Double-Diffusion MHD Free Convective Flow along a Sphere in the Presence of a Homogeneous Chemical Reaction and Soret and Dufour Effects
Applied and Computational Mathematics
Volume 6, Issue 1, February 2017, Pages: 34-44
Received: Jan. 5, 2017;
Accepted: Jan. 19, 2017;
Published: Feb. 23, 2017
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A. J. Chamkha, Mechanical Engineering Department, Prince Mohammad Bin Fahd University, Al-Khobar, Saudi Arabia; Prince Sultan Endowment for Energy and Environment, Prince Mohammad Bin Fahd University, Al-Khobar, Saudi Arabia
A. M. Aly, Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt
Z. A. S. Raizah, Department of Mathematics, Faculty of Science for Girls, Abha, King Khalid University, Asir, Saudia Arabia
A numerical solution is presented for the effects of chemical reaction, thermal radiation, Soret number, Dufour number and magnetic field on double-diffusion free convection flow along a sphere. The governing boundary-layer equations of the problem are formulated and transformed into non-similar form. The obtained equations are solved numerically by an efficient, iterative, tri-diagonal, implicit finite-difference method. The Roseland approximation is used to describe the radiative heat flux in the energy equation. Representative results for the fluid velocity, temperature and solute concentration profiles as well as the local heat and mass transfer rates for various values of the physical parameters are displayed in both graphical and tabular forms.
A. J. Chamkha,
A. M. Aly,
Z. A. S. Raizah,
Double-Diffusion MHD Free Convective Flow along a Sphere in the Presence of a Homogeneous Chemical Reaction and Soret and Dufour Effects, Applied and Computational Mathematics.
Vol. 6, No. 1,
2017, pp. 34-44.
S. P. Anjalidevi, R. Kandasamy, Effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate, Heat and Mass Transfer, 35 (6) (1999) 465-467.
S. P. Anjali Devi, R. Kandasamy, Effects of Chemical Reaction, Heat and Mass Transfer on MHD Flow past a Semi Infinite Plate, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 80 (10) (2000) 697-700.
A. Chamkha, M. A. Mansour, A. Aly, Unsteady MHD free convective heat and mass transfer from a vertical porous plate with Hall current, thermal radiation and chemical reaction effects, International Journal for Numerical Methods in Fluids, 65 (4) (2011) 432-447.
A. Chamkha, A. Aly, M. Mansour, Similarity solution for unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction/injection and chemical reaction effects, Chemical Engineering Communications, 197 (6) (2010) 846-858.
R. Muthucumaraswamy, P. Ganesan, On impulsive motion of a vertical plate with heat flux and diffusion of chemically reactive species, Forschung im Ingenieurwesen, 66 (1) (2000) 17-23.
R. Muthucumaraswamy, P. Ganesan, First-order chemical reaction on flow past an impulsively started vertical plate with uniform heat and mass flux, Acta Mechanica, 147 (1) (2001) 45-57.
H. S. Takhar, A. J. Chamkha, G. Nath, Flow and mass transfer on a stretching sheet with a magnetic field and chemically reactive species, International Journal of Engineering Science, 38 (12) (2000) 1303-1314.
R. Muthucumaraswamy, Effects of a chemical reaction on a moving isothermal vertical surface with suction, Acta Mechanica, 155 (1) (2002) 65-70.
J. A. Weaver, R. Viskanta, Natural convection due to horizontal temperature and concentration gradients—2. Species interdiffusion, Soret and Dufour effects, International Journal of Heat and Mass Transfer, 34 (12) (1991) 3121-3133.
M. S. Malashetty, S. N. Gaikwad, Effect of cross diffusion on double diffusive convection in the presence of horizontal gradients, International Journal of Engineering Science, 40 (7) (2002) 773-787.
C. Soret, Influence de la temperature sur la distribution des sels dans leurs solutions,, C. R. Acad. Sci. Paris 91 (1880) 289-291.
E. D, Analysis Of Heat And Mass Transfer, Taylor & Francis, 1986.
N. G. Kafoussias, E. W. Williams, Thermal-diffusion and diffusion-thermo effects on mixed free-forced convective and mass transfer boundary layer flow with temperature dependent viscosity, International Journal of Engineering Science, 33 (9) (1995) 1369-1384.
M. Mansour, N. El-Anssary, A. Aly, Effects of chemical reaction and thermal stratification on MHD free convective heat and mass transfer over a vertical stretching surface embedded in a porous media considering Soret and Dufour numbers, Chemical engineering journal, 145 (2) (2008) 340-345.
A. Chamkha, A. Aly, Heat and mass transfer in stagnation-point flow of a polar fluid towards a stretching surface in porous media in the presence of Soret, Dufour and chemical reaction effects, Chemical Engineering Communications, 198 (2) (2010) 214-234.
I. S. H. R. Grief, L. C. Lin, Laminar convection of a radiating gas in a vertical channel, J. Fluid Mech, 45 (1971) 513–520.
W. G. V. A. C. Cogley, S. E. Gill, Differential approximation for radiative transfer in a non-gray-gas near equilibrium, AIAA J, 6 (1968) 551–553.
M. M. Molla, M. Taher, M. M. Chowdhury, M. A. Hossain, Magnetohydrodynamic natural convection flow on a sphere in presence of heat generation, Nonlinear Analysis: Modelling and Control, 10 (4) (2005) 349-363.
R. Nazar, N. Amin, Free convection boundary layer on an isothermal sphere in a micropolar fluid, International communications in heat and mass transfer, 29 (3) (2002) 377-386.
R. Nazar, N. Amin, I. Pop, Free convection boundary layer on an isothermal horizontal circular cylinder in a micropolar fluid, Heat Transfer, 2 (2002) 525-530.
M. Mansour, M. El-Hakiem, S. El Kabeir, Heat and mass transfer in magnetohydrodynamic flow of micropolar fluid on a circular cylinder with uniform heat and mass flux, Journal of Magnetism and Magnetic Materials, 220 (2) (2000) 259-270.
M. M. Alam, M. Alim, M. M. Chowdhury, Viscous dissipation effects on MHD natural convection flow along a sphere, Journal of Mechanical Engineering, 36 (2006) 44-48.
M.-J. Huang, Laminar free convection from a sphere with blowing and suction, Journal of heat transfer, 109 (2) (1987) 529-532.
C.-Y. Cheng, Natural convection heat and mass transfer from a sphere in micropolar fluids with constant wall temperature and concentration, International Communications in Heat and Mass Transfer, 35 (6) (2008) 750-755.
A. J. Chamkha, A. Rashad, A. M. Aly, Non-Darcy Natural Convection of a Nanofluid about a Permeable Vertical Cone Embedded in a Porous Medium, International Journal of Microscale and Nanoscale Thermal and Fluid Transport Phenomena, 4 (2) (2013) 99.
A. Chamkha, A. M. Aly, M. Mansour, Effects of Chemical Reaction and Pressure Work on Free Convection over a Stretching Cone Embedded in a Porous Medium, International Journal of Industrial Mathematics, 4 (4) (2012) 319-333.
A. Chamkha, A. M. Aly, Heat and Mass Transfer by Free Convective Flow of a Polar Fluid along a Sphere Embedded in a Porous Medium, Journal of Energy, Heat and Mass Transfer, 34 (2012) 19-47.
A. J. Chamkha, A. Rashad, A. M. Aly, Transient natural convection flow of a nanofluid over a vertical cylinder, Meccanica, 48 (1) (2013) 71-81.
N. A. Khan, F. Sultan, On the double diffusive convection flow of Eyring-Powell fluid due to cone through a porous medium with Soret and Dufour effects, AIP Advances, 5 (5) (2015) 057140.
C. S. K. Raju, N. Sandeep, A. Malvandi, Free convective heat transfer of MHD Cu-kerosene nanofluid over a cone with temperature dependent viscosity, Acta Astronautica, 129 (2016) 419-428.
E. Sparrow, R. Cess, Radiation Heat Transfer, 1978, Hemisphere, Wahington, DC.
F. Blottner, Finite difference methods of solution of the boundary-layer equations, AIAA Journal, 8 (2) (1970) 193-205.