Chemically Reacting MHD Mixed Convection Variable Viscosity Blasius Flow Embedded in a Porous Medium

Abstract:

In this paper, the combined effects of magnetic field, buoyancy forces, nth order chemical reaction, heat source, viscous dissipation, Joule heating and variable viscosity on mixed convection Blasius flow of a conducting fluid over a convectively heated permeable plate embedded in a porous medium is investigated. The fluid properties are assumed to be constant except for the density variation with the temperature and reacting chemical species concentration. The nonlinear governing differential equations were obtained and solved numerically using the Runge-Kutta-Fehlberg method with shooting technique. The dimensionless velocity, temperature and concentration profiles are shown graphically. The effects of pertinent parameters on the skin friction, Nusselt number and Sherwood number are examined. It is found that skin friction decreases while Nusselt number and Sherwood number increase with a decrease in the fluid viscosity in the presence of magnetic field.

• Periodical: Defect and Diffusion Forum (Volume 374)
• Pages: 83-91
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.374.83
• Online since: April 2017
• Authors: Oluwole Daniel Makinde*, S.R. Mishra
• Keywords: Buoyancy Force, Chemical Reaction, MHD Blasius Flow, Permeable Plate, Porous Medium, Variable Viscosity

References

[1] H. Blasius, Grenzschichten in Flussigkeiten mit kleiner Reibung, Z. Math. Phys. 56(1908)1-37.

[2] H. Schlichting, K. Gersten Boundary layer theory, Heidelberg Springer Verlag, Berlin, (2000).

[3] O. D. Makinde: Effects of viscous dissipation and Newtonian heating on boundary layer flow of nanofluids over a flat plate. International Journal of Numerical Methods for Heat and Fluid flow, 23(8) (2013) 1291-1303.

DOI: 10.1108/hff-12-2011-0258

[4] R. C. Bataller, Radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition. Applied Mathematics and Computation, 206 (2008) 832–840.

DOI: 10.1016/j.amc.2008.10.001

[5] S. Das, R. N. Jana, O. D. Makinde, Magnetohydrodynamic mixed convective slip over an inclined porous plate with viscous dissipation and Joule heating. Alexandria Engineering Journal, 54(2) (2015) 251-261.

DOI: 10.1016/j.aej.2015.03.003

[6] A. Aziz, A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Commun. Nonlinear Sci. Numer. Simulat., 14 (2009) 1064-1068.

DOI: 10.1016/j.cnsns.2008.05.003

[7] W.A. Khan, R. Culham, O.D. Makinde, Hydromagnetic blasius flow of power‐law nanofluids over a convectively heated vertical plate. The Canadian Journal of Chemical Engineering, 93 (10) (2015) 1830-1837.

DOI: 10.1002/cjce.22280

[8] E.M. Hady, A.Y. Bakier, R.S.R. Gorla, Mixed convection boundary layer flow on a continuous flat plate with variable viscosity, Heat Mass Transfer 31 (1996) 169.

DOI: 10.1007/bf02333315

[9] M.A. Hossain, K. Khanafer, K. Vafai, The effect of radiation on free convection flow of fluid with variable viscosity from a porous vertical plate, Int. J. Therm. Sci. 40 (2001) 115–124.

DOI: 10.1016/s1290-0729(00)01200-x

[10] O.D. Makinde, W.A. Khan, J.R. Culham: MHD variable viscosity reacting flow over a convectively heated plate in a porous medium with thermophoresis and radiative heat transfer. International Journal of Heat and Mass Transfer, 93 (2016) 595–604.

DOI: 10.1016/j.ijheatmasstransfer.2015.10.050

[11] S. J. Kim, K. Vafai, Analysis of natural convection about a vertical plate embedded in porous medium, International journal of Heat and Mass Transfer, 32 (1989) 665-677.

DOI: 10.1016/0017-9310(89)90214-7

[12] O. D. Makinde: MHD mixed-convection interaction with thermal radiation and nth order chemical reaction past a vertical porous plate embedded in a porous medium. Chemical Engineering Communications, 198 (4) (2011) 590-608.

DOI: 10.1080/00986445.2010.500151

[13] F.S. Ibrahim, A.M. Elaiw, A.A. Bakr, Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi-infinite vertical permeable moving plate with heat source and suction, Commun. Nonlinear Sci. Numer. Simul. 13 (6) (2008).

DOI: 10.1016/j.cnsns.2006.09.007

[14] O. D. Makinde, A. Ogulu, The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field, Chem. Eng. Commun. 195 (2008) 1575–1584.

DOI: 10.1080/00986440802115549

[15] A. Apelblat, Mass transfer with a chemical reaction of the first order: analytical solutions, Chem. Eng. J. 19 (1980) 19–37.

DOI: 10.1016/0300-9467(80)85074-x

[16] A.Y. Ghaly, M.A. Seddeek, Chebyshev finite difference method for the effect of chemical reaction, heat and mass transfer on laminar flow along a semiinfinite horizontal plate with temperature dependent viscosity, Chaos Solitons Fractals, 19 (2004).

DOI: 10.1016/s0960-0779(03)00069-9

[17] O. D. Makinde, MHD mixed-convection interaction with thermal radiation and nth order chemical reaction past a vertical porous plate embedded in a porous medium. Chem. Eng. Comm. 198 (2011) 590–608.

DOI: 10.1080/00986445.2010.500151

[18] J.G. Michael, R.N. Philip, Numerical method for the solution of large systems of differential equations of the boundary-layer type, NASA TN D-7068, (1972).