Skip to main content
SpringerLink
Log in

Unsteady MHD natural convection flow with exponentially accelerated free-stream past a vertical plate in the presence of hall current and rotation

  • Published:
Rendiconti del Circolo Matematico di Palermo Series 2 Aims and scope Submit manuscript

Abstract

Investigation of unsteady MHD natural convection flow of an electrically conducting, viscous, incompressible and heat absorbing fluid past an infinite vertical plate through a fluid saturated porous medium with exponentially accelerated free-stream in a rotating system with Hall effects is carried out. Exact solution for fluid temperature and fluid velocity are obtained using Laplace transform technique. Expressions for the shear stresses at the plate due to primary and secondary flows and rate of heat transfer at the plate are also derived. In order to get some physical insight into the flow pattern, asymptotic behavior of the solution for fluid temperature and fluid velocity are analyzed for small as well as large values of time. It is interesting to note that there exists reverse flow in the secondary flow direction due to presence of thermal buoyancy force.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Cheng, P., Minkowycz, W.J.: Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. J. Geophys. Res. 82, 2040–2044 (1977)

    Article  Google Scholar 

  2. Raptis, A.A., Singh, A.K.: Free-convection flow past an impulsively started vertical plate in a porous medium by finite difference method. Astrophys. Space Sci. 112, 259–265 (1985)

    Article  MATH  Google Scholar 

  3. Nakayama, A., Koyama, H.: A general similarity transformation for combined free and forced convection flows within a fluid saturated porous medium. J. Heat Transf. 109, 1041–1045 (1987)

    Article  Google Scholar 

  4. Hsieh, J.C., Chen, T.S., Armaly, B.F.: Nonsimilarity solutions for mixed convection from vertical surfaces in porous media: variable surface temperature or heat flux. Int. J. Heat Mass Transf. 36(6), 1485–1493 (1993)

    Article  MATH  Google Scholar 

  5. Bakier, A.Y., Mansour, M.A., Gorla, R.S.R., Ebiana, A.B.: Nonsimilar solutions for free convection from a vertical plate in porous media. Heat Mass Transf. 33, 145–148 (1997)

    Article  Google Scholar 

  6. Vasseur, P., Degan, G.: Free convection along a vertical heated plate in a porous medium with anisotropic permeability. Int. J. Numer. Methods Heat Fluid Flow 8, 43–63 (1998)

    Article  MATH  Google Scholar 

  7. Elbashbeshy, E.M.A., Bazid, M.A.: The mixed convection along a vertical plate with variable surface heat flux embedded in porous medium. Appl. Math. Comput. 125, 317–324 (2002)

    MATH  Google Scholar 

  8. Bachok, N., Ishak, A., Pop, I.: Mixed convection boundary layer flow over a permeable vertical flat plate embedded in an anisotropic porous medium, Math. Prob. Eng. 2010, Article ID-659023, 12. doi:10.1155/2010/659023 (2010)

  9. Aldoss, T.K., Al-Nimr, M.A., Jarrah, M.A., Al-Sha’er, B.J.: Magnetohydrodynamic mixed convection from a vertical plate embedded in a porous medium. Numer. Heat Transf. Part A: Appl.: Int. J. Comput. Methodol. 28, 635–645 (1995)

    Article  Google Scholar 

  10. Kim, Y.J., Lee, J.C.: Analytical studies on MHD oscillatory flow of a micropolar fluid over a vertical porous plate. Surf. Coat. Tech. 171, 187–193 (2002)

    Article  Google Scholar 

  11. EL-Kabeir, S.M.M., Rashad, A.M., Gorla, R.S.R.: Unsteady MHD combined convection over a moving vertical sheet in a fluid saturated porous medium with uniform surface heat flux. Math. Comput. Model. 46, 384–397 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Aydin, O., Kaya, A.: MHD mixed convection of a viscous dissipating fluid about a permeable vertical flat plate. Appl. Math. Model. 33, 4086–4096 (2009)

    Article  MATH  Google Scholar 

  13. Pal, D.: Magnetohydrodynamic non-Darcy mixed convection heat transfer from a vertical heated plate embedded in a porous medium with variable porosity. Commun. Nonlinear Sci. Numer. Simul. 15, 3974–3987 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kumar, A., Singh, A.K.: Unsteady MHD free convective flow past a semi-infinite vertical wall with induced magnetic field. Appl. Math. Comput. 222, 462–471 (2013)

    MathSciNet  MATH  Google Scholar 

  15. Jha, B.K.: MHD free and forced convection flow past an infinite vertical plate with heat source. Astrophys. Space Sci. 183, 169–175 (1991)

    Article  MATH  Google Scholar 

  16. Sharma, R., Bhargava, R., Singh, I.V.: Combined effect of magnetic field and heat absorption on unsteady free convection and heat transfer flow in a micropolar fluid past a semi-infinite moving plate with viscous dissipation using element free Galerkin method. Appl. Math. Comput. 217, 308–321 (2010)

    MathSciNet  MATH  Google Scholar 

  17. Reddy, P.B.A., Reddy, N.B., Palani, G.: Convective flow past a vertical plate under the influence of magnetic field and thermal radiation subjected to a variable surface temperature in the presence of heat source/sink. Thermophys. Aeromech. 19, 489–501 (2012)

    Article  Google Scholar 

  18. Nandkeolyar, R., Das, M.: Unsteady MHD free convection flow of a heat absorbing dusty fluid past a flat plate with ramped wall temperature. Afr. Mat. 25, 779–798 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. Singh, A.K.: MHD free convection flow past an accelerated vertical porous plate in a rotating fluid. Astrophys. Space Sci. 103, 155–163 (1984)

    Article  MATH  Google Scholar 

  20. Raptis, A.A., Singh, A.K.: Rotation effects on MHD free-convection flow past an accelerated vertical plate. Mech. Res. Commun. 12, 31–40 (1985)

    Article  MATH  Google Scholar 

  21. Nanousis, N.: Thermal diffusion effects on MHD free convective and mass transfer flow past a moving infinite vertical plate in a rotating fluid. Astrophys. Space Sci. 191, 313–322 (1992)

    Article  MATH  Google Scholar 

  22. Bestman, A.R., Adjepong, S.K.: Unsteady hydromagnetic free-convection flow with radiative heat transfer in a rotating fluid. Astrophys. Space Sci. 143, 73–80 (1988)

    Article  Google Scholar 

  23. Seth, G.S., Nandkeolyar, R., Ansari, MdS: Effect of rotation on unsteady hydromagnetic natural convection flow past an impulsively moving vertical plate with ramped temperature in a porous medium with thermal diffusion and heat absorption. Int. J. Appl. Math. Mech. 7, 52–69 (2011)

    Google Scholar 

  24. Lighthill, M.J.: The response of laminar skin friction and heat transfer to fluctuations in the stream velocity. Proc. R. Soc. Lond. A 224, 1–23 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  25. Lin, C.C.: Motion in the boundary layer with a rapidly oscillating external flow. Proc. 9th Int. Congress Appl. Mech. Brussels 4, 155–167 (1957)

  26. Warsi, Z.U.A.: Motion in a three-dimensional boundary layer with a rapidly oscillating external flow. J. Phys. Soc. Jpn. 19, 121–124 (1964)

    Article  Google Scholar 

  27. Messiha, S.A.S.: Laminar boundary layers in oscillating flow along an infinite flat plate with variable suction. Math. Proc. Camb. Philos. Soc. 62, 329–337 (1966)

    Article  MATH  Google Scholar 

  28. Soundalgekar, V.M.: Free convection effects on the oscillatory flow past an infinite, vertical, porous plate with constant suction: II. Proc. R. Soc. Lond. A 333, 37–50 (1973)

    Article  MATH  Google Scholar 

  29. Raptis, A., Perdikis, C.P.: Oscillatory flow through a porous medium by the presence of free convective flow. Int. J. Eng. Sci. 23, 51–55 (1985)

    Article  MATH  Google Scholar 

  30. Gholizadeh, A.: MHD oscillatory flow past a vertical porous plate through porous medium in the presence of thermal and mass diffusion with constant heat source. Astrophys. Space Sci. 174, 303–310 (1990)

    Article  MATH  Google Scholar 

  31. Patil, P.M., Roy, S.: Unsteady mixed convection flow from a moving vertical plate in a parallel free stream: Influence of heat generation or absorption. Int. J. Heat Mass Transf. 53, 4749–4756 (2010)

    Article  MATH  Google Scholar 

  32. Seth, G.S., Jana, R.N., Maiti, M.K.: Unsteady hydromagnetic flow past a porous plate in a rotating medium with time-dependent free stream. Rev. Roum. Sci. Tech. Ser. Mech. Appl. 26, 383–400 (1981)

    MATH  Google Scholar 

  33. Das, S., Mandal, C., Jana, R.N.: Unsteady mixed convection flow past a vertical plate with Newtonian heating. Int. J. Energy Tech. 6, 1–9 (2014)

    Google Scholar 

  34. Seth, G.S., Kumbhakar, B., Sarkar, S.: Unsteady hydromagnetic natural convection flow with heat and mass transfer of a thermally radiating and chemically reactive fluid past a vertical plate with Newtonian heating and time dependent free-stream. Int. J. Heat Tech. 32, 87–94 (2014)

    Google Scholar 

  35. Cowling, T.G.: Magnetohydrodynamics. Interscience Publishers, New York (1957)

    MATH  Google Scholar 

  36. Hossain, M.A., Mohammad, K.: Effect of Hall current on hydromagnetic free convection flow near an accelerated porous plate. Jpn. J. Appl. Phys. 27, Article ID-1531. doi:10.1143/JJAP.27.1531 (1988)

  37. Pop, I., Watanabe, T.: Hall effect on magnetohydrodynamic free convection about a semi-infinite vertical flat plate. Int. J. Eng. Sci. 32, 1903–1911 (1994)

    Article  MATH  Google Scholar 

  38. Siddiqa, S., Hossain, M.A., Gorla, R.S.R.: Hall current effects on magnetohydrodynamic natural convection flow with strong cross magnetic field. Int. J. Therm. Sci. 71, 196–204 (2013)

    Article  Google Scholar 

  39. Kinyanjui, M., Chaturvedi, N., Uppal, S.M.: MHD Stokes problem for a vertical infinite plate in a dissipative rotating fluid with Hall current. Energy Convers. Manag. 39, 541–548 (1998)

    Article  MATH  Google Scholar 

  40. Takhar, H.S., Chamkha, A.J., Nath, G.: MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity. Int. J. Eng. Sci. 40, 1511–1527 (2002)

    Article  MATH  Google Scholar 

  41. Seth, G.S., Mahato, G.K., Sarkar, S.: Effects of Hall current and rotation on MHD natural convection flow past an impulsively moving vertical plate with ramped temperature in the presence of thermal diffusion and heat absorption. Int. J. Energy Tech. 5, 1–12 (2013)

    Google Scholar 

  42. Cebeci, T.: Convective Heat Transfer. Horizons Publishing Inc., Long Beach (2002)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Indian School of Mines, Dhanbad, 826004, India

    G. S. Seth

  2. Department of Mathematics, National Institute of Technology Meghalaya, Shillong, 793003, India

    B. Kumbhakar

  3. School of Applied Sciences (Mathematics), KIIT University, Bhubaneswar, 751024, India

    S. Sarkar

Authors
  1. G. S. Seth
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Kumbhakar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Sarkar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. S. Seth.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Seth, G.S., Kumbhakar, B. & Sarkar, S. Unsteady MHD natural convection flow with exponentially accelerated free-stream past a vertical plate in the presence of hall current and rotation. Rend. Circ. Mat. Palermo, II. Ser 66, 263–283 (2017). https://doi.org/10.1007/s12215-016-0250-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12215-016-0250-1

Keywords

Mathematics Subject Classification

Search

Navigation