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.
Similar content being viewed by others
References
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
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
Ganesan P, Palani G (2003) Natural convection effects on impulsively started inclined plate with heat and mass transfer. Heat Mass Transf 39:277–283
Georgantopoulos GA (1979) Effects of free convection on the hydromagnetic accelerated flow past a vertical porous limiting surface. Astrophys Space Sci 65:433–442
Raptis A, Singh AK (1983) MHD free convection flow past an accelerated vertical plate. Int Comm Heat Mass Transf 10:313–321
Raptis A, Singh AK (1985) Rotation effects on MHD free convection flow past an accelerated vertical plate. Mech Res Comm 12:31–40
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
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
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
Ranganathan P, Viskanta R (1984) Mixed convection boundary layer flow along a vertical surface in a porous medium. Numer Heat Transf 7:305–317
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
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
Lai FC, Kulacki FA (1991) Non-Darcy mixed convection along a vertical wall in a saturated porous medium. J Heat Transf 113:252–254
Nield DA, Bejan A (2006) Convection in porous media, 3rd edn. Springer, USA
Vafai K (2005) Handbook of porous media, 2nd edn. Taylor and Francis Group, USA
Pop I, Ingham DB (2002) Transport phenomena in porous media-II. Pergamon Press, UK
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
Raptis A (1986) Flow through a porous medium in the presence of a magnetic field. Int J Energy Res 10:97–100
Sahoo DG, Sahoo PK (1986) Hydromagnetic free convection and mass transfer through a porous medium. Ind J Tech 24:553–556
Jha BK (1991) MHD free-convection and mass-transform flow through a porous medium. Astrophys Space Sci 175:283–289
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
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
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
Helmy KA (1998) MHD unsteady free convection flow past a vertical porous plate. ZAMM 78:255–270
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
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
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
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
Chang LC, Yang KT, Lloyd JR (1983) Radiation-natural convection interactions in two dimensional complex enclosures. ASME J Heat Transf 105:89–95
Cess RD (1966) The interaction of thermal radiation with free convection heat transfer. Int J Heat Mass Transf 9:1269–1277
Hossain MA, Takhar HS (1996) Radiation effects on mixed convection along a vertical plate with uniform surface temperature. Heat Mass Transf 31:243–248
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
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
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
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
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
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
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
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
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
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
Bestman AR, Adjepong SK (1988) Unsteady hydromagnetic free-convection flow with radiative heat transfer in a rotating fluid. Astrophys Space Sci 143:73–80
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
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
Kelleher M (1971) Free convection from a vertical plate with discontinuous wall temperature. ASME J Heat Trans 93:349–356
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
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
Chandran P, Sacheti NC, Singh AK (2005) Natural Convection near a vertical plate with ramped wall temperature. Heat Mass Trans 41:459–464
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
Cramer KR, Pai SI (1973) Magnetofluid dynamics for engineers and applied physicists. McGraw-Hill, New York
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
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00231-010-0740-1