Abstract
The effect of melting phenomenon on the steady mixed convection boundary layer flow about a vertical surface embedded in a fluid-saturated porous medium is numerically studied. The boundary layer partial differential equations are transformed into a set of nonlinear ordinary differential equations by using similarity transformation and then are solved using the shooting method for different values of the mixed convection and melting parameters. Results show that dual solutions exist for a certain range of these parameters. The results also indicate that the melting phenomenon reduces the heat transfer rate and expedites the boundary layer separation.
This is a preview of subscription content, log in via an institution to check access.
References
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 Fluids 22, 529–543 (2003)
Bakier, A.Y.: Aiding and opposing mixed convection flow in melting from a vertical flat plate embedded in a porous medium. Transport Porous Media 29, 127–139 (1997)
Cheng, P., Minkowycz, W.J.: Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. J. Geophys. Res. 82, 2040–2049 (1977)
Epstein, M., Cho, D.H.: Melting heat transfer in steady laminar flow over a flat plate. ASME J. Heat Transfer 76, 531–533 (1976)
Gorla, R.S.R., Mansous, M.A., Hassanien, I.A., Bakier, A.Y.: Mixed convection effect on melting from a vertical plate in a porous medium. Transport Porous Media 36, 245–254 (1999)
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. Transport Porous Media 77, 267–285 (2009)
Kazmierczak, M., Poulikakos, D., Pop, I.: Melting from a flat plate embedded in a porous medium in the presence of steady natural convection. Numer. Heat Transfer 10, 571–581 (1986)
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)
Nield, D.A., Bejan, A.: Convection in porous media (4th edition). Springer, New York (2013)
Roşca, N.C., Pop, I.: Mixed convection stagnation point flow past a vertical flat plate with a second order slip: heat flux case. Int. J. Heat Mass Transfer 65, 102–109 (2013)
Weidman, P.D., Kubitschek, D.G., Davis, A.M.J.: The effect of transpiration on self similar boundary layer flow over moving surfaces. Int. J. Eng. Sci. 44, 730–737 (2006)
Acknowledgments
The authors gratefully acknowledge the financial support received in the form of research grant: Fundamental Research Grant Scheme (203/PMATHS/6711234) from the Ministry of Higher Education, Malaysia. They also wish to express many thanks to the very competent Reviewers for the valuable comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ahmad, S., Pop, I. Melting Effect on Mixed Convection Boundary Layer Flow About a Vertical Surface Embedded in a Porous Medium: Opposing Flows Case. Transp Porous Med 102, 317–323 (2014). https://doi.org/10.1007/s11242-014-0291-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-014-0291-x