Abstract
The unsteady mixed convection boundary-layer flow near the two-dimensional stagnation point on a vertical permeable surface embedded in a fluid-saturated porous medium with suction and a temperature slip effect is studied numerically. Similarity equations are obtained through the application of a similarity transformation technique. The shooting method is used to solve these similarity equations for different values of the mixed convection, wall mass suction, the unsteadiness and the slip parameters. Results show that multiple solutions exist for certain ranges of these parameters. Some limiting forms are then discussed, namely strong suction, the free convection limit, the situation when there is a large temperature slip and when the time dependence dominates.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ali M.E., Magyari E.: Unsteady fluid and heat flow induced by a submerged stretching surface while its steady motion is slowed down gradually. Int. J. Heat Mass Transf. 50, 188–195 (2007)
Aly E.H., Elliott L., Ingham D.B.: Mixed convection boundary-layer flow over a vertical surface embedded in a porous medium. Eur. J. Mech. B 22, 529–543 (2003)
Andersson H.I., Aarseth J.B., Dandapat B.S.: Heat transfer in a liquid film on an unsteady stretching surface. Int. J. Heat Mass Transf. 43, 69–74 (2000)
Birkhoff G.: Hydrodynamics, a Study in Fact and Similitude, Revised edn. Princeton University Press, Princeton (1960)
Cheng P.: Similarity solutions for mixed convection from horizontal impermeable surfaces in saturated porous media. Int. J. Heat Mass Transf. 20, 893–898 (1977)
Fang T.-G., Zhang J., Yao S.-S.: Viscous flow over an unsteady shrinking sheet with mass transfer. Chin. Phys. Lett. 26, 014703-1–014703-4 (2009)
Harris S.D., Ingham D.B., Pop I.: Transient free convection on a vertical plate subjected to a change in surface heat flux in porous media. Fluid Dynamics Res. 18, 313–324 (1996)
Harris S.D., Ingham D.B., Pop I.: Thermal capacity effect on transient free convection adjacent to a vertical surface in a porous medium. Transp. Porous Media 46, 1–18 (2002)
Harris S.D., Ingham D.B., Pop I.: Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transp. Porous Media 77, 267–285 (2009)
Ingham, D.B., Pop, I. (eds): Transport Phenomena in Porous Media III. Elsevier, Oxford (2005)
Merkin J.H.: Mixed convection boundary layer flow on a vertical surface in a saturated porous medium. J. Eng. Math. 14, 301–313 (1980)
Merkin J.H.: On dual solutions occurring in mixed convection in a porous medium. J. Eng. Math. 20, 171–179 (1985)
Merrill K., Beauchesne M., Previte J., Paullet J., Weidman P.: Final steady flow near a stagnation point on a vertical surface in a porous medium. Int. J. Heat Mass Transf. 49, 4681–4686 (2006)
Mukhopadhyay S., Andersson H.: Effects of slip and heat transfer analysis of flow over an unsteady stretching surface. Heat Mass Transf. 45, 1447–1452 (2009)
Nazar R., Amin N., Pop I.: Unsteady mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium. Int. J. Heat Mass Transfer 47, 2681–2688 (2004)
Nield D.A., Bejan A.: Convection in Porous Media, 3rd edn. Springer, New York (2006)
Pop I., Ingham D.B.: Convective Heat Transfer: Mathematical and Computational Modeling of Viscous Fluids and Porous Media. Pergamon Press, Oxford (2001)
Slater L.J.: Confluent hypergeometric functions. Cambridge University Press, Cambridge (1960)
Tie-Gang F., Ji Z., Shan-Shan Y.: Viscous flow over an unsteady shrinking sheet with mass transfer. Chin. Phys. Let. 26, 014703-1–014703-4 (2009)
Vadasz, P. (eds): Emerging Topics in Heat and Mass Transfer in Porous Media. Springer, Berlin (2008)
Vafai, K. (eds): Handbook of Porous Media, 2nd edn. Taylor & Francis, New York (2005)
Vafai K.: Porous Media: Applications in Biological Systems and Biotechnology. CRC Press, Tokyo (2010)
Wang C.Y.: Liquid film on an unsteady stretching surface. Q. Appl. Math. 48, 601–610 (1990)
Yang K.T.: Unsteady laminar boundary layers in an incompressible stagnation flow, Trans. ASME J. Appl. Mech. 25, 421–427 (1958)
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Rohni, A.M., Ahmad, S., Pop, I. et al. Unsteady mixed convection boundary-layer flow with suction and temperature slip effects near the stagnation point on a vertical permeable surface embedded in a porous medium. Transp Porous Med 92, 1–14 (2012). https://doi.org/10.1007/s11242-011-9883-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-011-9883-x