Unsteady Couette Flow through a Porous Medium in a Rotating System

Affiliation(s)

Department of Applied Mathematics, Vidyasagar University, Midnapore, India.

Department of Mathematics, University of Gour Banga, English Bazar, India.

Department of Applied Mathematics, Vidyasagar University, Midnapore, India.

Department of Mathematics, University of Gour Banga, English Bazar, India.

ABSTRACT

An investigation has been made on an unsteady Couette flow of a viscous incompressible fluid through a porous me- dium in a rotating system. The solution of the governing equations has been obtained by the use of Laplace transform technique. It is found that the primary velocity decreases and the magnitude of the secondary velocity increases with an increase in rotation parameter. The fluid velocity components are decelerated by an increase of Reynolds number. An increase in porosity parameter leads to increase the primary velocity and the magnitude of the secondary velocity. It is also found that the solution for small time converges more rapidly than the general solution. The asymptotic behavior of the solution is analyzed for small as well as large values of rotation parameter and Reynolds number. It is observed that a thin boundary layer is formed near the moving plate of the channel and the thicknesses of the boundary layer increases with an increase in porosity parameter.

An investigation has been made on an unsteady Couette flow of a viscous incompressible fluid through a porous me- dium in a rotating system. The solution of the governing equations has been obtained by the use of Laplace transform technique. It is found that the primary velocity decreases and the magnitude of the secondary velocity increases with an increase in rotation parameter. The fluid velocity components are decelerated by an increase of Reynolds number. An increase in porosity parameter leads to increase the primary velocity and the magnitude of the secondary velocity. It is also found that the solution for small time converges more rapidly than the general solution. The asymptotic behavior of the solution is analyzed for small as well as large values of rotation parameter and Reynolds number. It is observed that a thin boundary layer is formed near the moving plate of the channel and the thicknesses of the boundary layer increases with an increase in porosity parameter.

KEYWORDS

Couette Flow; Rotation Parameter; Reynolds Number; Porous Medium; Rotating System and Boundary Layer

Couette Flow; Rotation Parameter; Reynolds Number; Porous Medium; Rotating System and Boundary Layer

Cite this paper

M. Jana, S. Das and R. Jana, "Unsteady Couette Flow through a Porous Medium in a Rotating System,"*Open Journal of Fluid Dynamics*, Vol. 2 No. 4, 2012, pp. 149-158. doi: 10.4236/ojfd.2012.24016.

M. Jana, S. Das and R. Jana, "Unsteady Couette Flow through a Porous Medium in a Rotating System,"

References

[1] G. K. Batchelor, “An Introduction to Fluid Dynamics,” Cambridge University Press, Cambridge, 1967.

[2] G. S. Seth, R. N. Jana and M. K. Maiti, “Unsteady Hydromagnetic Couette Flow in a Rotating System,” International Journal of Engineering Science, Vol. 20, No. 9, 1982, pp. 989-999. doi:10.1016/0020-7225(82)90034-9

[3] R. Ganapathy, “A Note on Oscillatory Couette Flow in a Rotating System,” Journal of Applied Mechanics, Vol. 61, No. 1, 1994, pp. 208-209. doi:10.1115/1.2901403

[4] A. S. Gupta, “Ekman Layer on a Porous Plate,” Physics of Fluids, Vol. 15, No. 5, 1972, pp. 930-931. doi:10.1063/1.1694002

[5] B. S. Mazumder, “An Exact Solution of Oscillatory Couette Flow in a Rotating System,” Journal of Applied Mechanics, Vol. 56, No. 4, 1991, pp. 1104-1107. doi:10.1115/1.2897694

[6] V. Vidyanidhi and S. D. Nigam, “Couette Flow between Rotating Parallel Plates under Constant Pressure Gradient,” Journal of Mathematical Physics, Vol. 1, 1967, pp. 85.

[7] R. N. Jana and N. Dutta, “Couette Flow and Heat Transfer in a Rotating System,” Acta Mechanica, Vol. 26, No. 1-4, 1977, pp. 301-306. doi:10.1007/BF01177152

[8] K. D. Singh and R. Sharma, “Three Dimensional Couette Flow through Porous Media,” Indian Journal of Pure and Applied Mathematics, Vol. 32, No. 12, 2001, pp. 1819- 1829.

[9] K. D. Singh, M. G. Gorla and H. Rajhans, “A Periodic Solution of Oscillatory Couette Flow through a Porous Medium in Rotating System,” Indian Journal of Pure and Applied Mathematics, Vol. 36, No. 3, 2005, pp. 151-159.

[10] M. Guria, R. N. Jana and S. K. Ghosh, “Unsteady Couette Flow in a Rotating System,” International Journal of Non-Linear Mechanics, Vol. 41, No. 6-7, 2006, pp. 838- 843. doi:10.1016/j.ijnonlinmec.2006.04.010

[11] B. K. Das, M. Guria and R. N. Jana, “Unsteady Couette Flow in a Rotating System,” Meccanica, Vol. 43, No. 5, 2008, pp. 517-521. doi:10.1007/s11012-008-9130-x

[12] S. Das, S. L. Maji, M. Guria and R. N. Jana, “Unsteady MHD Couette Flow in a Rotating System,” Mathematical and Computer Modelling, Vol. 50, No. 7-8, 2009, pp. 1211-1217.doi:10.1016/j.mcm.2009.05.036

[13] H. A. Attia, “Effect of Porosity on Unsteady Couette Flow with Heat Transfer in the Presence of Uniform Suction and Injection, Kragujevac Journal of Science, Vol. 31, No. 1, 2009, pp. 11-16.

[14] C. Israel-Cookey, E. Amos and C. Nwaigwe, “MHD Oscillatory Couette Flow of a Radiating Viscous Fluid in a Porous Medium with Periodic Wall Temperature,” American Journal of Scientific and Industrial Research, Vol. 1, No. 2, 2010, pp. 326-331.

[15] B. G. Prasad and R. Kumar, “Unsteady Hydromagnetic Couette Flow through a Porous Medium in a Rotating System,” Theoretical and Applied Mechanics Letters, Vol. 1, No. 4, 2011, Article ID: 042005. doi:10.1063/2.1104205

[16] S. Das, M. Jana and R. N. Jana, “Couette Flow through Porous Medium in a Rotating System, International Journal of Mathematical Archive, Vol. 2, No. 11, 2011, pp. 2318-2326.

[17] H. S. Carslaw and J. C. Jaeger, “Conduction of Heat in Solids,” Oxford University Press, Oxford, 1959, p. 297.

[1] G. K. Batchelor, “An Introduction to Fluid Dynamics,” Cambridge University Press, Cambridge, 1967.

[2] G. S. Seth, R. N. Jana and M. K. Maiti, “Unsteady Hydromagnetic Couette Flow in a Rotating System,” International Journal of Engineering Science, Vol. 20, No. 9, 1982, pp. 989-999. doi:10.1016/0020-7225(82)90034-9

[3] R. Ganapathy, “A Note on Oscillatory Couette Flow in a Rotating System,” Journal of Applied Mechanics, Vol. 61, No. 1, 1994, pp. 208-209. doi:10.1115/1.2901403

[4] A. S. Gupta, “Ekman Layer on a Porous Plate,” Physics of Fluids, Vol. 15, No. 5, 1972, pp. 930-931. doi:10.1063/1.1694002

[5] B. S. Mazumder, “An Exact Solution of Oscillatory Couette Flow in a Rotating System,” Journal of Applied Mechanics, Vol. 56, No. 4, 1991, pp. 1104-1107. doi:10.1115/1.2897694

[6] V. Vidyanidhi and S. D. Nigam, “Couette Flow between Rotating Parallel Plates under Constant Pressure Gradient,” Journal of Mathematical Physics, Vol. 1, 1967, pp. 85.

[7] R. N. Jana and N. Dutta, “Couette Flow and Heat Transfer in a Rotating System,” Acta Mechanica, Vol. 26, No. 1-4, 1977, pp. 301-306. doi:10.1007/BF01177152

[8] K. D. Singh and R. Sharma, “Three Dimensional Couette Flow through Porous Media,” Indian Journal of Pure and Applied Mathematics, Vol. 32, No. 12, 2001, pp. 1819- 1829.

[9] K. D. Singh, M. G. Gorla and H. Rajhans, “A Periodic Solution of Oscillatory Couette Flow through a Porous Medium in Rotating System,” Indian Journal of Pure and Applied Mathematics, Vol. 36, No. 3, 2005, pp. 151-159.

[10] M. Guria, R. N. Jana and S. K. Ghosh, “Unsteady Couette Flow in a Rotating System,” International Journal of Non-Linear Mechanics, Vol. 41, No. 6-7, 2006, pp. 838- 843. doi:10.1016/j.ijnonlinmec.2006.04.010

[11] B. K. Das, M. Guria and R. N. Jana, “Unsteady Couette Flow in a Rotating System,” Meccanica, Vol. 43, No. 5, 2008, pp. 517-521. doi:10.1007/s11012-008-9130-x

[12] S. Das, S. L. Maji, M. Guria and R. N. Jana, “Unsteady MHD Couette Flow in a Rotating System,” Mathematical and Computer Modelling, Vol. 50, No. 7-8, 2009, pp. 1211-1217.doi:10.1016/j.mcm.2009.05.036

[13] H. A. Attia, “Effect of Porosity on Unsteady Couette Flow with Heat Transfer in the Presence of Uniform Suction and Injection, Kragujevac Journal of Science, Vol. 31, No. 1, 2009, pp. 11-16.

[14] C. Israel-Cookey, E. Amos and C. Nwaigwe, “MHD Oscillatory Couette Flow of a Radiating Viscous Fluid in a Porous Medium with Periodic Wall Temperature,” American Journal of Scientific and Industrial Research, Vol. 1, No. 2, 2010, pp. 326-331.

[15] B. G. Prasad and R. Kumar, “Unsteady Hydromagnetic Couette Flow through a Porous Medium in a Rotating System,” Theoretical and Applied Mechanics Letters, Vol. 1, No. 4, 2011, Article ID: 042005. doi:10.1063/2.1104205

[16] S. Das, M. Jana and R. N. Jana, “Couette Flow through Porous Medium in a Rotating System, International Journal of Mathematical Archive, Vol. 2, No. 11, 2011, pp. 2318-2326.

[17] H. S. Carslaw and J. C. Jaeger, “Conduction of Heat in Solids,” Oxford University Press, Oxford, 1959, p. 297.