Soret and Dufour Effects on Unsteady MHD Mixed Convection Flow past a Radiative Vertical Porous Plate Embedded in a Porous Medium with Chemical Reaction

Affiliation(s)

Department of Mathematics, Birla Institute of Technology & Science, Pilani, Rajasthan, India.

Department of Mathematics, University of Rajasthan, Jaipur, India.

Department of Mathematics, D. S. College, Aligarh (U. P.), India.

Department of Mathematics, Birla Institute of Technology & Science, Pilani, Rajasthan, India.

Department of Mathematics, University of Rajasthan, Jaipur, India.

Department of Mathematics, D. S. College, Aligarh (U. P.), India.

ABSTRACT

The Soret and Dufour effects on unsteady MHD mixed convection flow past an infinite radiative vertical porous plate embedded in a porous medium in the presence of chemical reaction have been studied. A uniform magnetic field acts perpendicular to the porous surface. The Rosseland approximation has been used to describe the radiative heat flux in energy equation. The governing equations are solved numerically by applying explicit finite difference Method. The effects of various parameters on the velocity, temperature and concentration fields have been examined with the help of graphs.

The Soret and Dufour effects on unsteady MHD mixed convection flow past an infinite radiative vertical porous plate embedded in a porous medium in the presence of chemical reaction have been studied. A uniform magnetic field acts perpendicular to the porous surface. The Rosseland approximation has been used to describe the radiative heat flux in energy equation. The governing equations are solved numerically by applying explicit finite difference Method. The effects of various parameters on the velocity, temperature and concentration fields have been examined with the help of graphs.

Cite this paper

B. Sharma, K. Yadav, N. Mishra and R. Chaudhary, "Soret and Dufour Effects on Unsteady MHD Mixed Convection Flow past a Radiative Vertical Porous Plate Embedded in a Porous Medium with Chemical Reaction,"*Applied Mathematics*, Vol. 3 No. 7, 2012, pp. 717-723. doi: 10.4236/am.2012.37105.

B. Sharma, K. Yadav, N. Mishra and R. Chaudhary, "Soret and Dufour Effects on Unsteady MHD Mixed Convection Flow past a Radiative Vertical Porous Plate Embedded in a Porous Medium with Chemical Reaction,"

References

[1] D. A. Nield and A. Bejan, “Convection in Porous Media,” 2nd Edition, Springer-Verlag, Berlin, 1998.

[2] P. S. Hiremath, and P. M. Patil, “Free Convection Effects on Oscillatory Flow of Couple Stress Field through a Porous Medium,” Acta Mechanica, Vol. 98, No. 1-4, 1993, pp. 143-158. doi:10.1007/BF01174299

[3] B. K. Sharma, R. C. Chaudhary and P. K. Sharma, “Fluctuating Mass Transfer on Three-Dimensional Flow through a Porous Medium with Variable Permeability,” Advances in Theoretical and Applied Mathematics, Vol. 2, No. 3, 2007, pp. 257-267.

[4] K. A. Helmy, “MHD Unsteady Free Convection Flow past a Vertical Porous Plate,” ZAMM, Vol. 98, No. 4, 1998, pp. 255-270. doi:10.1002/(SICI)1521-4001(199804)78:4<255::AID-ZAMM255>3.0.CO;2-V

[5] R. C. Chaudhary and B. K. Sharma, “Combined Heat and Mass Transfer by Laminar Mixed Convection Flow from a Vertical Surface with Induced Magnetic Field,” Journal of Applied Physics, Vol. 99, No. 3, 2006, pp. 34901-3410. doi:10.1063/1.2161817

[6] B. K. Sharma and R. C. Chaudhary, “Hydromagnetic Unsteady Mixed Convection and Mass Transfer Flow past a Vertical Porous Plate Immersed in a Porous Medium with Hall Effect,” Engineering Transactions, Vol. 56, No. 1, 2008, pp. 3-23.

[7] M. F. El-Amin, “Magnetohydrodynamic Free Convection and Mass Transfer Flow in Micropolar Fluid with Constant Suction,” Journal of Magnetism and Magnetic Materials, Vol. 234, No. 3, 2001, pp. 567-574. doi:10.1016/S0304-8853(01)00374-2

[8] E. L. Cussler, “Diffusion Mass Transfer in Fluid Systems,” 2nd Edition, Cambridge University Press, Cambridge, 1998.

[9] U. N. Das, R. K. Deka and V. M. Soundalgekar, “Effects of Mass Transfer on Flow past an Impulsively Started Infinite Vertical Plate with Constant Heat Flux and Chemical Reaction,” Forschung im Ingenieurwesen, Vol. 60, No. 10, 1994, pp. 284-287. doi:10.1007/BF02601318

[10] R. Muthucumarswamy and P. Ganesan, “First Order Chemical Reaction on Flow past an Impulsively Started Vertical Plate with Uniform Heat and Mass Flux,” Acta Mechanica, Vol. 147, No. 1-4, 2001, pp. 45-57. doi:10.1007/BF01182351

[11] R. Muthucumarswamy, “Effects of a Chemical Reaction on Moving Isothermal Vertical Surface with Suction,” Acta Mechanica, Vol. 155, No. 1-2, 2002, pp. 65-70. doi:10.1007/BF01170840

[12] R. Kandasamy, K. Periasamy and K. K. Prashu Sivagnana, “Effects of Chemical Reaction, Heat and Mass Transfer along Wedge with Heat Source and Concentration in the Presence of Suction or Injection,” International Journal of Heat and Mass Transfer, Vol. 48, No. 7, 2005, pp. 13881394. doi:10.1016/j.ijheatmasstransfer.2004.10.008

[13] B. K. Sharma, A. K. Jha and R. C. Chaudhary, “Radiation Effect with Simultaneous Thermal and Mass Diffusion in MHD Mixed Convection Flow from a Vertical Surface with Ohmic Heating,” Romania Journal of Physics, Vol. 51, No. 7-8, 2006, pp. 715-727.

[14] B. K. Sharma, M. Agarwal and R. C. Chaudhary , “MHD Fluctuating Free Convective Flow with Radiation Embedded in Porous Medium Having Variable Permeability and Heat Source/Sink,” Journal of Technical Physics, Vol. 47, No. 1, 2006, pp. 47-58.

[15] B. K. Sharma, R. C. Chaudhary and M. Agarwal, “Radiation Effect on Temperature Distribution in Three-Dimensional Couette Flow with Injection or Suction,” Applied Mathematics and Mechanics, Vol. 28, No. 3, 2007, pp. 309-316. doi:10.1007/s10483-007-0304-z

[16] B. K. Sharma, R. C. Chaudhary and M. Agarwal, “Radiation Effect on Steady Free Convective Flow along a Uniform Moving Porous Vertical Plate in Presence of Heat Source/Sink and Transverse Magnetic Field,” Bulletin of Calcutta Mathematical Society, Vol. 100, 2008, pp. 529-538.

[17] E. R. G. Eckert and R. M. Drake, “Analysis of Heat and Mass Transfer,” McGraw-Hill, New York, 1972.

[18] Z. Dursunkaya and W. M. Worek, “Diffusion-Thermo and Thermal-Diffusion Effects in Transient and Steady Natural Convection from Vertical Surface,” International Journal of Heat and Mass Transfer, Vol. 35, No. 8, 1992, pp. 2060-2065. doi:10.1016/0017-9310(92)90208-A

[19] M. Anghel, H. S. Takhar and I. Pop, “Dufour and Soret Effects on Free-Convection Boundary Layer over a Vertical Surface Embedded in a Porous Medium,” Studia Universitatis Babes-Bolyai: Mathematica, Vol. XLV, No. 4, 2000, pp. 11-21.

[20] A. Postelnicu, “Influence of a Magnetic Field on Heat and Mass Transfer by Natural Convection from Vertical Surfaces in Porous Media Considering Soret and Dufour Effects,” International Journal of Heat and Mass Transfer, Vol. 47, No. 6-7, 2004, pp. 1467-1472. doi:10.1016/j.ijheatmasstransfer.2003.09.017

[21] M. S. Alam and M. M. Rahman, “Dufour and Soret Effects on MHD Free Convective Heat and Mass Transfer Flow past a Vertical Flat Plate Embedded in a Porous Medium,” Journal of Naval Architecture and Marine Engineering, Vol. 2, No. 1, 2005, pp. 55-65.

[22] A. Raptis and C. V. Massalas, “Magnetohydrodynamic Flow past a Plate by the Presence of Radiation,” Heat and Mass Transfer, Vol. 34, No. 2-3, 1998, pp. 107-109. doi:10.1007/s002310050237

[23] C. Perdikis and E. Rapti, “Unsteady MHD Flow in the Presence of Radiation,” International Journal of Applied Mechanics and Engineering, Vol. 11, No. 2, 2006, pp. 383-390.

[24] J. D. Hoffman, “Numerical Methods for Engineers and Scientists,” McGraw-Hill, New York, 1992.

[1] D. A. Nield and A. Bejan, “Convection in Porous Media,” 2nd Edition, Springer-Verlag, Berlin, 1998.

[2] P. S. Hiremath, and P. M. Patil, “Free Convection Effects on Oscillatory Flow of Couple Stress Field through a Porous Medium,” Acta Mechanica, Vol. 98, No. 1-4, 1993, pp. 143-158. doi:10.1007/BF01174299

[3] B. K. Sharma, R. C. Chaudhary and P. K. Sharma, “Fluctuating Mass Transfer on Three-Dimensional Flow through a Porous Medium with Variable Permeability,” Advances in Theoretical and Applied Mathematics, Vol. 2, No. 3, 2007, pp. 257-267.

[4] K. A. Helmy, “MHD Unsteady Free Convection Flow past a Vertical Porous Plate,” ZAMM, Vol. 98, No. 4, 1998, pp. 255-270. doi:10.1002/(SICI)1521-4001(199804)78:4<255::AID-ZAMM255>3.0.CO;2-V

[5] R. C. Chaudhary and B. K. Sharma, “Combined Heat and Mass Transfer by Laminar Mixed Convection Flow from a Vertical Surface with Induced Magnetic Field,” Journal of Applied Physics, Vol. 99, No. 3, 2006, pp. 34901-3410. doi:10.1063/1.2161817

[6] B. K. Sharma and R. C. Chaudhary, “Hydromagnetic Unsteady Mixed Convection and Mass Transfer Flow past a Vertical Porous Plate Immersed in a Porous Medium with Hall Effect,” Engineering Transactions, Vol. 56, No. 1, 2008, pp. 3-23.

[7] M. F. El-Amin, “Magnetohydrodynamic Free Convection and Mass Transfer Flow in Micropolar Fluid with Constant Suction,” Journal of Magnetism and Magnetic Materials, Vol. 234, No. 3, 2001, pp. 567-574. doi:10.1016/S0304-8853(01)00374-2

[8] E. L. Cussler, “Diffusion Mass Transfer in Fluid Systems,” 2nd Edition, Cambridge University Press, Cambridge, 1998.

[9] U. N. Das, R. K. Deka and V. M. Soundalgekar, “Effects of Mass Transfer on Flow past an Impulsively Started Infinite Vertical Plate with Constant Heat Flux and Chemical Reaction,” Forschung im Ingenieurwesen, Vol. 60, No. 10, 1994, pp. 284-287. doi:10.1007/BF02601318

[10] R. Muthucumarswamy and P. Ganesan, “First Order Chemical Reaction on Flow past an Impulsively Started Vertical Plate with Uniform Heat and Mass Flux,” Acta Mechanica, Vol. 147, No. 1-4, 2001, pp. 45-57. doi:10.1007/BF01182351

[11] R. Muthucumarswamy, “Effects of a Chemical Reaction on Moving Isothermal Vertical Surface with Suction,” Acta Mechanica, Vol. 155, No. 1-2, 2002, pp. 65-70. doi:10.1007/BF01170840

[12] R. Kandasamy, K. Periasamy and K. K. Prashu Sivagnana, “Effects of Chemical Reaction, Heat and Mass Transfer along Wedge with Heat Source and Concentration in the Presence of Suction or Injection,” International Journal of Heat and Mass Transfer, Vol. 48, No. 7, 2005, pp. 13881394. doi:10.1016/j.ijheatmasstransfer.2004.10.008

[13] B. K. Sharma, A. K. Jha and R. C. Chaudhary, “Radiation Effect with Simultaneous Thermal and Mass Diffusion in MHD Mixed Convection Flow from a Vertical Surface with Ohmic Heating,” Romania Journal of Physics, Vol. 51, No. 7-8, 2006, pp. 715-727.

[14] B. K. Sharma, M. Agarwal and R. C. Chaudhary , “MHD Fluctuating Free Convective Flow with Radiation Embedded in Porous Medium Having Variable Permeability and Heat Source/Sink,” Journal of Technical Physics, Vol. 47, No. 1, 2006, pp. 47-58.

[15] B. K. Sharma, R. C. Chaudhary and M. Agarwal, “Radiation Effect on Temperature Distribution in Three-Dimensional Couette Flow with Injection or Suction,” Applied Mathematics and Mechanics, Vol. 28, No. 3, 2007, pp. 309-316. doi:10.1007/s10483-007-0304-z

[16] B. K. Sharma, R. C. Chaudhary and M. Agarwal, “Radiation Effect on Steady Free Convective Flow along a Uniform Moving Porous Vertical Plate in Presence of Heat Source/Sink and Transverse Magnetic Field,” Bulletin of Calcutta Mathematical Society, Vol. 100, 2008, pp. 529-538.

[17] E. R. G. Eckert and R. M. Drake, “Analysis of Heat and Mass Transfer,” McGraw-Hill, New York, 1972.

[18] Z. Dursunkaya and W. M. Worek, “Diffusion-Thermo and Thermal-Diffusion Effects in Transient and Steady Natural Convection from Vertical Surface,” International Journal of Heat and Mass Transfer, Vol. 35, No. 8, 1992, pp. 2060-2065. doi:10.1016/0017-9310(92)90208-A

[19] M. Anghel, H. S. Takhar and I. Pop, “Dufour and Soret Effects on Free-Convection Boundary Layer over a Vertical Surface Embedded in a Porous Medium,” Studia Universitatis Babes-Bolyai: Mathematica, Vol. XLV, No. 4, 2000, pp. 11-21.

[20] A. Postelnicu, “Influence of a Magnetic Field on Heat and Mass Transfer by Natural Convection from Vertical Surfaces in Porous Media Considering Soret and Dufour Effects,” International Journal of Heat and Mass Transfer, Vol. 47, No. 6-7, 2004, pp. 1467-1472. doi:10.1016/j.ijheatmasstransfer.2003.09.017

[21] M. S. Alam and M. M. Rahman, “Dufour and Soret Effects on MHD Free Convective Heat and Mass Transfer Flow past a Vertical Flat Plate Embedded in a Porous Medium,” Journal of Naval Architecture and Marine Engineering, Vol. 2, No. 1, 2005, pp. 55-65.

[22] A. Raptis and C. V. Massalas, “Magnetohydrodynamic Flow past a Plate by the Presence of Radiation,” Heat and Mass Transfer, Vol. 34, No. 2-3, 1998, pp. 107-109. doi:10.1007/s002310050237

[23] C. Perdikis and E. Rapti, “Unsteady MHD Flow in the Presence of Radiation,” International Journal of Applied Mechanics and Engineering, Vol. 11, No. 2, 2006, pp. 383-390.

[24] J. D. Hoffman, “Numerical Methods for Engineers and Scientists,” McGraw-Hill, New York, 1992.