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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
Article

Abstract

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.

Keywords

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.

Nomenclature

Cp

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

g

acceleration due to gravity

K

permeability of the porous medium

L

length of thermal line source

Pex

local Peclet number

Q

strength of thermal line source

Rax,Rex

local Rayleigh and Reynolds numbers, respectively

T, T

temperatures in the boundary layer and in the freestream, respectively

T*

equivalent source temperature

u, ν

velocity components in thex andy directions, respectively

Ut8

free-stream velocity

x, y

distances along and perpendicular to the surface

α

equivalent thermal diffusivity

β

coefficient of thermal expansion

η,η1

pseudo-similarity variables

ξ

buoyancy parameter

ξ1

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

ψ

dimensional stream function

Superscript

partial derivative with respect to eitherη orη1

Subscripts

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

Zusammenfassung

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.

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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

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