Skip to main content
Log in

MHD natural convection flow with radiative heat transfer past an impulsively moving plate with ramped wall temperature

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

Influence of radiation on unsteady hydromagnetic natural convection transient flow near an impulsively moving vertical flat plate with ramped wall temperature in a porous medium is studied. Exact solution of momentum and energy equations, under Boussinesq approximation, is obtained in closed form by Laplace transform technique. The variations in fluid velocity and temperature are shown graphically whereas numerical values of skin friction and Nusselt number are presented in tabular form.

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

Access this article

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

Instant access to the full article PDF.

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

Similar content being viewed by others

References

  1. Chandran P, Sacheti NC, Singh AK (1998) Unsteady hydromagnetic free convection flow with heat flux and accelerated boundary motion. J Phys Soc Jpn 67:124–129

    Article  MATH  Google Scholar 

  2. Chandran P, Sacheti NC, Singh AK (2001) Exact solutions for the convective flow of fluids of different Prandtl numbers near an infinite vertical plate in a rotating system. Int J Appl Mech Eng 6:573–590

    Google Scholar 

  3. Ganesan P, Palani G (2003) Natural convection effects on impulsively started inclined plate with heat and mass transfer. Heat Mass Transf 39:277–283

    Article  Google Scholar 

  4. Georgantopoulos GA (1979) Effects of free convection on the hydromagnetic accelerated flow past a vertical porous limiting surface. Astrophys Space Sci 65:433–442

    Article  MathSciNet  Google Scholar 

  5. Raptis A, Singh AK (1983) MHD free convection flow past an accelerated vertical plate. Int Comm Heat Mass Transf 10:313–321

    Article  Google Scholar 

  6. Raptis A, Singh AK (1985) Rotation effects on MHD free convection flow past an accelerated vertical plate. Mech Res Comm 12:31–40

    Article  MATH  Google Scholar 

  7. Sacheti NC, Chandran P, Singh AK (1994) An exact solution for unsteady magnetohydrodynamic free convection flow with constant heat flux. Int Comm Heat Mass Transf 21:131–142

    Article  Google Scholar 

  8. Makinde OD, Olanrewaju PO (2010) Buoyancy effects on thermal boundary layer over a vertical plate with a convective surface boundary condition. J Fluid Eng 132:044502

    Article  Google Scholar 

  9. Cheng P, Minkowycz WJ (1977) 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

    Article  Google Scholar 

  10. Ranganathan P, Viskanta R (1984) Mixed convection boundary layer flow along a vertical surface in a porous medium. Numer Heat Transf 7:305–317

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  12. Hsieh JC, Chen TS, Armaly BF (1993) Non-similarity solutions for mixed convection from vertical surfaces in porous media: variable surface temperature or heat flux. Int J Heat Mass Transf 36:1485–1493

    Article  MATH  Google Scholar 

  13. Lai FC, Kulacki FA (1991) Non-Darcy mixed convection along a vertical wall in a saturated porous medium. J Heat Transf 113:252–254

    Article  Google Scholar 

  14. Nield DA, Bejan A (2006) Convection in porous media, 3rd edn. Springer, USA

    Google Scholar 

  15. Vafai K (2005) Handbook of porous media, 2nd edn. Taylor and Francis Group, USA

    Book  Google Scholar 

  16. Pop I, Ingham DB (2002) Transport phenomena in porous media-II. Pergamon Press, UK

    MATH  Google Scholar 

  17. Raptis A, Kafousias N (1982) Heat transfer in flow through a porous medium bounded by an infinite vertical plate under the action of a magnetic field. Int J Energy Res 6:241–245

    Article  Google Scholar 

  18. Raptis A (1986) Flow through a porous medium in the presence of a magnetic field. Int J Energy Res 10:97–100

    Article  Google Scholar 

  19. Sahoo DG, Sahoo PK (1986) Hydromagnetic free convection and mass transfer through a porous medium. Ind J Tech 24:553–556

    Google Scholar 

  20. Jha BK (1991) MHD free-convection and mass-transform flow through a porous medium. Astrophys Space Sci 175:283–289

    Article  MATH  Google Scholar 

  21. Aldoss TK, Al-Nimr MA, Jarrah MA, Al-Shaer BJ (1995) Magnetohydrodynamic mixed convection from a vertical plate embedded in a porous medium. Numer Heat Transf 28:635–645

    Article  Google Scholar 

  22. Takhar HS, Ram PC (1991) Free convection in hydromagnetic flows of a viscous heat-generating fluid with wall temperature oscillation and hall currents. Astrophys Space Sci 183:193–198

    Article  MATH  Google Scholar 

  23. Takhar HS, Ram PC (1994) Magnetohydrodynamic free convection flow of water at 4°C through a porous medium. Int Comm Heat Mass Transf 21:371–376

    Article  Google Scholar 

  24. Helmy KA (1998) MHD unsteady free convection flow past a vertical porous plate. ZAMM 78:255–270

    Article  MATH  MathSciNet  Google Scholar 

  25. Kim YJ (2000) Unsteady MHD convective heat transfer past a semi-infinite vertical porous moving plate with variable suction. Int J Eng Sci 38:833–845

    Article  Google Scholar 

  26. Ibrahim FS, Hassanien IA, Bakr AA (2004) Unsteady Magnetohydrodynamic micropolar fluid flow and heat transfer over a vertical porous medium in the presence of thermal and mass diffusion with constant heat source. Canad J Phys 82:775–790

    Article  Google Scholar 

  27. Makinde OD, Sibanda P (2008) Magnetohydrodynamic mixed-convective flow and heat and mass transfer past a vertical plate in a porous medium with constant wall suction. J Heat Transf 130:112602

    Article  Google Scholar 

  28. Makinde OD (2009) On MHD boundary layer flow and mass transfer past a vertical plate in a porous medium with constant heat flux. Int J Numer Methods Heat Fluid Flow 19:546–554

    Article  Google Scholar 

  29. Chang LC, Yang KT, Lloyd JR (1983) Radiation-natural convection interactions in two dimensional complex enclosures. ASME J Heat Transf 105:89–95

    Article  Google Scholar 

  30. Cess RD (1966) The interaction of thermal radiation with free convection heat transfer. Int J Heat Mass Transf 9:1269–1277

    Article  MATH  Google Scholar 

  31. Hossain MA, Takhar HS (1996) Radiation effects on mixed convection along a vertical plate with uniform surface temperature. Heat Mass Transf 31:243–248

    Article  Google Scholar 

  32. Takhar HS, Beg OA, Kumari M (1998) Computational analysis of coupled radiation-convection dissipative non-gray gas flow in a non Darcy porous medium using the Keller-box implicit difference scheme. Int J Energy Res 22:141–159

    Article  Google Scholar 

  33. Chamkha AJ (1997) Solar radiation assisted natural convection in a uniform porous medium supported by a vertical flat plate. ASME J Heat Transf 119:89–96

    Article  Google Scholar 

  34. Muthucumaraswamy R, Ganesan P (2003) Radiation effects on flow past an impulsively started infinite vertical plate with variable temperature. Int J Appl Mech Eng 8:125–129

    MATH  Google Scholar 

  35. Ghosh SK, Beg OA (2008) Theoretical analysis of radiative effects on transient free convection heat transfer past a hot vertical surface in porous media. Nonlinear Anal Medelling Control 13:419–432

    MATH  Google Scholar 

  36. Takhar HS, Gorla RSR, Soundalgekar VM (1996) Radiation effects on MHD free convection flow of a gas past a semi infinite vertical plate. Int J Numer Methods Heat Fluid Flow 6:77–83

    Article  MATH  Google Scholar 

  37. Chamkha AJ (2000) Thermal radiation and buoyancy effects on hydromagnetic flow over an accelerating permeable surface with heat source or sink. Int J Eng Sci 38:1699–1712

    Article  Google Scholar 

  38. Azzam GEA (2002) Radiation effects on the MHD mixed free-forced convective flow past a semi-infinite moving vertical plate for high temperature differences. Phys Scr 66:71–76

    Article  MATH  Google Scholar 

  39. Cookey CI, Ogulu A, Omubo-Pepple VB (2003) Influence of viscous dissipation and radiation on unsteady MHD free-convection flow past an infinite heated vertical plate in a porous medium with time-dependent suction. Int J Heat Mass Transf 46:2305–2311

    Article  MATH  Google Scholar 

  40. Mahmoud Mostafa AA (2009) Thermal radiation effect on unsteady MHD free convection flow past a vertical plate with temperature dependent viscosity. Canad J Chem Eng 87:47–52

    Article  Google Scholar 

  41. Ogulu A, Makinde OD (2009) Unsteady hydromagnetic free convection flow of a dissipative and radiating fluid past a vertical plate with constant heat flux. Chem Eng Commun 196:454–462

    Article  Google Scholar 

  42. Bestman AR, Adjepong SK (1988) Unsteady hydromagnetic free-convection flow with radiative heat transfer in a rotating fluid. Astrophys Space Sci 143:73–80

    Article  Google Scholar 

  43. Mbeledogu IU, Ogulu A (2007) Heat and mass transfer of an unsteady MHD natural convection flow of a rotating fluid past a vertical porous flat plate in the presence of radiative heat transfer. Int J Heat Mass Transf 50:1902–1908

    Article  MATH  Google Scholar 

  44. Hayday AA, Bowlus DA, McGraw RA (1967) Free convection from a vertical plate with step discontinuities in surface temperature. ASME J Heat Trans 89:244–250

    Google Scholar 

  45. Kelleher M (1971) Free convection from a vertical plate with discontinuous wall temperature. ASME J Heat Trans 93:349–356

    Article  Google Scholar 

  46. Kao TT (1975) Laminar free convective heat transfer response along a vertical flat plate with step jump in surface temperature. Lett Heat Mass Trans 2:419–428

    Article  Google Scholar 

  47. Lee S, Yovanovich MM (1991) Laminar natural convection from a vertical plate with a step change in wall temperature. ASME J Heat Trans 113:501–504

    Article  Google Scholar 

  48. Chandran P, Sacheti NC, Singh AK (2005) Natural Convection near a vertical plate with ramped wall temperature. Heat Mass Trans 41:459–464

    Article  Google Scholar 

  49. Seth GS, Ansari MdS (2010) MHD natural convection flow past an impulsively moving vertical plate with ramped wall temperature in the presence of thermal diffusion with heat absorption. Int J Appl Mech Eng 15:199–215

    Google Scholar 

  50. Cramer KR, Pai SI (1973) Magnetofluid dynamics for engineers and applied physicists. McGraw-Hill, New York

    Google Scholar 

  51. Bestman AR (1985) Free convection heat transfer to steady radiating non-Newtonian MHD flow past a vertical porous plate. Int J Numer Methods Eng 21:899–908

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Md. S. Ansari.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Seth, G.S., Ansari, M.S. & Nandkeolyar, R. MHD natural convection flow with radiative heat transfer past an impulsively moving plate with ramped wall temperature. Heat Mass Transfer 47, 551–561 (2011). https://doi.org/10.1007/s00231-010-0740-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-010-0740-1

Keywords

Navigation