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MHD flow of a visco-elastic fluid through a porous medium between infinite parallel plates with time dependent suction

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Abstract

This work provides a comprehensive theoretical analysis of MHD unsteady free convection viscoelastic fluid flow through a porous medium. The medium is treated as incompressible and optically transparent. The flow of the fluid is initiated by shearing action of the moving wall with time dependent suction. Radiative heat flow is considered in temperature equation. The coupled non-linear problem has been solved asymptotically. Approximate solutions have been obtained for the mean velocity, mean temperature using multi parameter perturbation technique. The originality of the present study is to investigate the effect of viscoelastic property of the fluid (Walters B′ model) on the flow and heat transfer phenomena when the flow is permeated through a porous medium with uniform porous matrix subject to transverse magnetic field and time dependent fluctuative suction at the boundary surface. The case of viscous flow has been discussed as a particular case on comparison with the result reported earlier and it is in good agreement. Flow reversal is indicated incase of viscoelastic fluid with high heat capacity in the presence of magnetic field. The higher cooling of the plate in case of viscoelastic flow also causes a flow reversal.

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References

  1. BEARD D. W., WALTERS K. Elastico-viscous boundary layer flow. Two dimensional flow near a stagnation point[J]. Proceedings of the Cambridge Philosophical Society, 1964, 60(3): 667–674.

    Article  MathSciNet  Google Scholar 

  2. CHOWDHURY M. K., ISLAM M. N. MHD free convection flow of viscoelastic fluid past an infinite vertival porous plate[J]. Heat and Mass Transfer, 2000, 36(5): 439–447.

    Article  Google Scholar 

  3. ABEL M. S., KHAN S. K. and PRASAD K. V. Study of viscoelastic fluid flow and heat transfer over a stretching sheet with variable viscosity[J]. International Journal of Non-Linear Mechanics, 2002, 37(1): 81–88.

    Article  Google Scholar 

  4. ASGHAR S., MOHYUDDIN M. R. and HAYAT T. et al. The flow of non-Newtonian fluid induced due to oscillation of a porous plate[J]. Mathematical Problems in Engineering, 2004, 2: 133–143.

    Google Scholar 

  5. KHAN S. K., SANJAYANAND E. Viscoelastic boundary layer MHD flow through a porous medium over a porous quadratic stretching sheet[J]. Archives of Mechanics, 2004, 56(3): 191–204.

    MATH  Google Scholar 

  6. KHAN S. K. Heat transfer in viscoelastic fluid flow over a stretching surface with heat source/sink, suction/blowing and radiation[J]. International Journal of Heat and Mass transfer, 2006, 49(3): 628–639.

    Article  MathSciNet  Google Scholar 

  7. YAMAMOTO K., YOSHIDA Z. Suction and injection flow with convective acceleration through porous wall[J]. Journal of the Physical Society of Japan, 1974, 37(3): 774–779.

    Article  Google Scholar 

  8. CHAWLA S. S., SINGH S. Oscillatory flow past a porous bed[J]. Acta Mechanics, 1979, 34(3-4): 205–213.

    Google Scholar 

  9. RAPTIS A., PEREDIKIS C. and TZIVANIDIS G. Free convection flow through a porous medium bounded by a vertical surface[J]. Journal of Physics D Applied Physics, 1981, 14(7): L99–L102.

    Article  Google Scholar 

  10. SINGH A. K., SINGH A. K. and SINGH N. P. Heat and mass transfer in MHD flow of a viscous fluid past a vertical plate under oscillatory suction velocity[J]. Indian Journal of Pure and Applied Mathematics, 2003, 34(3): 429–442.

    MATH  Google Scholar 

  11. FERDOWS M., SATTAR M. A. and SIDDIQUI M. N. A. Numerical approach on parameters of the thermal radiation interaction with convection in boundary layer flow at a vertical[J]. Thammasat International Journal of Non-Linear Mechanics, 2004, 9(3): 19–23.

    Google Scholar 

  12. MISHRA S. R., DASH G. C. and ACHARYA M. Mass and heat transfer effect on MHD flow of a visco-elastic fluid through porous medium with oscillatory suction and heat source[J]. International Journal of Heat and Mass Transfer, 2013, 57(2): 433–438..

    Article  Google Scholar 

  13. MASSOUDI M., PHUOE T. X. Unsteady motion of a non-linear viscoelastic fluid[J]. International Journal of Non-Linear Mechanics, 2009, 44(10): 1063–1072.

    Article  Google Scholar 

  14. SOCHI T. Non-Newtonian flow in porous media[J]. Polymer, 2010, 51(22): 5007–5023.

    Article  Google Scholar 

  15. ALHARBI S., BAZID M. and GENDY M. Heat and mass transfer in MHD visco-elastic fluid flow through a porous medium over a stretching sheet with chemical reaction[J]. Applied Mathematics, 2010, 1(6): 446–455.

    Article  Google Scholar 

  16. KUMAR J. G., SATYANARAYAN P. V. Mass transfer effect on MHD unsteady free convective Walters memory flow with constant suction and heat sink[J]. International Journal of Applied Mathematics and Mechanics, 2011, 7(19): 97–109.

    Google Scholar 

  17. SIVRAJ R., RUSHI KUMAR B. Unsteady MHD dusty visco-elastic fluid Couette flow in an irregular channel with varying mass diffusion[J]. International Journal of Heat and Mass Transfer, 2012, 55(11-12): 3076–3089.

    Google Scholar 

  18. Nhan-Phan-Thein. Understanding viscoelasticity. An introduction to Rheology[M]. 2nd Edition, Berlin, Germany, Springer.

  19. HASSANIEN I. A. Unsteady hydromagnetic flow through a porous medium between two infinite parallel porous plates with time varying suction[J]. Astrophysucs and Space Science, 1991, 175(1): 135–147.

    Article  Google Scholar 

  20. ALAGOA K. D., TAY G. and ABBEY T. M. Radiative and free convective effects of a MHD flow through a porous medium between infinite parallel plates with time dependent suction[J]. Astrophysics and Space Science, 1998, 260: 455–468.

    Article  Google Scholar 

  21. BESTMANN A. R. Free convection effects on the flow past a vertical porous plate set impulsively into motion with negligible dissipation[J]. Acta Physical Academiae Scientiarum Hungaricae, 1979, 46(3): 129–136.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, College of Basic Science and Humanities, OUAT, Bhubaneswar, 751003, India

    S. Baag & M. R. Acharya

  2. Department of Mathematics, ITER, SOA University, Bhubaneswar, 751030, India

    G. C. Dash & S. R. Mishra

Authors
  1. S. Baag
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  2. M. R. Acharya
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  3. G. C. Dash
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  4. S. R. Mishra
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Correspondence to S. Baag.

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Biography: BAAG S. (1976-), Female, Ph. D., Assistant Professor

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Baag, S., Acharya, M.R., Dash, G.C. et al. MHD flow of a visco-elastic fluid through a porous medium between infinite parallel plates with time dependent suction. J Hydrodyn 27, 738–747 (2015). https://doi.org/10.1016/S1001-6058(15)60536-4

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  • DOI: https://doi.org/10.1016/S1001-6058(15)60536-4

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