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Theoretical solution of simultaneous heat and mass transfer by free convection about a vertical flat plate

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Abstract

In this paper we present a numerical solution for stationary simultaneous heat and mass transfer in the laminar boundary layer on a vertical flat plate. The theory is based on a simple physical model that treats the two buoyancy effects (originating from temperature and concentration differences) as mutually independant and additional forces.

Results are given for the case of Pr=0.71, Sc=0.63 and equally directed body forces. Our experimental data for the same conditions show close agreement and these seems to be no need for a more complicated theory.

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Abbreviations

a :

thermal diffusivity

A :

empirical constant

B :

total pressure

c :

transformation constant

C :

mass fraction, = ratio of partial density to total density

D :

mass diffusivity

f :

dimensionless stream function (7)

g :

acceleration of gravity

Gr x , Gr L :

local and mean Grashof number (12)

L :

plate height

M 1, M 2 :

molecular weights

n 1, n 2 :

molar densities

Nu x , Nu L :

local and mean Nusselt number (11)

p :

vapour pressure

Pr :

Prandtl number = ν/a

Sc :

Schmidt number = ν/D

Sh x , Sh L :

local and mean Sherwood number (11)

T :

fluid temperature

u :

vertical velocity component

v :

horizontal velocity component

x :

vertical coordinate

y :

horizontal coordinate

β 1, β 2 :

coefficients defined in (5)

δ :

parameter defined in (10)

ε 1, ε 2 :

coefficients defined in (5)

η :

similarity variable (7)

ϑ :

dimensionless temperature (4)

ω :

dimensionless mass fraction (4)

Θ :

temperature difference T–T ∞

Θ 0 :

temperature difference T 0–T ∞

ν :

kinematic viscosity

Π 0 :

vapour pressure difference P 0–P ∞

ρ :

total density

ψ :

stream function (6)

Ω :

mass fraction difference C–C ∞

Ω 0 :

mass fraction difference C 0–C ∞

1:

concerning air

2:

concerning vapour

0:

conditions at surface

∞:

conditions at infinite distance

References

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  5. Bottemanne, F. A., Thesis, Delft (1970). Also appeared as Meded. Landbouwhoge-school — Wageningen 70-11 (1970).

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Authors and Affiliations

  1. Lab. of Physics and Meteorology, Wageningen, The Netherlands

    F. A. Bottemanne

Authors
  1. F. A. Bottemanne
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Bottemanne, F.A. Theoretical solution of simultaneous heat and mass transfer by free convection about a vertical flat plate. Appl. Sci. Res. 25, 137–149 (1972). https://doi.org/10.1007/BF00382290

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  • DOI: https://doi.org/10.1007/BF00382290

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