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Combined heat and mass transfer by laminar natural convection from a vertical plate

Gleichzeitiger Wärme-und Stoffübergang bei laminarer natürlicher Konvektion an einer senkrechten Platte

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Abstract

Simultaneous heat and mass transfer in buoyancy-induced laminar boundary-layer flow along a vertical plate is studied for any ratio of the solutal buoyancy force to the thermal buoyancy force by using a new similarity transformation. The effects of the buoyancy ratio and Lewis number on the rates of heat and mass transfer are presented explicitly for most practical gaseous solutions (Pr=0.7, 0.21≤Sc≤2.1) and aqueous solutions (Pr=7, 140≤Sc≤1400). Very accurate correlations of the mass transfer and heat transfer rates are developed for the cases of single and combined buoyancy forces.

Zusammenfassung

Unter Verwendung einer neuen Ähnlichkeitstransformation wird der gleichzeitige Wärme- und Stoffübergang in einer auftriebsinduzierten laminaren Grenzschichtströmung entlang einer senkrechten Platte bei beliebigem Verhältnis der Dichteänderungen infolge von Konvektions-oder Temperaturunterschieden untersucht. Der Einfluß dieses Auftriebsverhältnisses und der Lewis-Zahl auf den Wärme- und Stoffübergang ist für die meisten gasförmigen Mischungen (Pr=0,7, 0,21≤Sc≤2,1) und wäßrigen Lösungen (Pr=7, 140≤Sc≤1400) dargestellt. Sehr genaue Korrelationsbeziehungen zur Berechnung des Wärme- und Stoffübergangs infolge einfach und in Kombination wirkender Auftriebskräfte werden angegeben.

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Abbreviations

C :

species concentration, mol/m3

D :

molecular diffusivity, m2/s

f :

dimensionless stream function, ψ/αλ

g :

gravitational acceleration, m/s2

h :

local heat transfer coefficient, J/s m2K

h m :

local mass transfer coefficient, mol/m2s

J :

molecular flux, mol/m2s

k :

thermal conductivity of fluid, J/s m K

Le :

Lewis number,D/α

Nu :

local Nusselt number,hx/k

Pr :

Prandtl number,v/α

Ra C :

local concentration Rayleigh number,gγ(C 0−C ∞)x 3/Dv

Ra T :

local thermal Rayleigh number,gβ(T 0−T ∞)x 3/αv

Sc :

Schmidt number,v/D

Sh :

Sherwood number,h m x/D

T :

fluid temperature, K

u :

velocity component inx direction, m/s

v :

velocity component iny direction, m/s

x :

coordinate parallel to the plate, m

y :

coordinate normal to the plate, m

α:

thermal diffusivity, m2/s

β:

thermal expansion coefficient, K1

γ:

concentration expansion coefficient, m3/mol

ζ:

Ra 1/4 C /Ra 1/4 T

η:

dimensionless coordinate, (y/x)λ

θ:

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

λ:

Ra 1/4 T +Ra 1/4 C

⋎:

kinematic viscosity, m2/s

ξ:

parameter of relative driving force, (1+Ra 1/4 T /Ra 1/4 C )−1

ϱ:

density, kg/m3

ϕ:

dimensionless concentration, (C−C ∞)/(C 0−C ∞)

ψ:

stream function

C :

uniform surface concentration

T :

uniform surface temperature

0:

at the plate surface

∞:

far from the plate surface

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Authors and Affiliations

  1. Department of Chemical Engineering, National Central University, 320, Chungli, Taiwan, P.R. China

    H. -T. Lin & C. -M. Wu

Authors
  1. H. -T. Lin
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  2. C. -M. Wu
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This work was supported by a grant NSC 84-2214-E-008-005 from the National Science Council of Republic of China.

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Lin, H.T., Wu, C.M. Combined heat and mass transfer by laminar natural convection from a vertical plate. Heat and Mass Transfer 30, 369–376 (1995). https://doi.org/10.1007/BF01647440

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  • DOI: https://doi.org/10.1007/BF01647440

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