The steady two-dimensional radiative MHD boundary layer flow of an incompressible, viscous, electrically conducting fluid caused by a nonisothermal linearly stretching sheet placed at the bottom of fluid saturated porous medium in the presence of viscous dissipation and chemical reaction is studied. The governing system of partial differential equations is converted to ordinary differential equations by using the similarity transformations, which are then solved by shooting method. The dimensionless velocity, temperature, and concentration are computed for different thermophysical parameters, namely, the magnetic parameter, permeability parameter, radiation parameter, wall temperature parameter, Prandtl number, Eckert number, Schmidt number, and chemical reaction. 1. Introduction The fluid flows with chemical reaction have attracted the attention of engineers and scientists in the recent times. Such flows have key importance in many processes including drying evaporation at the surface of a water body, energy transfer in a wet cooling tower, flow in a desert cooler, generating electric power, food processing, groves of fruit trees, and crops damage because of freezing. There is always a molecular diffusion of species in the presence of chemical reaction within or at the boundary during several practical diffusive operations. There are two types of reactions, namely, homogeneous and heterogeneous. A homogeneous reaction takes place uniformly in the entire given phase whereas a heterogeneous reaction exists in a restricted region or within the boundary of a phase. The smog formation is an important example representing a first-order homogeneous chemical reaction. Several researchers in view of such facts are engaged in the discussion of flows with chemical reactions. For-instance Seddeek and Almushigeh [1] investigated the effects of radiation and variable viscosity on MHD free convective flow and mass transfer over a stretching sheet with chemical reaction. Kandasamy et al. [2] presented group analysis for Soret and Dufour effects on free convective heat and mass transfer with thermophoresis and chemical reaction over a porous stretching surface in the presence of heat source/sink. Pal and Talukdar [3] presented the combined effects of Joule heating and chemical reaction on unsteady magnetohydrodynamic mixed convection with viscous dissipation over a vertical plate in the presence of porous media and thermal radiation. Joneidi et al. [4] presented analytical treatment of MHD free convection flow over a stretching sheet with chemical reaction. Anjalidevi
References
[1]
M. A. Seddeek and A. A. Almushigeh, “Effects of radiation and variable viscosity on MHD free convective flow and mass transfer over a stretching sheet with chemical reaction,” Applied Mathematics and Computation, vol. 5, no. 1, pp. 181–197, 2010.
[2]
R. Kandasamy, T. Hayat, and S. Obaidat, “Group theory transformation for Soret and Dufour effects on free convective heat and mass transfer with thermophoresis and chemical reaction over a porous stretching surface in the presence of heat source/sink,” Nuclear Engineering and Design, vol. 241, no. 6, pp. 2155–2161, 2011.
[3]
D. Pal and B. Talukdar, “Combined effects of Joule heating and chemical reaction on unsteady magnetohydrodynamic mixed convection of a viscous dissipating fluid over a vertical plate in porous media with thermal radiation,” Mathematical and Computer Modelling, vol. 54, no. 11-12, pp. 3016–3036, 2011.
[4]
A. A. Joneidi, G. Domairry, and M. Babaelahi, “Analytical treatment of MHD free convective flow and mass transfer over a stretching sheet with chemical reaction,” Journal of the Taiwan Institute of Chemical Engineers, vol. 41, no. 1, pp. 35–43, 2010.
[5]
S. P. Anjalidevi and R. Kandasamy, “Effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate,” Heat and Mass Transfer, vol. 35, no. 6, pp. 465–467, 1999.
[6]
M. A. Seddeek, A. A. Darwish, and M. S. Abdelmeguid, “Effects of chemical reaction and variable viscosity on hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media with radiation,” Communications in Nonlinear Science and Numerical Simulation, vol. 12, no. 2, pp. 195–213, 2007.
[7]
A. M. Salem and M. Abd El-Aziz, “Effect of Hall currents and chemical reaction on hydromagnetic flow of a stretching vertical surface with internal heat generation/absorption,” Applied Mathematical Modelling, vol. 32, no. 7, pp. 1236–1254, 2008.
[8]
D. A. Nield and A. Bejan, Convection in Porous Media, Springer, New York, NY, USA, 2nd edition, 1999.
[9]
M. S. Abel, S. K. Khan, and K. V. Prasad, “Convective heat and mass transfer in a visco-elastic fluid flow through a porous medium over a stretching sheet,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 11, no. 8, pp. 779–792, 2001.
[10]
P. Vyas and N. Srivastava, “Radiative MHD flow over a non-isothermal stretching sheet in a porous medium,” Applied Mathematical Sciences, vol. 4, no. 49-52, pp. 2475–2484, 2010.
[11]
K. Vajravelu and A. Hadjinicolaou, “Convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream,” International Journal of Engineering Science, vol. 35, no. 13-12, pp. 1237–1244, 1997.
[12]
S. Mohammed Ibrahim and N. Bhaskar Reddy, “Similarity solution of heat and mass transfer for natural convection over a moving vertical plate with internal heat generation and a convective boundary condition in the presence of thermal radiation, viscous dissipation and chemical reaction,” ISRN Thermodynamics, vol. 2013, Article ID 790604, 10 pages, 2013.
[13]
S. Shateyi, P. Sibanda, and S. S. Motsa, “Magnetohydrodynamic flow past a vertical plate with radiative heat transfer,” Journal of Heat Transfer, vol. 129, pp. 1708–1714, 2007.
[14]
O. D. Makinde and P. Sibanda, “Magnetohydrodynamic mixed-convective flow and heat and mass transfer past a vertical plate in a porous medium with constant wall suction,” Journal of Heat Transfer, vol. 130, no. 11, pp. 1–8, 2008.
[15]
D. Pal and B. Talukdar, “Perturbation analysis of unsteady magnetohydrodynamic convective heat and mass transfer in a boundary layer slip flow past a vertical permeable plate with thermal radiation and chemical reaction,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 7, pp. 1813–1830, 2010.
[16]
O. D. Makinde and A. Aziz, “MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition,” International Journal of Thermal Sciences, vol. 49, no. 9, pp. 1813–1820, 2010.
[17]
R. Cortell, “Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet,” Physics Letters A: General, Atomic and Solid State Physics, vol. 372, no. 5, pp. 631–636, 2008.
[18]
F. S. Ibrahim, A. M. Elaiw, and A. A. Bakr, “Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi infinite vertical permeable moving plate with heat source and suction,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 6, pp. 1056–1066, 2008.
[19]
S. Shateyi, “Thermal radiation and buoyancy effects on heat and mass transfer over a semi-infinite stretching surface with suction and blowing,” Journal of Applied Mathematics, vol. 2008, Article ID 414830, 12 pages, 2008.
[20]
S. Shateyi and S. S. Motsa, “Thermal radiation effects on heat and mass transfer over an unsteady stretching surface,” Mathematical Problems in Engineering, vol. 2009, Article ID 965603, 13 pages, 2009.
[21]
V. Aliakbar, A. Alizadeh-Pahlavan, and K. Sadeghy, “The influence of thermal radiation on MHD flow of Maxwellian fluids above stretching sheets,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 3, pp. 779–794, 2009.
[22]
B. Gebhart, “Effects of viscous dissipation in natural convection,” Journal of Fluid Mechanics, vol. 14, pp. 225–232, 1962.
[23]
P. Vyas and N. Srivastava, “On dissipative radiative MHD boundary layer flow in a porous medium over a non-isothermal stretching sheet,” Journal of Applied Fluid Mechanics, vol. 5, no. 4, pp. 23–31, 2012.
[24]
B. Gebhart and J. Mollendorf, “Viscous dissipation in external natural convection flows,” Journal of Fluid Mechanics, vol. 38, no. 1, pp. 97–107, 1969.
[25]
D. A. Nield, “Resolution of a Paradox involving viscous dissipation and nonlinear drag in a porous medium,” Transport in Porous Media, vol. 41, no. 3, pp. 349–357, 2000.
[26]
D. A. S. Rees, E. Magyari, and B. Keller, “The development of the asymptotic viscous dissipation profile in a vertical free convective boundary layer flow in a porous medium,” Transport in Porous Media, vol. 53, no. 3, pp. 347–355, 2003.
[27]
M. Q. Brewster, Thermal Radiation Transferproperties, John Wiley & Sons, New York, NY, USA, 1972.
[28]
A. J. Chamkha, “Hydromagnetic natural convection from an isothermal inclined surface adjacent to a thermally stratified porous medium,” International Journal of Engineering Science, vol. 35, no. 10-11, pp. 975–986, 1997.