An investigation on an unsteady MHD natural convection flow with radiative heat transfer of a viscous, incompressible, electrically conducting and optically thick fluid past an impulsively moving vertical plate with ramped temperature in a porous medium in the presence of a Hall current and thermal diffusion is carried out. An exact solution of momentum and energy equations, under Boussinesq and Rosseland approximations, is obtained in a closed form by the Laplace transform technique for both ramped temperature and isothermal plates. Expressions for the skin friction and Nusselt number for both ramped temperature and isothermal plates are also derived. The numerical values of fluid velocity and fluid temperature are displayed graphically versus the boundary layer coordinate y for various values of pertinent flow parameters for both ramped temperature and isothermal plates. The numerical values of the skin friction due to primary and secondary flows are presented in tabular form for various values of pertinent flow parameters.
Abramowitz M. and Stegun I.A. (1972): Handbook of Mathematical Functions. - New York: Dover Publications Inc.
Aldoss T.K. Al-Nimr M.A. Jarrah M.A. and Al-Shaer B.J. (1995): Magnetohydrodynamic mixed convection from a vertical plate embedded in a porous medium. - Heat Transfer vol.28 pp.635-645.
Azzam G.E.A. (2002): Radiation effects on the MHD mixed free forced convective flow past a semi-infinite moving vertical plate for high temperature differences. - Phys. Scr. vol.66 pp.71-76.
Bestman A.R. (1985): Free convection heat transfer to steady radiating non-Newtonian MHD flow past a vertical porous plate. - Int. J. Methods Eng. vol.21 pp.899-908.
Cess R.D. (1966): The interaction of thermal radiation with free convection heat transfer. - Int. J. Heat Mass Transfer vol.9 pp.1269-1277.
Chamkha A.J. (1997a): Transient MHD free convection from a porous medium supported by a surface. - Fluid/Particle Separation Journal vol.10 pp.101-107.
Chamkha A.J. (1997b): Hydromagnetic natural convection from an isothermal inclined surface adjacent to a thermally stratified porous medium. - Int. J. Engng. Sci. vol.35 pp.975-986.
Chamkha A.J. (1997c): Solar radiation assisted natural convection in a uniform porous medium supported by a vertical flat plate. - ASME J. Heat Transfer vol.119 pp.89-96.
Chamkha A.J. (2000): Thermal radiation and buoyancy effects on hydromagnetic flow over an accelerating permeable surface with heat source or sink. - Int. J. Engng. Sci. vol.38 pp.1699-1712.
Chamkha A.J. Takhar H.S. and Soundalgekar V.M. (2001): Radiation effects on free convection flow past a semiinfinite vertical plate with mass transfer. - The Chemical Engineering Journal vol.84 pp.335-342.
Chang L.C. Yang K.T. and Lloyd J.R. (1983): Radiation-natural convection interactions in two dimensional complex enclosures. - ASME J. Heat Transfer vol.105 pp.89-95.
Cheng P. and Minkowycz W.J. (1977): Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. - J. Geophys. Res. vol.82 pp.2040-2044.
Cookey C.I. Ogulu A. and Omubo-Pepple V.B. (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 Transfer vol.46 pp.2305-2311.
Cramer K.R. and Pai S.I. (1973): Magnetofluid Dynamics for Engineers and Applied Physicists. - New York: McGraw Hill Book Company.
Ede A.J. (1967): Advances in Heat Transfer. - New York: Academic Press vol.4 pp.1-64.
Gebhart B. (1973): Advances in Heat Transfer. - NewYork: Academic Press vol.9 pp.273-348.
Ghosh S.K. and Bég O.A. (2008): Theoretical analysis of radiative effects on transient free convection heat transfer past a hot vertical surface in porous media. - Nonlinear Anal. Modeling Control vol.13 pp.419-432.
Hayday A.A. Bowlus D.A. and McGraw R.A. (1967): Free convection from a vertical plate with step discontinuities in surface temperature. - ASME J. Heat Transfer vol.89 pp.244-250.
Hossain M.A. and Takhar H.S. (1996): Radiation effects on mixed convection along a vertical plate with uniform surface temperature. - Heat Mass Transfer vol.31 pp.243-248.
Hsieh J.C. Chen T.S. and Armaly B.F. (1993): Non-similarity solutions for mixed convection from vertical surfaces in porous media: variable surface temperature or heat flux. - Int. J. Heat Mass Transfer vol.36 pp.1485-1493.
Ibrahim F.S. Hassanien I.A. and Bakr A.A. (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. vol.82 pp.775-790.
Jaluria Y. (1980): Natural Convection Heat and Mass Transfer. - Oxford: Pergamon Press.
Kao T.T. (1975): Laminar free convective heat transfer response along a vertical flat plate with step jump in surface temperature. - Lett. Heat Mass Transfer vol.2 pp.419-428.
Kelleher M. (1971): Free convection from a vertical plate with discontinuous wall temperature. - ASME J. Heat Transfer vol.93 pp.349-356.
Kim Y.J. (2000): Unsteady MHD convective heat transfer past a semi-infinite vertical porous moving plate with variable suction. - Int. J. Engng. Sci. vol.38 pp.833-845.
Lai F.C. and Kulacki F.A. (1991): Non-Darcy mixed convection along a vertical wall in a saturated porous medium. - J. Heat Transfer vol.113 pp.252-254.
Lee S. and Yovanovich M.M. (1991): Laminar natural convection from a vertical plate with a step change in wall temperature. - ASME J. Heat Transfer vol.113 pp.501-504.
Mahmoud Mostafa A.A. (2009): Thermal radiation effect on unsteady MHD free convection flow past a vertical plate with temperature dependent viscosity. - Canad. J. Chem. Eng. vol.87 pp.47-52.
Makinde O.D. (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 vol.19 pp.546-554.
Makinde O.D. and 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 Transfer vol.130 pp.112602-1-8.
Muthucumaraswamy R. and Ganesan P. (2003): Radiation effects on flow past an impulsively started infinite vertical plate with variable temperature. - Int. J. Appl. Mech. Eng. vol.8 pp.125-129.
Nakayama A. and Koyama H. (1987): A general similarity transformation for combined free and forced convection flows within a fluid saturated porous medium. - ASME J. Heat Transfer vol.109 pp.1041-1045.
Nield D.A. and Bejan A. (2006): Convection in Porous Media. - USA: Springer 3rd edn.
Ogulu A. and Makinde O.D. (2009): Unsteady hydromagnetic free convection flow of a dissipative and radiating fluid past a vertical plate with constant heat flux. - Chem. Eng. Commun. vol.196 pp.454-462.
Patra R.R. Das S. Jana R.N. and Ghosh S.K. (2012): Transient approach to radiative heat transfer free convection flow with ramped wall temperature. - J. Appl. Fluid Mech. vol.5 pp.9-13.
Pop I. and Ingham D.B. (2002): Transport Phenomena in Porous Media-II. - UK: Pergamon Press.
Raithby G.D. and Hollands K.G.T. (1985): Natural convection In: Handbook of Heat Transfer Fundamentals (W.M.
Rohsenow et al. Ed.). - New York: McGraw Hill 2nd edn.
Raptis A. (1986): Flow through a porous medium in the presence of a magnetic field. - Int. J. Energy Res. vol.10 pp.97-100.
Raptis A. and 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. vol.6 pp.241-245.
Raptis A. and Massalas C.V. (1998): Magnetohydrodynamic flow past a plate in the presence of radiation. - Heat and Mass Transfer vol.34 pp.107-109.
Sparrow E.M. and Cess R.D. (1970): Radiation Heat Transfer. - Brook/Cole Belmont California.
Vafai K. (2005): Handbook of Porous Media. - USA: Taylor and Francis Group 2nd edn.