Dufour Effects on Unsteady Hydromagnetic Radiative Fluid Flow past a Vertical Plate through Porous Medium

Author(s)
Jagdish Prakash^{*},
Avula Golla Vijaya Kumar,
Desu Bhanumathi,
Sibyala Vijaya Kumar Varma

Affiliation(s)

Department of Mathematics, University of Botswana, Gaborone, Botswana.

Department of Mathematics, Sree Vidyanikethan Engineering College.

Department of Mathematics, S.V. University, Tirupati, India.

Department of Mathematics, University of Botswana, Gaborone, Botswana.

Department of Mathematics, Sree Vidyanikethan Engineering College.

Department of Mathematics, S.V. University, Tirupati, India.

ABSTRACT

The objective of the present study is to investigate diffusion-thermo (Dufour effect) and radiation effects on unsteady MHD free convection flow past an impulsively started infinite vertical plate with variable temperature and uniform mass diffusion in the presence of transverse applied magnetic field through porous medium. At time t > 0, the plate is given an impulsive motion with constant velocity in the vertical upward direction against to the gravitational field. At the same time the plate temperature is raised linearly with time t and the level of concentration near the plate is raised to . A magnetic field of uniform strength is applied normal to the direction to the flow. The dimen- sionless governing equations are solved in closed form by Laplace-transform technique. The effect of flow parameters on velocity, temperature, concentration, the rate of heat transfer and the rate of mass transfer are shown through graphs.

The objective of the present study is to investigate diffusion-thermo (Dufour effect) and radiation effects on unsteady MHD free convection flow past an impulsively started infinite vertical plate with variable temperature and uniform mass diffusion in the presence of transverse applied magnetic field through porous medium. At time t > 0, the plate is given an impulsive motion with constant velocity in the vertical upward direction against to the gravitational field. At the same time the plate temperature is raised linearly with time t and the level of concentration near the plate is raised to . A magnetic field of uniform strength is applied normal to the direction to the flow. The dimen- sionless governing equations are solved in closed form by Laplace-transform technique. The effect of flow parameters on velocity, temperature, concentration, the rate of heat transfer and the rate of mass transfer are shown through graphs.

KEYWORDS

MHD; Heat and Mass Transfer; Diffusion-Thermo (Dufour Number); Vertical Plate; Porous Medium

MHD; Heat and Mass Transfer; Diffusion-Thermo (Dufour Number); Vertical Plate; Porous Medium

Cite this paper

J. Prakash, A. Kumar, D. Bhanumathi and S. Varma, "Dufour Effects on Unsteady Hydromagnetic Radiative Fluid Flow past a Vertical Plate through Porous Medium,"*Open Journal of Fluid Dynamics*, Vol. 2 No. 4, 2012, pp. 159-171. doi: 10.4236/ojfd.2012.24017.

J. Prakash, A. Kumar, D. Bhanumathi and S. Varma, "Dufour Effects on Unsteady Hydromagnetic Radiative Fluid Flow past a Vertical Plate through Porous Medium,"

References

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[2] V. M. Soundalgekar, S. K. Gupta and N. S. Birajdar, “Ef- fects of Mass Transfer and Free Convection Currents on MHD Stokes Problem for a Vertical Plate,” Nuclear En- gineering and Design, Vol. 53, No. 3, 1979, pp. 339-346.

[3] V. M. Soundalgekar, M. R. Patil and M. D. Jahagirdar, “MHD Stokes Problem for a Vertical Plate with Variable Temperature,” Nuclear Engineering and Design, Vol. 64, No. 1, 1981, pp. 39-42. doi:10.1016/0029-5493(81)90030-3

[4] M. Kumari and G. Nath, “Development of Two Dimensional Boundary Layer with an Applied Magnetic Field Due to an Impulsive Motion,” Indian Journal of Pure and Applied Mathematics, Vol. 30, No. 7, 1999, pp. 695-708.

[5] W. G. England and A. F. Emery, “Thermal Radiation Effects on the Laminar Free Convection Boundary Layer of an Absorbing Gas,” Journal of Heat Transfer, Vol. 91, No. 1, 1969, pp. 37-44. doi:10.1115/1.3580116

[6] V. M. Soundalgekar and H. S. Takhar, “Radiation Effects on Free Convection Flow past a Semi-Infinite Vertical Plate,” Modeling, Measurement and Control, Vol. 51, 1993, pp. 31-40.

[7] 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

[8] A. Raptis and C. Perdikis, “Radiation and Free Convection Flow past a Moving Plate,” International Journal of Applied Mechanics and Engineering, Vol. 4, No. 4, 1999, pp. 817-821.

[9] U. N. Das, R. K. Deka and V. M. Soundalgekar, “Radiation Effects on Flow past an Impulsively Started Vertical Infinite Plate,” Journal of Theoretical Mechanics, Vol. 1, 1996, pp. 111-115.

[10] R. Muthucumaraswamy, K. E. Sathappan, and R. Natarajan, “Mass Transfer Effects on Exponentially Accelerated Isothermal Vertical Plate,” International Journal of Applied Mathematics and Mechanics, Vol. 4, No. 6, 2004, pp. 19-25.

[11] V. Rajesh and S. V. K. Varma, “Radiation and Mass Transfer Effects on MHD Free Convection Flow past an Exponentially Accelerated Vertical Plate with Variable Temperature,” ARPN Journal of Engineering and Applied Sciences, Vol. 4, No. 6, 2009, pp. 20-26.

[12] A. G. Vijaya Kumar and S. V. K. Varma, “Thermal Radiation and Mass Transfer Effects on MHD Flow past an Impulsively Started Exponentially Accelerated Vertical Plate with Variable Temperature and Mass Diffusion,” Far East Journal of Applied Mathematics, Vol. 55, No. 2 2011, pp. 93-115.

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

[14] 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 Mass Transfer, Vol. 35, No. 8, 1992, pp. 2060-2065. doi:10.1016/0017-9310(92)90208-A

[15] 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,” Mathematics, Vol. 11, No. 4, 2000, pp. 11-21.

[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 Dofour Effects,” International Journal of Hear and Mass Transfer, 47, No. 6-7, 2004, pp. 1467-1472.

[17] M. S. Alam, M. M. Rahman and M. A. Smad, “Dufour and Soret Effects on Unsteady MHD Free Convection and Mass Transfer Flow past a Vertical Porous Plate in a Porous Medium,” Nonlinear Analysis: Modelling and Control, Vol. 11, No. 3, 2005, pp. 217-226.

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

[1] B. C. Sakiadis, “Boundary Layer Behavior on Continuous Solid Surfaces: II. Boundary Layer on a Continuous Solid Flat Surfaces,” AIChE Journal, Vol. 7, No. 2, 1961, pp. 221-225. doi:10.1002/aic.690070211

[2] V. M. Soundalgekar, S. K. Gupta and N. S. Birajdar, “Ef- fects of Mass Transfer and Free Convection Currents on MHD Stokes Problem for a Vertical Plate,” Nuclear En- gineering and Design, Vol. 53, No. 3, 1979, pp. 339-346.

[3] V. M. Soundalgekar, M. R. Patil and M. D. Jahagirdar, “MHD Stokes Problem for a Vertical Plate with Variable Temperature,” Nuclear Engineering and Design, Vol. 64, No. 1, 1981, pp. 39-42. doi:10.1016/0029-5493(81)90030-3

[4] M. Kumari and G. Nath, “Development of Two Dimensional Boundary Layer with an Applied Magnetic Field Due to an Impulsive Motion,” Indian Journal of Pure and Applied Mathematics, Vol. 30, No. 7, 1999, pp. 695-708.

[5] W. G. England and A. F. Emery, “Thermal Radiation Effects on the Laminar Free Convection Boundary Layer of an Absorbing Gas,” Journal of Heat Transfer, Vol. 91, No. 1, 1969, pp. 37-44. doi:10.1115/1.3580116

[6] V. M. Soundalgekar and H. S. Takhar, “Radiation Effects on Free Convection Flow past a Semi-Infinite Vertical Plate,” Modeling, Measurement and Control, Vol. 51, 1993, pp. 31-40.

[7] 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

[8] A. Raptis and C. Perdikis, “Radiation and Free Convection Flow past a Moving Plate,” International Journal of Applied Mechanics and Engineering, Vol. 4, No. 4, 1999, pp. 817-821.

[9] U. N. Das, R. K. Deka and V. M. Soundalgekar, “Radiation Effects on Flow past an Impulsively Started Vertical Infinite Plate,” Journal of Theoretical Mechanics, Vol. 1, 1996, pp. 111-115.

[10] R. Muthucumaraswamy, K. E. Sathappan, and R. Natarajan, “Mass Transfer Effects on Exponentially Accelerated Isothermal Vertical Plate,” International Journal of Applied Mathematics and Mechanics, Vol. 4, No. 6, 2004, pp. 19-25.

[11] V. Rajesh and S. V. K. Varma, “Radiation and Mass Transfer Effects on MHD Free Convection Flow past an Exponentially Accelerated Vertical Plate with Variable Temperature,” ARPN Journal of Engineering and Applied Sciences, Vol. 4, No. 6, 2009, pp. 20-26.

[12] A. G. Vijaya Kumar and S. V. K. Varma, “Thermal Radiation and Mass Transfer Effects on MHD Flow past an Impulsively Started Exponentially Accelerated Vertical Plate with Variable Temperature and Mass Diffusion,” Far East Journal of Applied Mathematics, Vol. 55, No. 2 2011, pp. 93-115.

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

[14] 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 Mass Transfer, Vol. 35, No. 8, 1992, pp. 2060-2065. doi:10.1016/0017-9310(92)90208-A

[15] 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,” Mathematics, Vol. 11, No. 4, 2000, pp. 11-21.

[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 Dofour Effects,” International Journal of Hear and Mass Transfer, 47, No. 6-7, 2004, pp. 1467-1472.

[17] M. S. Alam, M. M. Rahman and M. A. Smad, “Dufour and Soret Effects on Unsteady MHD Free Convection and Mass Transfer Flow past a Vertical Porous Plate in a Porous Medium,” Nonlinear Analysis: Modelling and Control, Vol. 11, No. 3, 2005, pp. 217-226.

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