A Mixed Convection Boundary Layer Flow over a Vertical Wall in a Porous Medium, with Exponentially Varying Fluid Viscosity


This study investigates a mixed convection boundary layer flow over a vertical wall embedded in a highly porous medium. The fluid viscosity is assumed to decrease exponentially with temperature. The boundary layer equations are transformed into a non-similar form using an appropriate non-similar variable ξ and a pseudo-similar variable η. The non-similar equations are solved using an efficient local non-similarity method. The effect of viscosity variation parameter on the heat transfer, skin friction and the velocity and temperature distribution within the boundary layer is investigated. The viscosity variation parameter, the viscous dissipation parameter and non-simi-larity variable are shown to have a significant effect on velocity and thermal boundary layer and also on the skin friction coefficient and heat transfer at the wall.

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Mureithi, E. (2014) A Mixed Convection Boundary Layer Flow over a Vertical Wall in a Porous Medium, with Exponentially Varying Fluid Viscosity. Journal of Applied Mathematics and Physics, 2, 795-802. doi: 10.4236/jamp.2014.28087.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Nield, D.A. and Bejan, A. (2006) Convection in Porous Media. Springer and Business Media, New York.
[2] Pop, I.I. and Ingham, D.B., Eds. (2001) Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media. Elsevier Science & Technology Books, The Netherlands.
[3] Kaviany, M. (1995) Principles of Heat Transfer in Porous Media. Springer-Verlag, New York.
[4] Vafai, K., Ed. (2005) Handbook of Porous Media. Taylor & Francis, New York.
[5] Karabis, A., Kafoussias, N. and Xenos, M. (1995) Numerical Study of the Combined Forced-Free Convection Boundary Layer Flow through a Highly Permeable Porous Medium. Mechanics Research Communications, 22, 503-510.
[6] Chen, C.H. (1998) Non-Similar Solutions for Non-Darcy Mixed Convection from a Non-Isothermal Horizontal Surface in a Porous Medium. International Journal of Engineering Science, 36, 251-263.
[7] Vafai, K. and Tien, C.L. (1981) Boundary and Inertia Effect on Flow and Heat Transfer in Porous Media. International Journal of Heat and Mass Transfer, 24, 195-203.
[8] Hong, J.T., Tien, C.L. and Kaviany, M. (1985) Non-Darcy on Vertical Plate Natural Convection in Porous Media with High Porosities. International Journal of Heat and Mass Transfer, 28, 2149-2157.
[9] Hossain, M.A. and Munir, M.S. (2000) Mixed Convection Flow from a Vertical Flat Plate with Temperature Dependent Viscosity. International Journal of Thermal Sciences, 39, 173-183.
[10] Jayanthi, S. and Kumari, M. (2007) Effect of Variable Viscosity on Non-Darcy Free or Mixed Convection Flow on a Vertical Surface in an Non-Newtonian Fluid Saturated Porous Medium. Applied Mathematics and Computation, 186, 1643-1659.
[11] Sparrow, E.M., Quack, H. and Boerner, C.J. (1970) Local Non-Similarity Boundary Layer Solutions. AIAA, 8, 1936-1942.
[12] Sparrow, E.M. and Yu, H.S. (1971) Local Non-Similarity Thermal Boundary Layer Solutions. Journal of Heat Transfer, 93, 328-334.
[13] Gorla, R.S.R., Bakier, A.Y. and Byrd, L. (1996) Effects of Thermal Dissipation and Stratification on Combined Convection on a Vertical Surface Embedded in a Porous Medium. Transport in Porous Media, 25, 275-282.
[14] Mureithi, E.W. and Mason, D.P. (2010) Local Non-Similarity Solutions for a Forced-Free Boundary Layer Flow with Viscous Dissipation. Mathematical and Computational Applications, 15, 558-573.
[15] Bég, O.A., Bakier, A.Y., Prasad, V.R. and Ghosh, S.K. (2009) Non-Similar Laminar Steady Electrically Conducting Forced Convection Liquid Metal Boundary Layer Flow with Induced Magnetic Field Effects. International Journal of Thermal Sciences, 48, 1596-1606.

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