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The concentration distribution is found to increase faster up to certain y value (distance from the plate) and decreases later as the Schmidt parameter (Sc) or Radiation parameter (R) become heavier. 84 Concentration 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 y Sc=0.78, t=0.2 Sc=0.96, t=0.2 Sc=1.30, t=0.2 Sc=1.60, t=0.2 Sc=2.01, t=0.2 Sc=0.78, t=0.4 Sc=0.96, t=0.4 Sc=1.30, t=0.4 Sc=1.60, t=0.4 Sc=2.01, t=0.4 Figure 8: Concentration profiles for different Sc with So=5, Pr=0.71, R=4 and H=1 Concentration 1.4 1.2 1 0.8 0.6 0.4 0.2 R=1, H=4, t=0.2 R=5, H=4, t=0.2 R=10,H=4, t=0.2 R=1, H=12,t=0.2 R=1, H=4, t=0.4 R=5, H=4, t=0.4 R=10,H=4, t=0.4 R=1, H=12,t=0.4 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 y Figure 9: Concentration profiles for different R with So=5, Sc=2.01, H=1 and Pr=0.71 Nu Sherwood number 10 9 8 7 6 5 4 3 2 1 Pr=0.71,R=1 Pr=0.71,R=2 Pr=0.71,R=3 Pr=7,R=1 Pr=7,R=2 Pr=7,R=3 0 0 0.5 1 1.5 2 2.5 3 3.5 4 t 0 -5 -10 -15 -20 -25 -30 -35 Figure 10: Nusselt Number So=1, Sc=2.01, R=2 So=2, Sc=2.01, R=2 So=3, Sc=2.01, R=2 So=1, Sc=4.0, R=2 So=1, Sc=6.0, R=2 So=1, Sc=2.01, R=6 So=1, Sc=2.01, R=10 0.5 1 1.5 2 2.5 3 3.5 4 t Figure 11: Sherwood number for different Sc, So and R Nusselt number is presented in Figure 10 against time t. From this figure the Nusselt number is observed to increase with increase in R for both water (Pr=7.0) and air (Pr=0.71). It is also observed that Nusselt number for water is higher than that of air (Pr=0.71). The reason is that smaller values of Pr are equivalent to increasing the thermal conductivities and therefore heat is able to diffuse away from the plate ACTA TECHNICA CORVINIENSIS – Bulletin of Engineering more rapidly than higher values of Pr, hence the rate of heat transfer is reduced. Finally, from Figure 11 it is seen that the Sherwood number decreases with increase in Sc (Schmidt number), So (Soret number) and R (radiation parameter). NOMENCLATURE a*-Absorption coefficient K-Permeability parameter H-Heat source parameter B 0 -External magnetic field C’-Species concentration C w ’-Concentration of the plate C ∞ ’-Concentration of fluid far away from the plate C-Dimensionless concentration Cp-Specific heat at constant pressure D-Chemical molecular diffusivity D 1 -Coefficient of thermal diffusivity g-Acceleration due to gravity G r -Thermal Grashof number G m -Mass Grashof number M-Magnetic field parameter Nu-Nusselt number P r -Prandtl number q r -Radiative heat flux in the y- direction R-Radiative parameter Sc-Schmidt number S 0 -Soret number Sh-Sherwood number T-Temperature of the fluid near the plate T w ’-Temperature of the plate T ∞ ’-Temperature of the fluid far away from the plate t’-Time t-Dimensionless time u’-Velocity of the fluid in the x’ - direction u o -Velocity of the plate u-Dimensionless velocity y’-Co-ordinate axis normal to the plate y-Dimensionless co-ordinate axis normal to the plate Greek symbols: К-Thermal conductivity of the fluid α-Thermal diffusivity β-Volumetric coefficient of thermal expansion β*-Volumetric coefficient of expansion with concentration μ-Coefficient of viscosity υ-Kinematic viscosity ρ-Density of the fluid σ-Electric conductivity θ-Dimensionless temperature erf-Error function erfc-Complementary error function Subscripts: ω-Conditions on the wall ∞-Free stream conditions REFERENCES [1] M.S. Alam, M.M. Rahman and M.A. Maleque, Local similarity solutions for unsteady MHD free convection and mass transfer flow past an impulsively started vertical porous plate with Dufour and Soret effects, Thammasat int.j.sci.tech. 10(3) (2005), 1-8. [2] M.S. Alam, M.M. Rahman and M.A. Samad, Numerical study of the combined free-forced convection and mass transfer flow past a vertical porous plate in a porous medium with heat 2013. Fascicule 2 [April–June]
ACTA TECHNICA CORVINIENSIS – Bulletin of Engineering generation and thermal diffusion, Nonlin. Anal.Model. Control 11(4) (2006), 331-343 [3] M.M. Alam and M. A. Sattar, Transient MHD heat and mass transfer flow with thermal diffusion in a rotating system, J. Energy Heat Mass trans. 21 (1999)m 9-21. [4] U.N. Das, R.K. Deka and V.M. Soundalgekar, Radiation effects on flow past an impulsively started vertical infinite plate, J.theo. Mech. 1(1996), 111-115. [5] M.A. Hossain and H. S. Takhar, Radiation effect on mixed convection along a vertical plate with uniform surface temperature, Heat Mass Trans. 31(1996), 243-248. [6] B. K. Jha and A. K. Singh, Soret effects on freeconvection and mass transfer flow in the Stokes problem for a infinite vertical plate, Astrophys. Space Sci. 173(2) (1990). [7] N.G. Kafoussias, MHD thermal –diffusion effects on free convective and mass transfer flow over an infinite vertical moving plate. Astrophys.Space Sci. 192(1) (1992), 11-19. [8] M. Kumari and G. Nath, Development of twodimensional boundary layer with an applied magnetic field due to an impulsive motion, Indian J. pure Appl. Math. 30 (1999), 695-708. [9] R. Muthucumaraswamy and B. Janakiraman, MHD and radiation effects on moving isothermal vertical plate with variable mass diffusion, Theo. Appl. Mech. 33(1) (2006), 17-29. [10] A. Raptis and C. Perdikis, Radiation and free convection flow past a moving plate, Int. J.Appl Mech. Eng. 4(1999), 817-821. [11] 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 Eng. Des. 53(1979), 339-346. [12] V.M. Soundalgekar, M.R.Patil and M.D. Jahagirdar, MHD Stokes problem for a vertical plate with variable temperature, Nuclear Eng. Des. 64(1981), 39-42. [13] V.M. Soundalgekar and H.S. Takhar, Radiation effects on free convection flow past a semiinfinite vertical plate, Model. Measure.Comrol (1993), 31-40. [14] V. Rajesh and S.V.K. Varma, Thermal diffusion and radiation effects on MHD flow past an infinite vertical plate with variable temperature and mass diffusion, JP Journal of Heat and Mass Transfer, Vol3, Issue1,Feb(2009). [15] A.G.V. Kumar and S.V.K. Varma, Thermal diffusion and Radiation effects on MHD flow through porous medium with variable temperature and variable mass diffusion, Int. J. of Fluids Engineering, Vol.3, No.3, (2011), pp.353-368. ACTA TECHNICA CORVINIENSIS – BULLETIN of ENGINEERING ISSN: 2067-3809 [CD-Rom, online] copyright © UNIVERSITY POLITEHNICA TIMISOARA, FACULTY OF ENGINEERING HUNEDOARA, 5, REVOLUTIEI, 331128, HUNEDOARA, ROMANIA http://acta.fih.upt.ro 2013. Fascicule 2 [April–June] 85
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ROLE OF METAMODELING Detailed resea
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