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Diffusion of a chemically reactive species of a power-law fluid past a stretching surface. (English) Zbl 1228.76153
Summary: A numerical solution for the steady magnetohydrodynamic (MHD) non-Newtonian power-law fluid flow over a continuously moving surface with species concentration and chemical reaction has been obtained. The viscous flow is driven solely by the linearly stretching sheet, and the reactive species emitted from this sheet undergoes an isothermal and homogeneous one-stage reaction as it diffuses into the surrounding fluid. Using a similarity transformation, the governing non-linear partial differential equations are transformed into coupled nonlinear ordinary differential equations. The governing equations of the mathematical model show that the flow and mass transfer characteristics depend on six parameters, namely, the power-law index, the magnetic parameter, the local Grashof number with respect to species diffusion, the modified Schmidt number, the reaction rate parameter, and the wall concentration parameter. Numerical solutions for these coupled equations are obtained by the Keller-Box method, and the solutions obtained are presented through graphs and tables. The numerical results obtained reveal that the magnetic field significantly increases the magnitude of the skin friction, but slightly reduces the mass transfer rate. However, the surface mass transfer strongly depends on the modified Schmidt number and the reaction rate parameter; it increases with increasing values of these parameters. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially shear-thinning phenomena. Shear thinning reduces the wall shear stress.
MSC:
76R50Diffusion (fluid mechanics)
65L12Finite difference methods for ODE (numerical methods)
76V05Interacting phases (fluid mechanics)
References:
[1]Chin, D. T.: Mass transfer to a continuous moving sheet electrode, J. electroanal. Chem. 122, 643-646 (1975)
[2]Griffith, R. M.: Velocity, temperature and concentration distributions during fiber spinning, Ind. eng. Chem. fundam. 3, 245-250 (1964)
[3]Sakiadis, B. C.: Boundary layer behavior on continuous solid surfaces: I. Boundary layer equations for two-dimensional and axisymmetric flow, Aiche J. 7, 26-28 (1961)
[4]Tsou, F.; Sparrow, E.; Goldstein, R. J.: Flow and heat transfer in the boundary layer on a continuous moving surface, Int. J. Heat mass transfer 10, 219-235 (1967)
[5]Crane, L. J.: Flow past a stretching plate, Z. angew. Math. phys. 21, 645-647 (1970)
[6]Gupta, P. S.; Gupta, A. S.: Heat and mass transfer on a stretching sheet with suction or blowing, Can. J. Chem. eng. 55, 744-746 (1977)
[7]Grubka, L. J.; Bobba, K. M.: Heat transfer characteristics of a continuous stretching surface with variable temperature, Trans. ASME, J. Heat transfer 107, 248-250 (1985)
[8]Cortell, R.: Flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/absorption and suction/blowing, Fluid dynam. Res. 37, 231-245 (2005) · Zbl 1153.76423 · doi:10.1016/j.fluiddyn.2005.05.001
[9]Cortell, R.: Internal heat generation and radiation effects on a certain free convection flow, Int. J. Nonlinear sci. 9, 468-479 (2010)
[10]Vujannovic, B.; Status, A. M.; Djukiv, D. J.: A variational solution of the Rayleigh problem for power law non-Newtonian conducting fluid, Ing. arch. 41, 381-386 (1972) · Zbl 0243.76003 · doi:10.1007/BF00533141
[11]Schowalter, W. R.: The application of boundary layer theory to power law pseudo plastic fluids: similar solutions, Aiche J. 6, 24-28 (1960)
[12]Acrivos, A.: A theoretical analysis of laminar natural convection heat transfer to non-Newtonian fluids, Aiche J. 6, 584-590 (1960)
[13]Lee, S. Y.; Ames, W. F.: Similar solutions for non-Newtonian fluids, Aiche J. 12, 700-708 (1966)
[14]Andersson, H. I.; Dandapat, B. S.: Flow of a power law fluid over a stretching sheet, Stab. appl. Anal. contin. Media 1, 339-347 (1991)
[15]Sahu, A. K.; Mathur, M. N.; Chaturani, P.; Bharatiya, S. S.: Momentum and heat transfer from a continuous moving surface to a power law fluid, Acta mech. 142, 119-131 (2000) · Zbl 0962.76006 · doi:10.1007/BF01190014
[16]Pavlov, K. B.: Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface, Magnin. gidrodinam. USSR 4, 146-147 (1974)
[17]Chakrabarti, A.; Gupta, A. S.: Hydromagnetic flow and heat transfer over a stretching sheet, Quart. appl. Math. 37, 73-78 (1979) · Zbl 0402.76012
[18]Cortell, R.: A note on magneto hydrodynamic flow of power law fluid over a stretching sheet, Appl. math. Comput. 168, 557-566 (2005) · Zbl 1081.76059 · doi:10.1016/j.amc.2004.09.046
[19]Cortell, R.: MHD flow and mass transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet with chemically reactive species, Chem. eng. Process. 46, 721-728 (2007)
[20]Prasad, K. V.; Vajravelu, K.: Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet, Int. J. Heat mass transfer 52, 4956-4965 (2009) · Zbl 1176.80038 · doi:10.1016/j.ijheatmasstransfer.2009.05.022
[21]Abel, M. Subhas; Datti, P. S.; Mahesha, N.: Flow and heat transfer in a power law fluid over a stretching sheet with variable thermal conductivity and non-uniform heat source, Int. J. Heat mass transfer 52, 2902-2913 (2009) · Zbl 1167.80304 · doi:10.1016/j.ijheatmasstransfer.2008.08.042
[22]Fan, J. R.; Shi, J. M.; Xu, X. Z.: Similarity solution of mixed convection with diffusion and chemical reaction over a horizontal moving plate, Acta mech. 126, 59-69 (1988) · Zbl 0902.76087 · doi:10.1007/BF01172799
[23]Fairbanks, D. F.; Wike, C. R.: Diffusion and chemical reaction in an isothermal laminar flow along a soluble flat plate, Ind. eng. Chem. res. 42, 471-475 (1950)
[24]Chambre, P. L.; Young, J. D.: On the diffusion of a chemically reactive species in a laminar boundary layer flow, Phys. fluids 1, 48-54 (1958) · Zbl 0084.41802 · doi:10.1063/1.1724336
[25]Dural, N.; Hines, A. L.: A comparison of approximate and exact solutions for homogeneous irreversible chemical reaction in the laminar boundary layer, Chem. eng. Commun. 96, 1-14 (1990)
[26]Andersson, H. I.; Hansen, O. R.; Holmedal, B.: Diffusion of chemically reactive species from a stretching sheet, Int. J. Heat mass transfer 37, 659-664 (1994) · Zbl 0900.76609 · doi:10.1016/0017-9310(94)90137-6
[27]Devi, S. P. A.; Kandaswamy, R.: Effects of chemical reaction heat and mass transfer on MHD flow past a semi infinite plate, Z. angew. Math. phys. 80, 697-701 (2000) · Zbl 0986.76097 · doi:10.1002/1521-4001(200010)80:10<697::AID-ZAMM697>3.0.CO;2-F
[28]Prasad, K. V.; Abel, M. Subhas; Datti, P. S.: Diffusion of chemically reactive species of a non-Newtonian fluid immersed in a porous medium over a stretching sheet, Internat. J. Non-linear mech. 38, 651-657 (2003)
[29]Cortell, R.: Toward an understanding of the motion and mass transfer with chemically reactive species for two classes of viscoelastic fluid over a porous stretching sheet, Chem. eng. Process. 46, 982-989 (2007)
[30]Denier, J. P.; Dabrowski, P. P.: On the boundary layer equations for power law fluids, Proc. R. Soc. lond. Ser. A 460, 3143-3158 (2004) · Zbl 1074.76002 · doi:10.1098/rspa.2004.1349
[31]Andersson, H. I.; Bech, K. H.; Dandapat, B. S.: Magnetohydrodynamic flow of a power law fluid over a stretching sheet, Internat. J. Non-linear mech. 27, 929-936 (1992) · Zbl 0775.76216 · doi:10.1016/0020-7462(92)90045-9
[32]Cebeci, T.; Bradshaw, P.: Physical and computational aspects of convective heat transfer, (1984)
[33]Keller, H. B.: Numerical methods for two-point boundary value problems, (1992)