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Unsteady natural convection heat and mass transfer in a saturated porous enclosure

Nichtstationäre natürliche Konvektion mit Wärme- und Stoffübergang in einem gesättigten porösen Medium

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Abstract

A detailed numerical study has been performed to investigate transient natural convection heat and mass transfer in a porous enclosure. Major dimensionless groups governing the present problem areRa,N,Le, φ andAr. Results are particular presented to illustrate the effects of the combined thermal and solutal buoyancy forces on the temporal evolution of local/average Nusselt and Sherwood numbers. The results show that with the increase in the Rayleigh number, the heat and mass transfer is enhanced as a result of greater buoyancy effect. Additionally, the increase in buoyancy ratioN results in an improvement in the heat and mass transfer rates and in the mean time causes a short time duration for the flow to approach the steady-state condition.

Zusammenfassung

Zur Ermittlung des nicht-stationären Wärmeund Stoffübergangs bei natürlicher Konvektion in einem porösen Medium wurde eine eingehende numerische Untersuchung aufgestellt. Die das Problem bestimmenden Hauptkennzahlen sind:Ra,N,Le, Φ undAr. Insbesondere werden Resultate mitgeteilt, die die Einflüsse der kombinierten thermischen und konzentrationsbedingten Auftriebskräfte auf die zeitliche Entwicklung der örtlichen und gemittelten Nusselt- und Sherwood-Zahlen erkennen lassen. Diese zeigen, daß bei ansteigender Rayleigh-Zahl der Wärme- und Stoffübergang infolge größeren Auftriebseffektes erhöht wird. Zusätzlich führt der Anstieg des AuftriebsverhältnissesN zu einer Verbesserung der Wärme- und Stoffübergangsverhältnisse und bewirkt gleichzeitig eine Verkürzung der Zeitspanne, welche der Strömungsvorgang zur Annäherung an den stationären Zustand benötigt.

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Abbreviations

Ar :

aspect ratio,H/L

c, C :

dimensional and dimensionless concentration

c 0,c 1 :

concentration of left and right walls, respectively

D :

equivalent mass diffusivity

g :

gravitational acceleration

H :

height of porous enclosure

K :

permeability of the saturated porous media

L :

width of porous enclosure

Le :

Lewis number, α/D

N :

buoyancy ratio,β*(c 1 −c 0)/[β(T 1 -T 0)]

Nu 0,Nu 1 :

local Nusselt numbers along the left and right walls, respectively

\(\overline {Nu_0 } ,\overline {Nu_1 } \) :

average Nusselt numbers along the left and right walls, respectively

Ra :

Darcy-Rayleigh number,K ϱ 0 g β(T 1 −T 0)L/(μα)

Sh 0,Sh 1 :

local Sherwood numbers along the left and right walls, respectively

\(\overline {Sh_0 } ,\overline {Sh_1 } \) :

average Sherwood numbers along the left and right walls, respectively

t :

time

T :

temperature

T 0,T 1 :

temperatures of left and right walls, respectively

u,v :

x- andy-velocity components

U,V :

dimensionlessx- andy-velocity components

x,y :

Cartesian coordinates, Fig. 1.

X,Y :

dimensionless Cartesian coordinates, Fig. 1

α :

thermal diffusivity of fluid-saturated porous medium

β :

volumetric coefficient of thermal expansion

β*:

volumetric coefficient of solutal expansion

μ :

viscosity

ϱ :

density

σ :

heat capacity ratio

τ :

dimensionless time

ϑ :

dimensionless temperature, (T −T 0)/(T 1 −T 0)

φ :

dimensionless porosity, ε/σ

ε :

porosity

ω :

stream function, Eq. (10)

0:

condition at left wall (i.e., atX = 0)

1:

condition at right wall (i.e., atX = 1)

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  1. Department of Mechanical Engineering, Chien Hsin College of Technology, Chung Li, Taiwan 32020 R.O.C.

    D. K. Lin

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Lin, D.K. Unsteady natural convection heat and mass transfer in a saturated porous enclosure. Wärme- und Stoffübertragung 28, 49–56 (1993). https://doi.org/10.1007/BF01579621

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  • DOI: https://doi.org/10.1007/BF01579621

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