MHD Fluctuating Flow of Non-Newtonian Fluid through a Porous Medium Bounded by an Infinite Porous Plate

ABSTRACT

In present paper, an investigation has been made on the fluctuating flow of a non-Newtonian second grade fluid through a porous medium over a semi-infinite porous plate in presence of a transverse magnetic field B0. The governing equations have been solved analytically and the expressions for the velocity and stress fields are obtained. The free stream velocity*U*(*t*) fluctuates in time about a non-zero constant mean. The effects of the permeability parameter K and magnetic field parameter *M* on velocity field have been analyzed quantitatively with the help of figures. It is noticed that the velocity field asymptotically approaches free stream velocity as it goes far away from the plate.

In present paper, an investigation has been made on the fluctuating flow of a non-Newtonian second grade fluid through a porous medium over a semi-infinite porous plate in presence of a transverse magnetic field B0. The governing equations have been solved analytically and the expressions for the velocity and stress fields are obtained. The free stream velocity

KEYWORDS

Fluctuating Flow, Second Grade Fluid, Porous Medium, Transverse Magnetic Field, Free Stream Velocity

Fluctuating Flow, Second Grade Fluid, Porous Medium, Transverse Magnetic Field, Free Stream Velocity

Cite this paper

Bose, D. and Basu, U. (2015) MHD Fluctuating Flow of Non-Newtonian Fluid through a Porous Medium Bounded by an Infinite Porous Plate.*Applied Mathematics*, **6**, 1988-1995. doi: 10.4236/am.2015.612176.

Bose, D. and Basu, U. (2015) MHD Fluctuating Flow of Non-Newtonian Fluid through a Porous Medium Bounded by an Infinite Porous Plate.

References

[1] Soundalgekar, V.M. and Puri, P. (1969) On Fluctuating Flow of an Elastic-Viscous Fluid past an Infinite Plate with Variable Suction. Journal of Fluid Mechanics, 35, 561-573.

http://dx.doi.org/10.1017/S0022112069001297

[2] Shen, F., Tan, W., Zhao, Y. and Masuoka, T. (2006) The Rayleigh-Stokes Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative Model. Nonlinear Analysis: Real World Applications, 7, 1072-1080.

http://dx.doi.org/10.1016/j.nonrwa.2005.09.007

[3] Varshney, C.L. (1979) Fluctuating Flow of Viscous Fluid through a Porous Medium Bounded by a Porous Plate. Indian Journal of Pure and Applied Mathematics, 10, 1558-1564.

[4] Lighthill, M.J. (1954) The Response of Laminar Skin Friction and Heat Transfer to Fluctuations in the Stream Velocity. Proceedings of the Royal Society A, 224, 1-23.

http://dx.doi.org/10.1098/rspa.1954.0137

[5] Messiha, S.A.S. (1966) Laminar Boundary Layer in Oscillating Flow along an Infinite Flat Plate with Variable Suction. Proceedings of the Cambridge Philosophical Society, 62, 329-337.

http://dx.doi.org/10.1017/S030500410003989X

[6] Stuart, J.T. (1955) A Solution of the Navier-Stokes and Energy Equations Illustrating the Response of Skin Friction and Temperature of an Infinite Plate Thermometer to Fluctuations in the Stream Velocity. Proceedings of the Royal Society A, 231, 116-130.

http://dx.doi.org/10.1098/rspa.1955.0160

[7] Gholizadeh, A. (1990) MHD Oscillatory Flow past a Vertical Porous Plate through Porous Medium in the Presence of Thermal and Mass Diffusion with Constant Heat Source. Astrophysics and Space Science, 174, 303-310.

http://dx.doi.org/10.1007/BF00642515

[8] Moniem, A.A. and Hassanin, W.S. (2013) Solution of MHD Flow past a Vertical Porous Plate through a Porous Medium under Oscillatory Suction. Applied Mathematics, 4, 694-702.

http://dx.doi.org/10.4236/am.2013.44096

[9] Venkateswarlu, M., Ramana Reddy, G.V. and Lakshmi, D.V. (2013) Unsteady MHD Flow of a Viscous Fluid past a Vertical Porous Plate under Oscillatory Suction Velocity. Advances in Applied Science Research, 4, 52-67.

[10] Soundalgekar, V.M. and Takhar, H.S. (1977) MHD Oscillatory Flow past a Semi Infinite Plate. AIAA Journal, 15, 457-458.

http://dx.doi.org/10.2514/3.60646

[1] Soundalgekar, V.M. and Puri, P. (1969) On Fluctuating Flow of an Elastic-Viscous Fluid past an Infinite Plate with Variable Suction. Journal of Fluid Mechanics, 35, 561-573.

http://dx.doi.org/10.1017/S0022112069001297

[2] Shen, F., Tan, W., Zhao, Y. and Masuoka, T. (2006) The Rayleigh-Stokes Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative Model. Nonlinear Analysis: Real World Applications, 7, 1072-1080.

http://dx.doi.org/10.1016/j.nonrwa.2005.09.007

[3] Varshney, C.L. (1979) Fluctuating Flow of Viscous Fluid through a Porous Medium Bounded by a Porous Plate. Indian Journal of Pure and Applied Mathematics, 10, 1558-1564.

[4] Lighthill, M.J. (1954) The Response of Laminar Skin Friction and Heat Transfer to Fluctuations in the Stream Velocity. Proceedings of the Royal Society A, 224, 1-23.

http://dx.doi.org/10.1098/rspa.1954.0137

[5] Messiha, S.A.S. (1966) Laminar Boundary Layer in Oscillating Flow along an Infinite Flat Plate with Variable Suction. Proceedings of the Cambridge Philosophical Society, 62, 329-337.

http://dx.doi.org/10.1017/S030500410003989X

[6] Stuart, J.T. (1955) A Solution of the Navier-Stokes and Energy Equations Illustrating the Response of Skin Friction and Temperature of an Infinite Plate Thermometer to Fluctuations in the Stream Velocity. Proceedings of the Royal Society A, 231, 116-130.

http://dx.doi.org/10.1098/rspa.1955.0160

[7] Gholizadeh, A. (1990) MHD Oscillatory Flow past a Vertical Porous Plate through Porous Medium in the Presence of Thermal and Mass Diffusion with Constant Heat Source. Astrophysics and Space Science, 174, 303-310.

http://dx.doi.org/10.1007/BF00642515

[8] Moniem, A.A. and Hassanin, W.S. (2013) Solution of MHD Flow past a Vertical Porous Plate through a Porous Medium under Oscillatory Suction. Applied Mathematics, 4, 694-702.

http://dx.doi.org/10.4236/am.2013.44096

[9] Venkateswarlu, M., Ramana Reddy, G.V. and Lakshmi, D.V. (2013) Unsteady MHD Flow of a Viscous Fluid past a Vertical Porous Plate under Oscillatory Suction Velocity. Advances in Applied Science Research, 4, 52-67.

[10] Soundalgekar, V.M. and Takhar, H.S. (1977) MHD Oscillatory Flow past a Semi Infinite Plate. AIAA Journal, 15, 457-458.

http://dx.doi.org/10.2514/3.60646