Skip to main content
SpringerLink
Log in

Combined convection in power-law fluids along a nonisothermal vertical plate in a porous medium

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

Abstract

The problem of combined convection from vertical surfaces in a porous medium saturated with a power-law type non-Newtonian fluid is investigated. The transformed conservation laws are solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The viscosity index ranged from 0.5 to 2.0.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

d :

particle diameter (m)

f :

dimensionless stream function

g :

acceleration due to gravity (m/s2)

h :

heat transfer coefficient (W/m2 K)

k :

thermal conductivity (W/mK)

K :

permeability coefficient of the porous medium (m1+n)

m :

consistency index for power-law fluid (pa sn)

n :

viscosity index

Nu:

Nusselt number

Pe:

Péclet number

qw :

wall heat flux (W/m2)

Ra* :

modified Rayleigh number

T :

temperature (K)

u, v :

velocity components in x and y directions (m/s)

x, y :

axial and normal coordinates (m)

α:

thermal diffusivity (m2/s)

β :

coefficient of thermal expansion (1/K)

η:

dimensionless distance

Θ:

dimensionless temperature

ϱ :

density (kg/m3)

ɛ :

porosity

χ :

combined convection nonsimilar parameter

ψ :

stream function

ω :

surface conditions

∞:

conditions far away from the surface

References

  1. Cheng, P. and Minkowycz, W. J.: 1977, Free convection about a vertical plate embedded in a porous medium with application to heat tranfer from a dike, J. Geophys. Res. 82, 2040–2044.

    Google Scholar 

  2. Gorla, R. S. R. and Zinalabedini, A. H.: 1987, Free convection from a vertical plate with nonuniform surface temperature and embedded in a porous medium, Trans. ASME, J. Energy Resourc. Technol. 109, 26–30.

    Google Scholar 

  3. Gorla, R. S. R. and Tornabene, R.: 1988, Free convection from a vertical plate with nonuniform surface heat flux and embedded in a porous medium, Transport in Porous Media 3, 95–106.

    Google Scholar 

  4. Minkowycz, W. J., Cheng, P. and Chang, C. H.: 1985, Mixed convection about a nonisothermal cylinder and sphere in a porous medium, Numerical Heat Transfer 8, 349–359.

    Google Scholar 

  5. Ranganathan, P. and Viskanta, R.: 1984, mixed convection boundary layer flow along a vertical surface in a porous medium, Numerical Heat Transfer 7, 305–317.

    Google Scholar 

  6. Nakayama, A. and Koyama, H.: 1987, A general similarity transformation for combined free and forced convection flows within a fluid-saturated porous medium, J. Heat Transfer 109, 1041–1045.

    Google Scholar 

  7. Nakayama, A. and Pop, I.: 1985, A unified similarity transformation for free, forced and mixed convection in Darcy and non-Darcy porous media, Int. J. Heat Mass Transfer 28, 683–697.

    Google Scholar 

  8. Hsieh, J. C., Chen, T. S. and Armaly, B. F.: 1993, Nonsimilarity solutions for mixed convection from vertical surfaces in porous media, Int. J. Heat Mass Transfer 36, 1485–1493.

    Google Scholar 

  9. Chen, H. T. and Chen, C. K.: 1987, Natural convection of non-Newtonian fluids about a horizontal surface in a porous medium, Trans. ASME, J. Energy Resour. Technol. 109, 119–123.

    Google Scholar 

  10. Mehta, K. N. and Rao, K. N.: 1994, Buoyancy-induced flow of non-Newtonian fluids in a porous medium past a vertical plate with nonuniform surface heat flux, Int. J. Eng. Sci. 32, 297–302.

    Google Scholar 

  11. Nakayama, A. and Koyama, H.: 1991, Buoyancy-induced flow of non-Newtonian fluids over a non-isothermal body of arbitrary shape in a fluid-saturated porous medium, Appl. Sci. Res. 48, 55–70.

    Google Scholar 

  12. Mehta, K. N. and Rao, K. N.: 1994, Buoyancy-induced flow of non-Newtonian fluids over a non-isothermal horizontal plate embedded in a porous medium, Int. J. Eng. Sci. 32, 521–525.

    Google Scholar 

  13. Christopher, R. H. and Middleman, S.: 1965: Power-law flow through a packed tube, I & EC Fundamentals 4, 422–426.

    Google Scholar 

  14. Dharmadhikari, R. V. and Kale, D. D.: 1985, Flow of non-Newtonian fluids through porous media, Chem. Eng. Sci. 40, 527–529.

    Google Scholar 

  15. Gorla, R. S. R., Lee, J. K., Nakamura, S. and Pop, I.: 1933, Effects on transverse magnetic field on mixed convection in wall plume of power law fluids, Int. J. Eng. Sci. 31, 1035–1045.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science, 560 012, Bangalore, India

    Mahesh Kumari

  2. Mechanical Engineering Department, Cleveland State University, 44115, Cleveland, OH, USA

    Rama Subba Reddy Gorla

Authors
  1. Mahesh Kumari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rama Subba Reddy Gorla
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kumari, M., Reddy Gorla, R.S. Combined convection in power-law fluids along a nonisothermal vertical plate in a porous medium. Transp Porous Med 24, 157–166 (1996). https://doi.org/10.1007/BF00139843

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00139843

Key words

Search

Navigation