Figure 3. Velocity profiles when Sc = 2.01, Pr = 0.71, R = 10, k = 5, M = 3 & t = 0.4.

Figure 4. Velocity profiles when M = 3, Pr = 0.71, Sc = 2.01, R = 10, k = 5, Du = 0.03 & t = 0.4.

Figure 5. Velocity profiles when M = 4, Pr = 0.71, R = 10, k = 5, Du = 0.03 & t = 0.4.

Figure 6. Velocity profiles when Sc = 2.01, M = 3, Pr = 0.71, R = 10, k = 5, Du = 0.03.

Figure 7. Velocity profiles when Sc = 2.01, Pr = 0.71, R = 10, M = 3, Du = 0.03 & t = 0.4.

Figure 8. Temperature profiles when R = 4, Pr = 0.71 & Sc = 2.01.

Figure 9. Temperature profiles when Du = 0.03, Pr = 0.71 & Sc = 2.01.

Figure 10. Temperature profiles when R = 4, Du = 0.03 & Sc = 2.01.

Figure 11. Concentration profiles.

Figure 12. Nusselt number.

Figure 13. Sherwood number.

effects of Prandtl number Pr on the temperature field. It is observed that an increase in the Prandtl number leads to decrease in the fluid temperature. It is due to the fact that thermal conductivity of the fluid decreases with increasing Pr, resulting a decrease in thermal boundary layer thickness.

The concentration profiles for different values of Schmidt number (Sc) and time t are presented in Figure 11. From this figure it is seen that the concentration decreases with increase in Sc while it increases with time t. Figure 12 reveals the rate of heat transfer coefficient in terms of Nusselt number for different values of radiation parameter R, Prandtl number Pr and Dufour number Dr respectively. It is observed that Nusselt number increases with increasing values of R or Pr but decreases as Du increases. Finally, from Figure 13 it is seen that Sherwood number increases with increase of Sc.

REFERENCES

- 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
- V. M. Soundalgekar, S. K. Gupta and N. S. Birajdar, “Effects of Mass Transfer and Free Convection Currents on MHD Stokes Problem for a Vertical Plate,” Nuclear Engineering and Design, Vol. 53, No. 3, 1979, pp. 339-346.
- 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
- 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.
- 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
- 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.
- 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
- 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.
- 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.
- 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.
- 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.
- 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.
- E. R. G. Eckert and R. M. Drake, “Analysis of Heat and Mass Transfer,” McGraw-Hill, New York, 1972.
- 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
- 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.
- 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.
- 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.
- 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.

Nomenclature

Absorption coefficient

External magnetic field

Species concentration

Concentration of the plate

Concentration of the fluid far away from the plate

Dimensionless concentration

Specific heat at constant pressure

Concentration susceptibility

Acceleration due to gravity

Thermal Grashof number

Mass Grashof number

Magnetic field parameter

Nusselt number

Prandtl number

Radiative heat flux in the y-direction

Coefficient of mass diffusivity

Radiative parameter

Schmidt number

Temperature of the fluid near the plate

Temperature of the plate

Temperature of the fluid far away from the plate

Time

Dimensionless time

Velocity of the fluid in the -direction

Velocity of the plate

Dimensionless velocity

Co-ordinate axis normal to the plate

Dimensionless co-ordinate axis normal to the plate

Greek Symbols

Thermal conductivity of the fluid

Thermal diffusivity

Volumetric coefficient of thermal expansion

Volumetric coefficient of expansion with concentration

μ Coefficient of viscosity

ν Kinematic viscosity

r Density of the fluid

ρ Electric conductivity

σ Dimensionless temperature

erf Error function

erfc Complementary error function

Subscripts

Conditions on the wall

Free stream conditions

NOTES

^{*}Corresponding author.