Soret and Dufour Effects on MHD Free Convection Flow of a Chemically Reacting Fluid Past over a Stretching Sheet with Heat Source/Sink
[1]
K. Gangadhar, Mathematics Department, Acharya Nagarjuna University Ongole Campus, Ongole, Andhra Pradesh, India.
[2]
S. Suneetha, Applied Mathematics Department, Yogi Vemana University, Kadapa, Andhra Pradesh, India.
A mathematical model is presented for a two-dimensional, steady, viscous, incompressible, electrically conducting and laminar MHD free convection flow with soret and dufour effects in the presence of porous medium and heat generation/absorption. The governing differential equations of the problem have been transformed into a system of non- dimensional differential equations, which are then solved numerically using a fourth-order Runge-Kutta method along with shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. The numerical values of skin-friction coefficient and Nusselt number at the plate are derived, discussed numerically for various values of physical parameters and presented through Tables. As the heat flux exponent parameter or suction/injection parameter increases, both the local Skin-friction coefficient and Sherwood number increase, whereas the Nusselt number decreases. It is observed that the local skin-friction coefficient and local Nusselt number decrease, whereas Sherwood number increases.
MHD, Free Convection, Heat and Mass Transfer, Soret and Dufour Effects, Porous Medium, Heat Generation/Absorption
[1]
Gupta, A. S., “Steady and transient free convection of an electrically conducting fluid from a vertical plate in the presence of magnetic field”, Appl. Sci. Res.. 9A, 319-333(1961).
[2]
Lykoudis, P. S., “Natural convection of an electrically conducting fluid in the presence of a magnetic field”, Int. J. Heat Mass Transfer,5, 23-34(1962).
[3]
Palani, G. and Srikanth, U., “MHD flow past a semi-infinite vertical plate with mass transfer. Nonlinear Analysis”, Modelling and Control, 14 (3) 345–356(2009).
[4]
Makinde, O. D., “On MHD heat and mass transfer over a moving vertical plate with a convective surface boundary condition”, The Canadian Journal of Chemical Engineering, 88, (6) 983–990(2010).
[5]
Takhar, H. S., Chamkha, A. J. and Nath G., “Flow and mass transfer on a stretching sheet with a magnetic field and chemically reactive species”, Int. J. Engng. Sci., 38, 1303-1310(2000).
[6]
Bergaman, T. L. and Srinivasan, R., Numerical solution of Soret indused double diffusive in an initially uniform concentration binary liquid”, Int. J. Heat Mass Transfer, Vol. 32(4), pp. 679-687(1989).
[7]
Zimmerman, G., Muller, U. Benard, C. “Convection in a two component system with Soret effect”, Int. J. Heat Mass Transfer, 35(9), 2245-2256(1992).
[8]
Postelnicu, A. “Influence of magnetic field on heat and mass transfer from vertical surfaces in porous media considering Soret and Dufour effects”, Int. J. Heat Mass Transfer, 47, 1467-1472(2004).
[9]
Ahammad, M. U. and Shirazul Hoque Mollah, Md. “ Numerical study of MHD free convection flow and mass transfer over a stretching sheet considering Soret and Dufour effects in the presence of magnetic field”, International Journal of Engineering & Technology, 11(5) 4-11(2011).
[10]
Pal, D. and Mondal, H., “Effects of Soret Dufour, chemical reaction and thermal radiation on MHD non-Darcy un- steady mixed convective heat and mass transfer over a stretching sheet”, Commun Nonlinear Sci. Numer. Simulat., 16, 1942-1958(2011).
[11]
Alam, M. S., Rahman, M. M., “Dufour and Soret effects on mixed convection flow past a vertical porous flat plate with variable suction”. Nonlinear Analysis, Modelling and Control, 11(1) 3-12(2006).
[12]
Gaikwad, S. N., Malashetty, M. S., Prasad, K. Rama, “An analytical study of linear and nonlinear double diffusive convection with Soret and Dufour effects in couple stress fluid”, International Journal of Non-Linear Mechanics, 42. 903-913(2007).
[13]
Xu, H., “An explicit analytic solution for convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream”, Int. J. Engg. Sci., 43, 859–874(2005).
[14]
Abel, M.S. and Nandeppanavar Mahantesh, M.,” Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with space and temperature dependent heat source”, Int. J Appl. Mech. Eng., 13 (2)293–309(2008).
[15]
Pillai, K. M. C., Sai, K. S., Swamy, N. S., Nataraja, H.R., Tiwari, S. B. and Rao, B. N.,” Heat transfer in a viscoelastic boundary layer flow through a porous medium”, Comput. Mech., 34, 27–37(2004).
[16]
Hayat, T., Javed, T. and Abbas, Z., “Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space”, Int. J Heat Mass Transfer, 51, 4528–4534(2008).
[17]
Khan, S. K., Abel, M.S. and Sonth, R. M. “Viscoelastic MHD flow heat and mass transfer over a porous stretching sheet with dissipation of energy and stress work”, Heat Mass Transfer, 40, 47–57(2003).
[18]
Shankar, B., Prabhakar Reddy, B. And Ananda Rao, J., “Radiation and mass transfer effects on MHD free convection fluid flow embedded in a porous medium with heat generation/absorption”, Indian Journal of pure and applied physics, 48, 157-165(2010).
[19]
S. Suneetha, N. Bhaskar Reddy and V. Ramachandra Prasad,” Radiation and Mass Transfer Effects on MHD Free Convective Dissipative Fluid in the Presence of Heat Source/Sink”, Journal of Applied Fluid Mechanics, 4(1) 107-113(2011). (ISSN: 1735-3645).
[20]
Al-Azab, T. A., “Influence of chemical reaction on transient MHD free convection over a moving vertical plate”, Emirates Journal for Engineering Research, 12(3) 15–21(2007).
[21]
Chambre P.L. and Young J.D. (1958), On the diffusion of a chemically reactive species in a laminar boundary layer flow”, Phys. Fluids flow, 1, 48-54(1958).
[22]
Dekha R., Das U. N. and Soundalgekar V.M.,” Effects on mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction”, Forschungim Ingenieurwesen, 60,284-289(1994).
[23]
Muthucumarswamy R. and Ganesan P.”, Effect of the chemical reaction and injection on the flow characteristics in an unsteady upward motion of an isothermal plate”, J Appl. Mech. Tech. Phys. 42,665-671(2001).
[24]
S.Suneetha and N. Bhaskar Reddy, “Radiation and Darcy effects on unsteady MHD heat and mass transfer flow of a chemically reacting fluid past an impulsively started vertical plate with heat generation”, International Journal of Applied Mathematics and mechanics, 7(7),1-19(2011) (ISSN: 0973-0184).
[25]
Chamkha A. J., “Unsteady convective heat and mass transfer past a semi-infinite vertical moving porous plate with heat generation/absorption and chemical reaction”, Int. Comm. Heat Mass Transfer, 30,413-422(2003).
[26]
Seddeek M.A., Darwish A. and Abdelmeguid M. S., “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 Non-linerar Science and Numerical Simulation, 12,195-213(2007).
[27]
R. Kandasamy, K. Periasamy and K. K. Sivagnana Prabhu,“Chemical Reaction, Heat and Mass Transfer on MHD Flow over a Vertical Stretching Surface with Heat Source and Thermal Stratification Effects,” International Journal of Heat and Mass Transfer, 48(21) 4557- 4561(2005).
[28]
Kameswaran P. K., Narayana M., Sibanda P. and Murthy P. V. S. N., “Hydro magnetic nanofluid flow due to a stretching or shrinking sheet with viscous dissipation and chemical reaction effects, Int. J. Heat Mass Transfer”, 55, No. 25-26, 7587-7595(2012).
[29]
Liu, C., “A note on heat and mass transfer for a hydro magnetic flow over a stretching sheet”, Int. Comm. Heat Mass Trans., 32 1075–1084(2005).
[30]
Helmy, K. A, “Effects of the magnetic field on a non-Newtonian conducting fluid past a stretching plate”, Can. J. Phys., 72 290-292(1994).
[31]
Jain, M. K., Iyengar, S. R. K., and Jain, R. K., “Numerical Methods for Scientific and Engineering Computation”, Wiley Eastern Ltd., New Delhi, India 1985).
