Dufour and Soret Effect on Steady MHD Flow in Presence of Heat Generation and Magnetic Field past an Inclined Stretching Sheet

Affiliation(s)

Department of Mathematics, Comilla University, Kotbari, Comilla, Bangladesh.

Department of Mathematics, University of Dhaka, Dhaka, Bangladesh.

Department of Mathematics, Comilla University, Kotbari, Comilla, Bangladesh.

Department of Mathematics, University of Dhaka, Dhaka, Bangladesh.

ABSTRACT

An analysis of two-dimensional steady magneto-hydrodynamic free convection flow of an electrically conducting, viscous, incompressible fluid past an inclined stretching porous plate in the presence of a uniform magnetic field and thermal radiation with heat generation is made. Both the Dufour and Soret effects are considered for a hydrogen-air mixture as the non-chemically reacting fluid pair. The equations governing the flow, temperature and concentration fields are reduced to a system of joined non-linear ordinary differential equations by similarity transformation. Non-linear differential equations are integrated numerically by using Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Finally the significance of physical parameters which are of engineering interest are examined both in graphical and tabular form.

An analysis of two-dimensional steady magneto-hydrodynamic free convection flow of an electrically conducting, viscous, incompressible fluid past an inclined stretching porous plate in the presence of a uniform magnetic field and thermal radiation with heat generation is made. Both the Dufour and Soret effects are considered for a hydrogen-air mixture as the non-chemically reacting fluid pair. The equations governing the flow, temperature and concentration fields are reduced to a system of joined non-linear ordinary differential equations by similarity transformation. Non-linear differential equations are integrated numerically by using Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Finally the significance of physical parameters which are of engineering interest are examined both in graphical and tabular form.

Cite this paper

M. Karim, M. Samad and M. Hasan, "Dufour and Soret Effect on Steady MHD Flow in Presence of Heat Generation and Magnetic Field past an Inclined Stretching Sheet,"*Open Journal of Fluid Dynamics*, Vol. 2 No. 3, 2012, pp. 91-100. doi: 10.4236/ojfd.2012.23009.

M. Karim, M. Samad and M. Hasan, "Dufour and Soret Effect on Steady MHD Flow in Presence of Heat Generation and Magnetic Field past an Inclined Stretching Sheet,"

References

[1] R. S. R. Gorla, “Unsteady Mass Transfer in the Boundary Layer on a Continuous Moving Sheet Electrod,” Journal of the Electrochemical Society, Vol. 125, No. 6, 1978, pp. 865-869. doi:10.1149/1.2131569

[2] D. T. Chin, “Mass Transfer to a Continuous Moving Sheet Electrode,” Journal of the Electrochemical Society, Vol. 122, No. 5, 1975, pp. 643-646. doi:10.1149/1.2134281

[3] L. E. Erickson, L. T. Fan and V. G. Fox, “Heat and Mass Transfer on a Moving Continuous Flat Plate with Suction or Injection,” Industrial Engineering and Chemical Fundamentals, Vol. 5, 1966, pp. 19-25. doi:10.1021/i160017a004

[4] M. A. Samad and M. Mohebujjaman, “MHD Heat and Mass Transfer Free Convection Flow along a Vertical Stretching Sheet in Presence of Magnetic Field with Heat Generation,” Research Journal of Applied Science, Engineering and Technology, Vol. 1, No. 3, 2009, pp. 98-106.

[5] B. C. Sakiadis, “Boundary-Layer Behavior on Continuous Solid Surfaces: I. Boundary-Layer Equations for TwoDimensional and Axisymmetric Flow,” AIChE Journal, Vol. 7, No. 1, 1961, pp. 26-28. doi:10.1002/aic.690070108

[6] R. D. Cess, “The Interaction of Thermal Radiation with Free Convection Heat Transfer,” International Journal of Heat Mass Transfer, Vol. 9, No. 11, 1966, pp. 1269-1277. doi:10.1016/0017-9310(66)90119-0

[7] L. J. Crane, “Flow Past a Stretching Sheet,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 21, No. 4, 1970, pp. 645-647. doi:10.1007/BF01587695

[8] E. M. Sparrow, “Radiation Heat Transfer,” Augmented Edition, Hemisphere Publishing Corp., Washington DC, 1978.

[9] V. M. Soundalgekar, N. V. Vighnesam and I. Pop, “Combined Free and Forced Convection Flow Past a Vertical Porous Plate,” International Journal of Energy Research, Vol. 5, No. 3, 1981, pp. 215-226. doi:10.1002/er.4440050303

[10] W. H. H. Banks, “Similarity Solutions of the Boundary Layer Equation for a Stretching Wall,” Journal de Mecanique Theorique et Appliquee, Vol. 2, No. 3, 1983, pp. 375-392.

[11] J. B. McLeod and K. R. Rajagopal, “On the Uniqueness of Flow of a Navier-Stokes Fluid Due to a Stretching Boundary,” Archive for Rational Mechanics and Analysis, Vol. 98, No. 4, 1987, pp. 386-395. doi:10.1007/BF00276915

[12] C. K. Chen and M. I. Char, “Heat Transfer of a Continuous, Stretching Surface with Suction or Blowing,” Journal of Mathematical Analysis and Applications, Vol. 135, No. 2, 1988, pp. 568-580. doi:10.1016/0022-247X(88)90172-2

[13] M. A. Hossain and H. S. Takhar, “Radiation Effect on Mixed Convection along a Vertical Plate with Uniform Surface Temperature,” Heat and Mass Transfer, Vol. 31, No. 4, 1996, pp. 243-248. doi:10.1007/BF02328616

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

[15] M. A. Alabraba, A. R. Bestman and A. Ogulu, “Laminar Convection in Binary Mixed of Hydromagnetic Flow with Radiative Heat Transfer,” Astrophysics and Space Science, Vol. 195, No. 2, 1992, pp. 431-439. doi:10.1007/BF00646774

[16] 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 Mass Transfer, Vol. 47, No. 6-7, 2004, pp. 1467-1472. doi:10.1016/j.ijheatmasstransfer.2003.09.017

[17] M. S. Alam and M. M. Rahman, “Dufour and Soret Effects on Mixed Convection Flow Past a Vertical Porous Flat Plate with Variable Suction,” Nonlinear Analysis: Modelling and Contral, Vol. 11, No. 1, 2006, pp. 3-12.

[18] M. Enamul Karim, M. A. Samad and Md. Abdus Sattar, “Steady MHD Free Convection Flow with Thermal Radiation Past a Vertical Porous Plate Immersed in a Porous Medium,” Research Journal of Mathematics and Statistics, Vol. 3, 2011, pp. 141-147.

[19] K. A. Helmy, “MHD Boundary Layer Equations for Power Law Fluids with Variable Electric Conductivity,” Meccanica, Vol. 30, No. 2, 1995, pp. 187-200. doi:10.1007/BF00990456

[20] K. Vajravelu and A. Hadjinicolaou, “Heat Transfer in a Viscous Fluid over a Stretching Sheet with Viscous Dissipation and Internal Heat Generation,” International Communications in Heat Mass Transfer, Vol. 20, No. 3, 1993, pp. 417-430. doi:10.1016/0735-1933(93)90026-R

[21] P. R. Nachtsheim and P. Swigert, “Satisfaction of the Asymptotic Boundary Conditions in Numerical Solution of the Systems of Non-Linear Equations of Boundary Layer Type,” Ph.D. Thesis, NASA TN D-3004, Washington DC, 1965.

[1] R. S. R. Gorla, “Unsteady Mass Transfer in the Boundary Layer on a Continuous Moving Sheet Electrod,” Journal of the Electrochemical Society, Vol. 125, No. 6, 1978, pp. 865-869. doi:10.1149/1.2131569

[2] D. T. Chin, “Mass Transfer to a Continuous Moving Sheet Electrode,” Journal of the Electrochemical Society, Vol. 122, No. 5, 1975, pp. 643-646. doi:10.1149/1.2134281

[3] L. E. Erickson, L. T. Fan and V. G. Fox, “Heat and Mass Transfer on a Moving Continuous Flat Plate with Suction or Injection,” Industrial Engineering and Chemical Fundamentals, Vol. 5, 1966, pp. 19-25. doi:10.1021/i160017a004

[4] M. A. Samad and M. Mohebujjaman, “MHD Heat and Mass Transfer Free Convection Flow along a Vertical Stretching Sheet in Presence of Magnetic Field with Heat Generation,” Research Journal of Applied Science, Engineering and Technology, Vol. 1, No. 3, 2009, pp. 98-106.

[5] B. C. Sakiadis, “Boundary-Layer Behavior on Continuous Solid Surfaces: I. Boundary-Layer Equations for TwoDimensional and Axisymmetric Flow,” AIChE Journal, Vol. 7, No. 1, 1961, pp. 26-28. doi:10.1002/aic.690070108

[6] R. D. Cess, “The Interaction of Thermal Radiation with Free Convection Heat Transfer,” International Journal of Heat Mass Transfer, Vol. 9, No. 11, 1966, pp. 1269-1277. doi:10.1016/0017-9310(66)90119-0

[7] L. J. Crane, “Flow Past a Stretching Sheet,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 21, No. 4, 1970, pp. 645-647. doi:10.1007/BF01587695

[8] E. M. Sparrow, “Radiation Heat Transfer,” Augmented Edition, Hemisphere Publishing Corp., Washington DC, 1978.

[9] V. M. Soundalgekar, N. V. Vighnesam and I. Pop, “Combined Free and Forced Convection Flow Past a Vertical Porous Plate,” International Journal of Energy Research, Vol. 5, No. 3, 1981, pp. 215-226. doi:10.1002/er.4440050303

[10] W. H. H. Banks, “Similarity Solutions of the Boundary Layer Equation for a Stretching Wall,” Journal de Mecanique Theorique et Appliquee, Vol. 2, No. 3, 1983, pp. 375-392.

[11] J. B. McLeod and K. R. Rajagopal, “On the Uniqueness of Flow of a Navier-Stokes Fluid Due to a Stretching Boundary,” Archive for Rational Mechanics and Analysis, Vol. 98, No. 4, 1987, pp. 386-395. doi:10.1007/BF00276915

[12] C. K. Chen and M. I. Char, “Heat Transfer of a Continuous, Stretching Surface with Suction or Blowing,” Journal of Mathematical Analysis and Applications, Vol. 135, No. 2, 1988, pp. 568-580. doi:10.1016/0022-247X(88)90172-2

[13] M. A. Hossain and H. S. Takhar, “Radiation Effect on Mixed Convection along a Vertical Plate with Uniform Surface Temperature,” Heat and Mass Transfer, Vol. 31, No. 4, 1996, pp. 243-248. doi:10.1007/BF02328616

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

[15] M. A. Alabraba, A. R. Bestman and A. Ogulu, “Laminar Convection in Binary Mixed of Hydromagnetic Flow with Radiative Heat Transfer,” Astrophysics and Space Science, Vol. 195, No. 2, 1992, pp. 431-439. doi:10.1007/BF00646774

[16] 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 Mass Transfer, Vol. 47, No. 6-7, 2004, pp. 1467-1472. doi:10.1016/j.ijheatmasstransfer.2003.09.017

[17] M. S. Alam and M. M. Rahman, “Dufour and Soret Effects on Mixed Convection Flow Past a Vertical Porous Flat Plate with Variable Suction,” Nonlinear Analysis: Modelling and Contral, Vol. 11, No. 1, 2006, pp. 3-12.

[18] M. Enamul Karim, M. A. Samad and Md. Abdus Sattar, “Steady MHD Free Convection Flow with Thermal Radiation Past a Vertical Porous Plate Immersed in a Porous Medium,” Research Journal of Mathematics and Statistics, Vol. 3, 2011, pp. 141-147.

[19] K. A. Helmy, “MHD Boundary Layer Equations for Power Law Fluids with Variable Electric Conductivity,” Meccanica, Vol. 30, No. 2, 1995, pp. 187-200. doi:10.1007/BF00990456

[20] K. Vajravelu and A. Hadjinicolaou, “Heat Transfer in a Viscous Fluid over a Stretching Sheet with Viscous Dissipation and Internal Heat Generation,” International Communications in Heat Mass Transfer, Vol. 20, No. 3, 1993, pp. 417-430. doi:10.1016/0735-1933(93)90026-R

[21] P. R. Nachtsheim and P. Swigert, “Satisfaction of the Asymptotic Boundary Conditions in Numerical Solution of the Systems of Non-Linear Equations of Boundary Layer Type,” Ph.D. Thesis, NASA TN D-3004, Washington DC, 1965.