Skip to main content
Log in

Natural convection from a horizontal permeable surface in a porous medium - numerical and asymptotic solutions

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

Abstract

The equations which govern the similarity solution for free convection boundary-layer flow above a permeable, horizontal surface in a fluid-saturated porous medium are considered. These are seen to depend on the dimensionless parameters γ and m measuring mass transport rate and the wall temperature variation, respectively. Numerical solutions are presented for a wide range of values of γ and m. Asymptotic solutions are obtained for ¦γ¦ large (for both fluid injection, γ > 0, and fluid withdrawal, γ < 0) and for m large. These are compared with the numerical solutions.

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

    Google Scholar 

  2. Ene, H. I. and Polisevski, D.: Thermal Flow in Porous Media, Reidel, Dordrecht, 1987.

    Google Scholar 

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

    Google Scholar 

  4. Chang, I. D. and Cheng, P.: Matched asymptotic expansions for free convection about an impermeabl horizontal surface in a porous medium, Int. J. Heat Mass Transfer 26 (1983), 163–174.

    Google Scholar 

  5. Pop, I. and Cheng, P.: The growth of a thermal layer in a porous medium adjacent to a suddenly heated semi-infinite horizontal surface, Int. J. Heat Mass Transfer 26 (1983), 1574–1576.

    Google Scholar 

  6. Ingham, D. B., Merkin, J. H. and Pop, I.: Flow past a suddenly cooled horizontal flat surface in a saturated porous medium, Acta Mechanica 56 (1985), 205–217.

    Google Scholar 

  7. Nakayama, A. and Koyama, H.: Integral treatment of buoyancy-induced flows in a porous medium adjacent to horizontal surfaces with variable wall temperature, Int. J. Heat Fluid Flow 8 (1987), 240–242.

    Google Scholar 

  8. Merkin, J. H. and Zhang, G.: On the similarity solutions for free convection in a saturated porous medium adjacent to impermeable horizontal surfaces, Wärme und Stoffübertr 25 (1990), 179–184.

    Google Scholar 

  9. Mehta, K. H. and Rao, K. N.: Buoyancy induced flow of non-Newtonian fluids over a nonisothermal horizontal plate embedded in a porous medium, Int. J. Engng. Sci. 32 (1994), 521–525.

    Google Scholar 

  10. Lai, F. C. and Kulacki, F. A.: Non-Darcy convection from horizontal impermeable surfaces in saturated porous media, Int. J. Heat Mass Transfer 30 (1987), 2189–2192.

    Google Scholar 

  11. Kumari, M., Pop, I. and Nath, G.: Nonsimilar boundary layer for non-Darcy mixed convection flow about a horizontal surface in a saturated porous medium, Int. J. Engng. Sci. 28 (1990), 253–263.

    Google Scholar 

  12. Chaudhary, M. A., Merkin, J. H., and Pop, I.: Similarity solutions in free convection boundarylayer flows adjacent to vertical permeable surfaces in porous media. I Prescribed surface temperature, European J. Mech., B. Fluids 14 (1995), 217–237.

    Google Scholar 

  13. Merkin, J. H.: Free convection boundary layers in a saturated porous medium with lateral mass, Int. J. Heat Mass Transfer 21 (1978), 1499–1504.

    Google Scholar 

  14. Merkin, J. H.: Natural convection boundary-layer flow on a vertical surface with Newtonian heating, Int. J. Heat Fluid Flow. 15 (1994), 392–398.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chaudhary, M.A., Merkin, J.H. & Pop, I. Natural convection from a horizontal permeable surface in a porous medium - numerical and asymptotic solutions. Transp Porous Med 22, 327–344 (1996). https://doi.org/10.1007/BF00161630

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00161630

Key words

Navigation