Soret and Dofour effects on MHD free convection in a micropolar fluid
Tóm tắt
This paper analyzes the flow and heat and mass transfer characteristics of the free convection on a vertical plate with variable wall temperature and concentration in a micropolar fluid in the presence of Soret and Dufour effects. A uniform magnetic field of magnitude
$$B_{0}$$
is applied normal to the plate. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The non-dimensional velocity, microrotation, temperature and concentration are presented graphically for various values of micropolar parameter, magnetic parameter, Dufour and Soret numbers. In addition, the Nusselt number, the Sherwood number, the skin-friction coefficient, the wall couple stress are shown in a tabular form.
Tài liệu tham khảo
Eringen, C.A.: Theory of micropolar fluids. J. Math. Mech. 16, 1–18 (1966)
Lukaszewicz, G.: Micropolar Fluids Theory and Applications. Birkhauser, Basel (1999)
Y\(\ddot{\text{ u }}\)r\(\ddot{\text{ u }}\)soy, M., Pakdemirli, M.: Group classification of a non-Newtonian fluid model using classical approach and equivalence transformations. Int. J. Non Linear Mech. 34, 341–346 (1999)
Eckeret, E.R.G., Drake, R.M.: Analysis of Heat and Mass Transfer. McGraw Hill, Newyork (1972)
Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-Uniform Gases. Cambridge University Press, Cambridge (1952)
Hirshfelder, J.O., Curtis, C.F., Bird, R.B.: Molecular Theory of Gases and Liquids. Wiley, New York (1954)
Huges, W.F., Young, F.J.: The Electro-Magneto Dynamics of fluids. Wiley, New York (1966)
Postenicu, A.: Influence of magnetic field on heat and mass transfer from a vertical surfaces in porous media considering Soret and Dufour effects. Int. J. Heat Mass Transf. 47, 1467–1472 (2004)
Alam, M.S., Rahman, M.M., Abdul Maleque, M., Ferdows, M.: Dufour and Soret effects on steady MHD combined free-forced convective and mass transfer flow past asemi-infinite vertical plate. Thammasat. Int. J. Sci. Tech. 11, 1–12 (2006)
Afify, A.A.: Similarity solution in MHD: Effects of thermal diffusion and diffusion thermo on free convective heat and mass transfer over a stretching surface considering suction or injection. Commun. Nonlinear Sci. Numer. Simul. 14, 2202–2214 (2009)
Rahman, G.M.A.: Thermal-diffusion and MHD for Soret and Dufour’s effects on Hiemenz flow and mass transfer of fluid flow through porous medium onto a stretching surface. Phys. B 405, 2560–2569 (2010)
Makinde, O.D.: On mhd mixed convection with soret and dufour effects past a vertical plate embedded in a porous medium. Lat. Am. Appl. Res. 41, 63–68 (2011)
Makinde, O.D., Olanrewaju, O.P.: Unsteady mixed convection with Soret and Dufour effects past a porous plate moving through a binary mixture of chemically reacting fluid. Chem. Eng. Comm. 198, 922–938 (2011)
Y\(\ddot{\text{ u }}\)r\(\ddot{\text{ u }}\)soy, M.: Similarity solutions for creeping flow and heat transfer in second grade fluids, Int. J. Non Linear Mech. 39, 665–672 (2004)
Pal, D., Talukdar, B.: Influence of fluctuating thermal and mass diffusion on unsteady MHD buoyancy-driven convection past a vertical surface with chemical reaction and Soret effects. Commun. Nonlinear Sci. Numer. Simul. 17, 1597–1614 (2012)
El-Hakiem, M.A., Mohammadein, A.A., El-Kabeir, S.M.M., Gorla, R.S.R.: Joule heating effects on magnetohydrodynamic free convection flow of a micropolar fluid. Int. Commun. Heat Mass Transf. 26(2), 219–227 (1999)
El-Amin, M.F.: Magnetohydrodynamic free convection and mass transfer flow in micropolar fluid with constant suction. J. Magn. Mater. 234, 567–574 (2001)
Rahman, M.M., Aziz, A., Lawatia, M.A.: Heat transfer in micropolar fluid along an inclined permeable plate with variable fluid properties. Int. J. Thermal Sci. 49, 993–1002 (2010)
Beg, O.A., Bhargava, R., Rawat, S., Kahya, E.: Numerical study of micropolar convective heat and mass transfer in a non-Darcy porous regime with Soret and Dufour effects. Emir. J. Eng. Res. 13, 51–66 (2008)
Rawat, S., Bhargava, R.: Finite element study of natural convection heat and mass transfer in a micropolar fluid satu rated porous regime with Soret/Dufour effects. Int. J. Appl. Math. Mech. 5, 58–71 (2009)
Srinivasacharya, D., Ramreddy, Ch.: Soret and Dufour Effects on mixed convection in a non-Darcy micropolar fluid. Int. J. Nonlinear Sci. 11(2), 246–255 (2011)
Y\(\ddot{\text{ u }}\)r\(\ddot{\text{ u }}\)soy, M.: Unsteady boundary layer flow of power-law fluid on stretching sheet surface. Int. J. Eng. Sci. 44, 325–332 (2006)
Cebeci, T., Bradshaw, P.: Physical and Computational Aspects of Convective Heat Transfer. Springer, Berlin (1984)
Ahmadi, G.: Self-similar solution of imcompressible micropolar boundary layer flow over a semi-infinite plate. Int. J. Eng. Sci. 14, 639–646 (1976)
Rees, D.A.S., Bassom, A.P.: The Blasius boundary-layer flow of a micropolar fluid. Int. J. Eng. Sci. 34, 113–124 (1996)
Merkin, J.H.: A note on the similarity solutions for free convection on a vertical plate. J. Eng. Math. 19, 189–201 (1985)
Postelnicu, A.: Heat and mass transfer by natural convection at a stagnation point in a porous medium considering Soret and Dufour effects. Heat Mass Transf. 46, 831–840 (2010)
Benano-Melly, L.B., Caltagirone, J.P., Faissat, B., Montel, F., Costeseque, P.: Modelling Soret coefficient measurement experiments in porous media considering thermal and solutal convection. Int. J. Heat Mass Transf. 44, 1285–1297 (2001)
Kafoussias, N.G., Williams, E.W.: Thermal-diffusion and diffusion-thermo effects on mixed free-forced convection and mass transfer boundary layer flow with temperature dependent viscosity. Int. J. Eng. Sci. 33, 1369–1384 (1995)
Anghel, M., Takhar, H.S., Pop, I.: Dufour and Soret effects on free convection boundary-layer over a vertical surface embedded in a porous medium. Stud. Univ. Babes-Bolyai. Math. XLV, 11–22 (2000)
Cheng, C.Y., Wang, C.C.: Forced convection in micropolar fluid flow over a wavy surface. Num. Heat Transf. A 37, 271–287 (2000)