Wärme - und Stoffübertragung

, Volume 22, Issue 3–4, pp 173–178 | Cite as

Darcian mixed convection plumes along vertical adiabatic surfaces in a saturated porous medium

  • M. Kumari
  • I. Pop
  • G. Nath


The mixed convection flow due to a line thermal source embedded at the leading edge of an adiabatic vertical plane surface immersed in a saturated porous medium has been studied. Both weakly and strongly buoyant plume regimes have been considered. The cases of buoyancy assisting and buoyancy opposing flow conditions have been incorporated in the analysis. The results are presented for the entire range of buoyancy parameter from the pure forced convection (ξ=0) to the pure free convection (ξ → ∞@#@) regimes. For buoyancy-assisting flow, the wall temperature and the velocity at the wall increase as the plume strength increases. However, they all decrease as the free-stream velocity increases. For buoyancyopposing flow, the temperature at the wall increases as the strength of the plume increases but velocity at the wall decreases.


Free Convection Forced Convection Mixed Convection Saturated Porous Medium Buoyant Plume 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



specific heat at a constant pressure

f, F

dimensionless stream functions for the case of weakly and strongly buoyant plume

F′, H

dimensionless velocity and temperature, respectively, for the case of strongly buoyant plume


acceleration due to gravity


permeability of the porous medium


length of thermal line source


local Peclet number


strength of thermal line source


local Rayleigh and Reynolds numbers, respectively

T, T

temperatures in the boundary layer and in the freestream, respectively


equivalent source temperature

u, ν

velocity components in thex andy directions, respectively


free-stream velocity

x, y

distances along and perpendicular to the surface


equivalent thermal diffusivity


coefficient of thermal expansion


pseudo-similarity variables


buoyancy parameter


forced convection parameter

μ, v

coefficient of viscosity and kinematic viscosity, respectively

ϱ, ϱ

densities in the boundary layer and in the free stream, respectively


dimensional stream function


partial derivative with respect to eitherη orη1


w, ∞

conditions at the wall and in the free stream, respectively

ξ, ξ1

partial derivative with respect to ξ and ξ1, respectively

Gemischte Darcy-Konvektion längs vertikaler adiabater Oberflächen in einem gesättigten porösen Medium


Es wurde die Mischkonvektion, hervorgerufen durch eine linienförmige Wärmequelle, studiert, die in einer Ecke einer adiabaten vertikalen ebenen Fläche eingetaucht ist und die wiederum in einem gesättigten porösen Medium eingebettet war. Es wurden sowohl schwache als auch starke Auftriebsströmungen betrachtet. Beide Felder, nämlich der auftriebsunterstützten und der auftriebsbehinderten Strömung, wurden in die Analyse eingearbeitet. Es werden Ergebnisse für den gesamten Bereich der Auftriebsströmung von reiner Zwangskonvektion bis zu reiner freier Konvektion dargestellt. Für auftriebsunterstützte Strömung erhöht sich die Wandtemperatur und die Geschwindigkeit der Wand, die Stärke der Auftriebswolke. Im Freistrombereich zeigt sich gegenteiliges Verhalten. Für auftriebsbehinderte Strömung steigt die Temperatur der Wand mit zunehmender Stärke der Auftriebswolke, jedoch die Geschwindigkeit an der Wand nimmt ab.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gebhart, B.: Natural convection flows and stability. Adv. in Heat Transfer 9 (1973) 297–301Google Scholar
  2. 2.
    Jaluria, Y.; Gebhart, B.: Buoyancy-induced flow arising from a line thermal source on an adiabatic vertical surface. Int. J. Heat Mass Transfer 20 (1977) 153–157Google Scholar
  3. 3.
    Liburdy, J. A.; Faeth, G. M.: Theory of a steady laminar thermal plume along a vertical adiabatic wall. Lett. Heat Mass Transfer 2 (1975) 407–418Google Scholar
  4. 4.
    Afzal, N.: Convective wall plume: Higher order analysis. Int. J. Heat Mass Transfer 23 (1980) 505–513Google Scholar
  5. 5.
    Sparrow, E. M.; Patankar, S. V.; Abdul-Wahed, R. M.: Development of wall and free plumes above a heated vertical plate. Trans. ASME, J. Heat Transfer 100 (1978) 184–190Google Scholar
  6. 6.
    Carey, V. P.; Mallendorf, J. C.: The temperature field above a concentrated heat source on a vertical adiabatic surface. Int. J. Heat Mass Transfer 20 (1977) 1059–1067Google Scholar
  7. 7.
    Jaluria, Y.: Mixed convection in wall plumes. ASME paper No. 81-HT-37, ASME/AIChE National Heat TransferGoogle Scholar
  8. 8.
    Afzal, N.: Mixed convection in a two-dimensional buoyant plume. J. Fluid Mech. 105 (1983) 147–168Google Scholar
  9. 9.
    Rao, K. V.; Armaly, B. F.; Chen, T. S.: Analysis of laminar mixed convective plumes along vertical adiabatic surface. Trans. ASME, J. Heat Transfer 106 (1984) 552–557Google Scholar
  10. 10.
    Cheng, P.: Heat transfer in geothermal systems. Adv. in Heat Transfer 9 (1978) 1–105Google Scholar
  11. 11.
    Ingham, D. B.; Brown, S. N.: Flow past a suddenly heated vertical plate in a porous medium. Proc. Roy. Soc. A 403 (1986) 51–80Google Scholar
  12. 12.
    Keller, H. B.: A new difference scheme for parabolic problems. In: Numerical solutions of partial differential equations. Ed. J. Bramble, Vol. 2, New York: Academic Press 1971Google Scholar
  13. 13.
    Keller, H. B.; Cebeci, T.: Accurate numerical methods for boundary layers. 1. Two-dimensional laminar flows. Proc. of the Second Intern. Conf. on Numer. Meth. in Fluid Dynamics, Lecture Notes in Physics, Vol. 8. Berlin, Heidelberg, New York: Springer 1971Google Scholar
  14. 14.
    Cheng, P.: Combined free and forced convection flow about inclined surfaces in porous media. Int. J. Heat Mass Transfer 20 (1977) 807–814Google Scholar
  15. 15.
    Merkin, J. H.: Mixed convection boundary layer flow on a vertical surfaces in a saturated porous medium. J. Engng. Math. 14 (1980) 301–313Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • M. Kumari
    • 1
  • I. Pop
    • 1
    • 2
  • G. Nath
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Faculty of MathematicsUniversity of ClujClujRomania

Personalised recommendations