Heat and Mass Transfer

, Volume 30, Issue 6, pp 369–376

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

  • H. -T. Lin
  • C. -M. Wu
Originals

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.

Nomenclature

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

hm

local mass transfer coefficient, mol/m2s

J

molecular flux, mol/m2s

k

thermal conductivity of fluid, J/s m K

Le

Lewis number,D

Nu

local Nusselt number,hx/k

Pr

Prandtl number,v

RaC

local concentration Rayleigh number,gγ(C0C)x3/Dv

RaT

local thermal Rayleigh number,gβ(T0T)x3v

Sc

Schmidt number,v/D

Sh

Sherwood number,hmx/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

Greek symbols

α

thermal diffusivity, m2/s

β

thermal expansion coefficient, K1

γ

concentration expansion coefficient, m3/mol

ζ

RaC1/4/RaT1/4

η

dimensionless coordinate, (y/x

θ

dimensionless temperature, (T−T)/(T0T)

λ

RaT1/4+RaC1/4

kinematic viscosity, m2/s

ξ

parameter of relative driving force, (1+RaT1/4/RaC1/4)−1

ϱ

density, kg/m3

ϕ

dimensionless concentration, (C−C)/(C0C)

ψ

stream function

Subscripts

C

uniform surface concentration

T

uniform surface temperature

0

at the plate surface

far from the plate surface

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

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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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • H. -T. Lin
    • 1
  • C. -M. Wu
    • 1
  1. 1.Department of Chemical EngineeringNational Central UniversityChungliTaiwan, P.R. China

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