Soret and Dufour effects on mixed convection unsteady MHD boundary layer flow over stretching sheet in porous medium with chemically reactive species

doi:10.1007/s10483-014-1830-9

Abstract

Abstract: This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of the stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations and solved numerically by the Runge-Kutta fourth order scheme in as- sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph- ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.

Key words: heat and mass transfer, boundary layer flow, porous media, magnetic field, Soret number, Dufour number

2010 MSC Number:

O357.4

A. NAYAK;S. PANDA;D. K. PHUKAN. Soret and Dufour effects on mixed convection unsteady MHD boundary layer flow over stretching sheet in porous medium with chemically reactive species. Applied Mathematics and Mechanics (English Edition), 2014, 35(7): 849-862.

TrendMD

References

[1] Nield, D. A. and Bejan, A. Convection in Porous Media, 3rd ed., Springer, New York (2006)
[2] Ingham, D. B. and Pop, I. Transport Phenomena in Porous Media, Vol. III, Pergamon, Oxford (2005)
[3] Vafai, K. Handbook of Porous Media, Taylor and Francis, New York (2005)
[4] Pop, I. and Ingham, D. B. Convective Heat Transfer: Mathematical and Computational Modeling of Viscous Fluids and Porous Media, Pergamon, Oxford (2001)
[5] Knobloch, E. Convection in binary fluids. Physics of Fluids, 23, 1918-1920 (1980)
[6] Taslim M. E. and Narusawa, U. Binary fluid convection and double diffusive convection in a porous medium. Journal of Heat Transfer, 108, 221-224 (1986)
[7] Parida, S. K., Acharya, M., Dash, G., and Panda, S. MHD heat and mass transfer in a rotating system with periodic suction. The Arabian Journal for Science and Engineering, 36, 1139-1151 (2011)
[8] Fan, J. R., Shi, J. M., and Xu, X. Z. Similarity solution of mixed convection with diffusion and chemical reaction over a horizontal moving plate. Acta Mechanica, 126, 59-69 (1998)
[9] Rashad, A. M. and El-Kabeir, S. M. M. Heat and mass transfer in transient flow by mixed convection boundary layer over a stretching sheet embedded in a porous medium with chemically reactive species. Journal of Porous Media, 13(1), 75-85 (2010)
[10] Saha, S. C. and Hossain, M. A. Natural convection flow with combined buoyancy effects due to thermal and mass diffusion in a thermally stratified media. Nonlinear Analysis: Modeling and Control, 9(1), 89-102 (2004)
[11] Tyvand, P. A. Thermohaline instability in anisotropic porous media. Water Resources Research, 16, 325-330 (1980)
[12] Patil, P., Paravathy, C. P., and Venkatakrishnan, K. S. Thermohaline instability in a rotating anisotropic porous medium. Applied Scientific Research, 46, 73-88 (1989)
[13] Chamkha, A. J., Al-Mudhaf, A., and Al-Yatama, J. Double diffusive convective flow of a micro- polar fluid over a vertical plate embedded in a porous medium with a chemical reaction. Interna- tional Journal of Fluid Mechanics Research, 6, 529-551 (2004) 862 A. NAYAK, S. PANDA, and D. K. PHUKAN
[14] Postelnicu, A. Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects. Heat and Mass Transfer, 43, 595-602 (2007)
[15] Postelnicu, A. Heat and mass transfer by natural convection at a stagnation point in a porous medium considering Soret and Dufour effects. Heat and Mass Transfer, 46, 831-840 (2010)
[16] Tsai, R. and Huang, J. S. Heat and mass transfer for Soret and Dufour's effects on Hiemenz flow through porous medium onto a stretching surface. International Journal of Heat and Mass Trasfer, 52, 2399-2406 (2009)
[17] Hayat, T., Mustafa, M., and Pop, I. Heat and mass transfer for Soret and Dufour's effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid. Communications in Nonlinear Science and Numerical Simulation, 15, 1183-1196 (2010)
[18] Gbadeyan, J. A., Ogunsola, A. S., Ogunsola, A. W., Agboola, O. O., and Olanrewaju, P. O. Heat and mass transfer for Soret and Dufour's effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid in the presence of magnetic field. Global Journal of Science and Frontier Research, 11(8), 96-114 (2011)
[19] Oladapo, O. P. Dufour and Soret effects of a transient free convective flow with radiative heat transfer past a flat plate moving through a binary mixture. The Pacific Journal of Science and Technology, 11(1), 163-172 (2010)
[20] Osalusi, E., Side, J., and Harris, R. Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer of a steady MHD convective and slip flow due to a rotating disk with viscous dissipation and Ohmic heating. International Communications in Heat and Mass Transfer, 35, 908-915 (2008)
[21] Affiy, A. A. Similarity solution in MHD: effects of thermal diffusion and diffusion thermo on free convective heat and mass transfer over a stretching surface considering suction or injection. Communications in Nonlinear Science and Numerical Simulation, 14, 2202-2214 (2009)
[22] Anwar, B. O., Bakier, A. Y., and Prasad, V. R. Numerical study of free convection magneto- hydrodynamic heat and mass transfer from a stretching surface to a saturated porous medium with Soret and Dufour effects. Computational Materials Science, 46, 57-65 (2009)
[23] Sallam, N. Thermal diffusion and diffusion-thermo effects on mixed convection heat and mass transfer in porous medium. Journal of Porous Media, 13(4), 331-345 (2010)
[24] Kuznetsov, A. V. and Nield, D. A. Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate. International Journal of Thermal Sciences, 50, 712-717 (2011)
[25] Ishak, A. and Nazar, R. Unsteady mixed convection boundary layer flow due to a stretching vertical surface. The Arabian Journal for Science and Engineering, 31, 165-182 (2006)
[26] Zaimi, K., Ishak, A., and Pop, I. Stretching surface in rotating viscoelastic fluid. Applied Mathe- matics and Mechanics (English Edition), 34(8), 945-952 (2013) DOI 10.1007/s10483-013-1719-9
[27] Rani, H. P., Reddy, G. J., and Kim, C. N. Transient analysis of diffusive chemical reactive species for couple stress fluid flow over vertical cylinder. Applied Mathematics and Mechanics (English Edition), 34(8), 985-1000 (2013) DOI 10.1007/s10483-013-1722-6