MHD forces on double diffusive free convection process along a vertical wavy surface embedded in a doubly stratified fluid-saturated Darcy porousmedium under the influence of Soret and Dufour effect
DOI:
https://doi.org/10.1080/17797179.2018.1439150Keywords:
Darcy, porous, Soret & Dufour, stratification, Boundary layer, MHDAbstract
The objective of this paper is to investigate the combined heat and mass transfer process near a vertical wavy semiinfinite surface embedded in a doubly stratified electrically conducting fluid-saturated Darcy porous medium under the influence of Soret and Dufour effects. The governing coupled non-dimensional partial differential equations are transformed to boundary layer equations using the two point local non-similarity transformation which is obtained by scale analysis. The resulting boundary layer equations are solved numerically by applying the Keller Box finite difference scheme. The heat and mass transfer has been analysed by plotting the Local, Average Nusselt and Sherwood numbers for various values of parameters influencing the model like: Mg (Magnetic field effect), a (amplitude of wavy surface), ST and SC (Thermal and Mass Stratification), Sr (Soret number), Df (Dufour number), Buoyancy ratio (B), Lewis number (Le).
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References
Boerner, C. J., Quack, H., & Sparrow, E. M. (1970). Local nonsimilarity boundary-layer
solutions. AIAA Journal, 8(11), 1936–1942.
Bejan, A., & Khair, K. R. (1985). Heat and mass transfer by natural convection in a porous
medium. International Journal of Heat and Mass Transfer, 28(5), 909–918.
Cheng, C.-Y. (2000). Natural convection heat and mass transfer near a vertical wavy surface
with constant wall temperature and concentration in a porous medium. International
Communications in Heat and Mass Transfer, 27(8), 1143–1154.
Cheng, C.-Y. (2009). Combined heat and mass transfer in natural convection flow from a
vertical wavy surface in a power-law fluid saturated porousmedium with thermal andmass
stratification. International Communications in Heat and Mass Transfer, 36(4), 351–356.
Elgazery,N. S.,&Elazem, N. Y. A. (2009). The effects of variable properties onMHDunsteady
natural convection heat and mass transfer over a vertical wavy surface. Meccanica, 44(5),
–586.
Ergun, S. (1952). Fluid flow through packed columns. Chemical Engineering Progress, 48,
–94.
Geindreau, C.,&Auriault, J.-L. (2002). Magnetohydrodynamic flows in porous media. Journal
of Fluid Mechanics, 466, 343–363.
Gorla, R. S. R., & Chamkha, A. (2011). Natural convective boundary layer flow over a
nonisothermal vertical plate embedded in a porous medium saturated with a nanofluid.
Nanoscale and Microscale Thermophysical Engineering, 15(2), 81–94.
Hady, F.M., Mohamed, R. A.,&Mahdy, A. (2006).MHDfree convection flow along a vertical
wavy surface with heat generation or absorption effect. International Communications in
Heat and Mass Transfer, 33(10), 1253–1263.
Ingham, D. B., & Pop, I. (2005). Transport phenomena in porous media (Vol. 3). Oxford:
Elsevier. ISBN 9780080444901,0-0804-4490-3.
Isaacson, E., & Keller, H. B. (1994). Analysis of numerical methods. New York, NY: Courier
Corporation.
Kabir, K. H., Alim, M. A., & Andallah, L. S. (2013). Effects of viscous dissipation on MHD
natural convectionflowalong a verticalwavy surface with heat generation. American Journal
of Computational Mathematics, 3(02), 91–98.
Keller, H. B., & Cebeci, T. (1971). Lecture notes in physics (Vol. 8, pp. 91–100). New York,
NY: Springer Verlag.
Kumar, B. V. R., & Shalini (2004). Double-diffusive natural convection induced by a wavy
surface in a stratified porous medium. Journal of Porous Media, 7(4). ISSN 1091-028X.
Mahdy, A. (2009).MHDnon-darcian free convection from a vertical wavy surface embedded
in porous media in the presence of Soret and Dufour effect. International Communications
in Heat and Mass Transfer, 36(10), 1067–1074.
Molla,Md. M.,Hossain, Md.A., & Yao, L. S. (2004). Natural convection flow along a vertical
wavy surface with uniform surface temperature in presence of heat generation/absorption.
International Journal of Thermal Sciences, 43(2), 157–163.
Narayana, P. A. L., & Sibanda, P. (2010). Soret and Dufour effects on free convection along
a vertical wavy surface in a fluid saturated darcy porous medium. International Journal of
Heat and Mass Transfer, 53(15), 3030–3034.
Nield, D. A., & Bejan, A. (2006). Convection in porousmedia. NewYork, NY: Springer Science
& Business Media.
Postelnicu, A. (2004). 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, 47(6), 1467–1472.
Roussellet, V., Niu, X., Yamaguchi, H., & Magoulés, F. (2011). Natural convection of
temperature-sensitive magnetic fluids in porous media. Advances in Applied Mathematics
and Mechanics, 3(01), 121–130.
Rees, D. A. S., & Pop, I. (1994). A note on free convection along a vertical wavy surface in a
porous medium. Journal of Heat Transfer, 116(2), 505–508.
Rees, D. A. S., & Pop, I. (1997). The effect of longitudinal surface waves on free convection
from vertical surfaces in porous media. International Communications in Heat and Mass
Transfer, 24(3), 419–425.
Tak, S. S. & Lodha, A. (2007). Influence of double stratification onMHDfree convection with
Soret and Dufour effects in a darcian porous media. PAMM, 7(1), 2100089–2100090.
Takhar, H. S., & Ram, P. C. (1994). Magnetohydrodynamic free convection flow of water at
c through a porous medium. International Communications in Heat and Mass Transfer,
(3), 371–376.
Tashtoush, B., & Al-Odat, M. (2004). Magnetic field effect on heat and fluid flow over a wavy
surface with a variable heat flux. Journal of Magnetism and Magnetic Materials, 268(3),
–363.
Tsai, R., & Huang, J. S. (2009). Numerical study of Soret and Dufour effects on heat and mass
transfer from natural convection flow over a vertical porousmedium with variable wall heat
fluxes. Computational Materials Science, 47(1), 23–30.
