. Fetecau and H. Qi, “Exact Solutions for the Flow of a Generalised Oldroyed-B Fluid Induced by a Suddenly Moved Plate between Two Side Walls Perpendicular to the Plate,” Proceedings of the Romanian Academy, Series A, Vol. 11, 2010, pp. 3-10.

[7] Y. Liu, L. Zheng, X. Zhang and F. Zong, “The Oscillating Flows and Heat Transfer of a Generalized Oldroyed-B Fluid in Magnetic Field,” International Journal of Applied Mathematics, Vol. 40, 2010, p. 4.