Journal of Porous Media

MAGNETOHYDRODYNAMIC FLOW PAST A POROUS PLATE IN PRESENCE OF RAYLEIGH TYPE STREAMING EFFECT

SINOPSIS

Invoking a suitable approximation method, we have analyzed the flow pattern generated due to the interaction of a standing sound wave in the presence of a transverse magnetic field with a fluid which is slowly discharged from the porous wall. Also, the superposition of a secondary flow field in the presence of a magnetic field and the velocity of discharge, ν₀, affects the flow pattern. This problem is tackled by invoking the method of successive approximations with respect to the small quantity U₀, the amplitude of velocity fluctuations in the sound wave. Notably, the impact of porous wall and magnetic field results in damping. It has been shown graphically that there will be no oscillations in the velocity due to the presence of the magnetic field.

REFERENCIAS

1. Acharya, M., Singh, L.P., and Dash, G.C., Heat and Mass Transfer over an Accelerating Surface with Heat Source in Presence of Suction andBlowing, Int. J. Eng. Sci, vol. 37, no. 2, pp. 189-211, 1999. .

2. Ali, N., Khan, S.U., Sajid, M., and Abbas, Z., Slip Effects in the Hydromagnetic Flow of a Viscoelastic Fluid through Porous Medium over a Porous Oscillatory Stretching Sheet, J. Porous Media, vol. 20, no. 3, pp. 249-262, 2017. .

3. Chandran, P., Sacheti, N.C., and Singh, A.K., Unsteady Hydromagnetic Free Convection Flow with Heat Flux and Accelerated Boundary Motion, J. Phys. Soc. Japan, vol. 67, no. 1, pp. 124-129,1998. .

4. Cuevas, S. and Ramos, E., Steady Streaming in Oscillatory Viscous Flow under a Transverse Magnetic Field, Phys. Fluids., vol. 9, no. 5, pp. 1430-1434, 1997. .

5. Das, S.S., Sahoo, S.K., and Dash, G.C., Numerical Solution of Mass Transfer Effects on Unsteady Flow past an Accelerated Vertical Porous Plate with Suction, Bulletin Malaysian Math. Sci. Soc, vol. 29, no. 1, pp. 33-42,2006. .

6. Das, S.S., Satapathy, A., Das, J.K., and Panda, J.P., Mass Transfer Effects on MHD Flow and Heat Transfer past a Vertical Porous Plate through a Porous Medium under Oscillatory Suction and Heat Source, Int. J. Heat Mass Transf., vol. 52, nos. 25-26, pp. 5962-5969, 2009. .

7. Ellahi, R., Tariq, M.H., Hassan, M., and Vafai, K., On Boundary Layer Nano-Ferroliquid Flow under the Influence of Low Oscil-lating Stretchable Rotating Disk, J. Molecular Liquids, vol. 229, pp. 339-345,2017. .

8. Fand, R.M. and Kaye, J.T., The Influence of Sound on Free Convection from a Horizontal Cylinder, J. Heat Transf., vol. 83, no. 2, pp. 133-143, 1961. .

9. Gupta, A.S., Effect of a Standing Sound Field on the Magnetohydrodynamic Flow past a Flat Plate, Zeitschrift fur Angewandte Mathematik undPhysik (ZAMP), vol. 17, no. 2, pp. 260-266, 1966. .

10. Gutfinger, C., Vainshtein, P., and Fichman, M., Enhancement of Heat and Mass Transfer by Sound Waves, in Institution of Chemical Engineers Symposium Series, vol. 135, pp. 37-42, 1994. .

11. Hamilton, M.F., Ilinskii, Y.A., and Zabolotskaya, E.A., Acoustic Streaming Generated by Standing Waves in Two-Dimensional Channels of Arbitrary Width, J. Acoustical Soc. America, vol. 113, no. 1, pp. 153-160, 2003. .

12. Hasimoto, H., Boundary Layer Growth on a Flat Plate with Suction or Injection, J. Phys. Soc. Japan, vol. 12, no. 1, pp. 68-72, 1957. .

13. Kawahara, N., Yarin, A.L., Brenn, G., Kastner, O., and Durst, F., Effect of Acoustic Streaming on the Mass Transfer from a Sublimating Sphere, Phys. Fluids, vol. 12, no. 4, pp. 912-923, 2000. .

14. Kestin, J. and Persen, L.N., The Effect of a Standing Sound Field on a Slow Stream Discharged from a Porous Wall, Appl. Sci. Res., Section A, vol. 11, nos. 4-6, pp. 361-375, 1963. .

15. Kim, Y. J., Unsteady MHD Convective Heat Transfer past a Semi-Infinite Vertical Porous Moving Plate with Variable Suction, Int. J Eng. Sci., vol. 38, no. 8, pp. 833-845, 2000. .

16. Landau, L.D. and Lifshitz, E.M., Fluid Mechanics, Oxford, UK: Pergamon, 1993. .

17. Lin, Y. and Farouk, B., Heat Transfer and Flow Characteristics in an Acoustically Driven Resonator with Internal Thin Parallel Plates, Proc. of 13th Int. Heat Trans. Conf., Sydney, Australia, August 13-18, 2006. .

18. Luchini, P. and Charru, F., Acoustic Streaming past a Vibrating Wall, Phys. Fluids, vol. 17, no. 12, pp. 122106-1-122106-7,2005. .

19. Mansutti, D., Pontrelli, G., and Rajagopal, K.R., Steady Flows of Non-Newtonian Fluids past a Porous Plate with Suction or Injection, Int. J. Numer. Methods Fluids, vol. 17, no. 11, pp. 927-941,1993. .

20. Nyborg, W.L., Acoustic Streaming near a Boundary, J. Acoustical Soc. America, vol. 30, no. 4, pp. 329-339, 1958. .

21. Panda, J.P., Dash, G.C., and Das, S.S., Unsteady Free Convective Flow and Mass Transfer of a Rotating Elastico-Viscous Liquid through Porous Media past a Vertical Porous Plate, AMSEJ. Mod. Meas. Cont. B, vol. 72, no. 3, pp. 47-59, 2003. .

22. Rayleigh, L., On the Circulation of Air Observed in Kundt's Tube, and on Some Acoustical Problems, Philosoph. Transact. Ser. I, vol. 175, pp. 1-21, 1884. .

23. Schlichting, H., Boundary Layer Theory, Oxford, UK: Pergamon, 1955. .

24. Srivastava, N., Rayleigh Type Streaming Effect on Magnetohydrodynamic Characteristics of Fluidized Bed Particles, Powder Technol., vol. 320, pp. 108-113, 2017a. .

25. Srivastava, N., Effect of Permeability on the Rayleigh-Type Acoustic Streaming, in Innovative Design and Development Practices in Aerospace and Automotive Engineering, Singapore: Springer, pp. 149-155, 2017b. .

26. Vainshtein, P., Rayleigh Streaming at Large Reynolds Number and Its Effect on Shear Streaming Flow, J. FluidMech., vol. 285, pp. 249-264, 1995. .

27. Westervelt, P.J., The Theory of Steady Rotational Flow Generated by a Sound Field, J. Acoustical Soc. America, vol. 25, pp. 60-67, 1953. .