Skip to main content
Log in

Mixed Convection on a Horizontal Surface Embedded in a Porous Medium: the Structure of a Singularity

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

The mixed convection boundary-layer flow on a horizontal impermeable surface embedded in a saturated porous medium and driven by a local heat source is considered. Similarity solutions are obtained for specific outer flow variations and these are shown to have a solution only for parameter values greater than some critical value. When this is not the case the solution develops a singularity at a finite distance from the leading edge. The nature of this singularity is also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bejan, A., Convective heat transfer in porous media, In: S. Kakac, R. K. Shah and W. Aung (eds), Handbook of Single-Phase Convective Heat Transfer, Chapter 16, Wiley, New York, 1987.

    Google Scholar 

  2. Nield, D. A. and Bejan, A.: Convection in Porous Media., Springer, New York, 1992.

    Google Scholar 

  3. Nakayama, A., PC-Aided Numerical Heat Transfer and Convective Flow, CRC Press, Tokyo, 1995.

    Google Scholar 

  4. Kimura, S., Kiwata, T., Okajima, A. and Pop, I.: Conjugate natural convection in porous media, In: Adv. Water Res., special issue: Adv. Heat Transfer in Porous Media 1997 (in press).

  5. Cheng, P. and Chang, I. D., Buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces, Int. J. Heat Mass Transfer 19(1976), 1267-1272

    Google Scholar 

  6. Merkin, J. H. and Zhang, G., On the similarity solutions for free convection in a saturated porous medium adjacent to impermeable horizontal surfaces, Warme-und Staffubertr. 25(1990), 179- 184.

    Google Scholar 

  7. Higuera, F. J. and Weidman, P. D., Natural convection beneath a downward facing heated plate in a porous medium, Eur. J. Mech. B/Fluids 14(1995), 29-40.

    Google Scholar 

  8. Chaudhary, M. A., Merkin, J. H. and Pop, I., Natural convection from a horizontal permeable surface in a porous medium-numerical and asymptotic solutions, Transport in Porous Media 22(1996), 327-3440.

    Google Scholar 

  9. Cheng, P., Similarity solutions for mixed convection from horizontal impermeable surfaces in saturated porous media, Int. J. Heat Mass Transfer 20(1977), 893-898.

    Google Scholar 

  10. Prasad, V., Lai, F.-C. and Kulacki, F. A., Mixed convection in horizontal porous layers heated from below, J. Heat Transfer 110(1988), 395-402.

    Google Scholar 

  11. Lai, F.-C. and Kulacki, F. A., The influence of surface mass flux on mixed convection from horizontal surfaces in a porous medium-variable surface heat flux, Int. J. Heat Mass Transfer 33(1990), 576-579.

    Google Scholar 

  12. Aldos, J. K., Chen, T. S. and Armaly, B. F., Non-similarity solutions for mixed convection from horizontal surfaces in a porous medium-variable surface heat flux, Int. J. Heat Mass Transfer 36(1993), 463-470.

    Google Scholar 

  13. Aldos, T. K., Chen, T. S. and Armaly, B. F., Non-similarity solutions for mixed convection from horizontal surfaces in a porous medium-variable wall temperature, Int. J. Heat Mass Transfer 36(1993), 471-477.

    Google Scholar 

  14. Daniels, P. G., A singularity in thermal boundary-layer flow on a horizontal surface, J. Fluid Mech. 242(1992), 419-440.

    Google Scholar 

  15. Merkin, J. H., Free convection above a uniformly heated horizontal circular disk, Int. J. Heat Mass Transfer 28(1985), 1157-1163.

    Google Scholar 

  16. Merkin, J. H., Free convection above a heated horizontal circular disk, J. Appl. Math. Phys. (ZAMP) 34(1983), 596-608.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Merkin, J.H., Pop, I. Mixed Convection on a Horizontal Surface Embedded in a Porous Medium: the Structure of a Singularity. Transport in Porous Media 29, 355–364 (1997). https://doi.org/10.1023/A:1006556111769

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1006556111769

Navigation