Abstract
Conjugate natural convection in a two-dimensional triangular enclosure filled with a porous medium is examined in this article. It is assumed that the solid vertical wall is of finite conductivity and that the temperature of the inclined wall is lower than that of the vertical wall, while the horizontal wall is adiabatic. A finite difference method is used to solve the governing equations of convection and conduction for different parameters as Rayleigh number, width of the vertical solid wall, aspect ratio of the enclosure and thermal conductivity ratio between solid and porous media. It is found that heat transfer increases with increasing Rayleigh number and aspect ratio of the triangle, decreasing wall thickness and with the increase of the wall conductivity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- A :
-
Aspect ratio, H/L
- g :
-
Gravitational acceleration
- H :
-
Height of triangle or cavity
- hy′:
-
Minimum height of partition
- hy :
-
Dimensionless minimum height of the partition, hy′/H
- K :
-
Permeability of the porous medium
- k :
-
Thermal conductivity ratio, k s /k f
- L :
-
Length of triangle or cavity
- Nu :
-
Mean Nusselt number
- Nu y :
-
Local Nusselt number
- Ra :
-
Rayleigh number
- T :
-
Temperature
- u, v :
-
Velocity components in x, y directions
- x, y :
-
Cartesian coordinates
- X, Y :
-
Non-dimensional coordinates
- w :
-
Dimensionless weight of the solid wall, w′/L
- w′:
-
Weight of solid wall
- α m :
-
Thermal diffusivity of the porous medium
- β :
-
Thermal expansion coefficient
- θ :
-
Non-dimensional temperature
- υ :
-
Kinematic viscosity
- ψ :
-
Stream function
- Ψ:
-
Non-dimensional stream function
- c :
-
Cold
- f :
-
Fluid
- h :
-
Hot
- s :
-
Solid
References
Nield D.A., Bejan A.: Convection in porous media, 3rd edn. Springer, New York (2006)
Ingham D.B., Pop I. (eds.): Transport Phenomena in Porous Media, vol. III. Elsevier, Oxford (2005)
Baytas A.C., Liaqat A., Grosan T., Pop I.: Conjugate natural convection in a square porous cavity. Heat Mass Transf. 37, 467–473 (2001)
Mbaye M., Bilgen E., Vasseur P.: Natural-convection heat transfer in an inclined porous layer boarded by a finite-thickness wall. Int. J. Heat Fluid Flow 14, 284–291 (1993)
Saeid N.H.: Conjugate natural convection in a vertical porous layer sandwiched by finite thickness walls. Int. Comm. Heat Mass Transf. 34, 210–216 (2007)
Saeid N.H.: Conjugate natural convection in a porous enclosure: effect of conduction in one of the vertical walls. Int. J. Therm. Sci. 46, 531–539 (2007)
Du Z.G., Bilgen E.: Coupling of wall conduction with natural convection in a rectangular enclosure. Int. J. Heat Mass Transf. 35, 1969–1975 (1992)
Chang W.J., Lin H.C.: Wall heat conduction effect on natural convection in an enclosure filled with a non-Darcian porous medium. Numer. Heat Transf. Part A 25, 671–684 (1994)
Kimura S., Kiwata T., Okajima A., Pop I.: Conjugate natural convection in porous media. Adv. Water Resour. 20, 111–126 (1997)
Vaszi A.Z., Elliot L., Ingham D.B., Pop I.: Conjugate free convection from vertical fins embedded in a porous medium. Numer. Heat Transf. Part A 43, 743–770 (2003)
Liu J.Y., Minkowycz W.J., Cheng P.: Conjugate mixed convection heat transfer analysis of a plate fin embedded in a porous medium. Numer. Heat Transf. Part A 9, 575–590 (1986)
Varol Y., Oztop H.F., Yilmaz T.: Two-dimensional natural convection in a porous triangular enclosure with a square body. Int. Comm. Heat Mass Transf. 34, 238–247 (2007)
Varol Y., Oztop H.F., Varol A.: Natural convection in porous triangular enclosures with a solid adiabatic fin attached to the horizontal wall. Int. Comm. Heat Mass Transf. 34, 19–27 (2007)
Varol Y., Oztop H.F., Pop I.: Influence of inclination angle on buoyancy-driven convection in triangular enclosure filled with a fluid-saturated porous medium. Heat Mass Transf. 44, 617–624 (2008)
Varol Y., Oztop H.F., Varol A.: Free convection heat transfer and flow field in triangular enclosures filled with porous media. J. Porous Media 11, 103–115 (2008)
Bejan A.: On the boundary layer regime in a vertical enclosure filled with a porous medium. Lett. Heat Mass Transf. 6, 93–102 (1979)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Oztop, H.F., Varol, Y. & Pop, I. Effects of wall conduction on natural convection in a porous triangular enclosure. Acta Mech 200, 155–165 (2008). https://doi.org/10.1007/s00707-008-0029-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-008-0029-3