Active Thermal Cooling Technologies - Low Energy Cooling for Sustainable Buildings - page 187

(kgm − 3 ) and the angle ϕ of the heat exchanging walls to the horizontal (in this case,
90 ◦ ):

3 m S µ S
ρ S g sin ϕ

1
3

δ S = (5.18)

The mass transfer of water vapour from the liquid water film to the adjacent air flow
depends on the mass transfer coefficient and on the wetting of the surface (Kast, 1988).
The driving force in the transport process is the difference in vapour pressure between
the air and the water film interface. The mass transfer (kg s − 1 ) in flow direction y can
be calculated from the following equation:

A β A M
R m T

p H 2 O T A,in

p S,H 2 O T W,in

m W = − (5.19)

The mass transfer coefficient β A (m s − 1 ) depends on the flow pattern in the heat
exchanger channels and can be calculated from the heat transfer coefficient h c,A , using
the thermal diffusivity a a (m 2 s − 1 ), the diffusion conduct coefficient δ a (m 2 s − 1 ) and
the parameter n = 1 / 3 for laminar air flow:

a a
δ a

− (1 − n )

h c,A
c P,a ρ a

β A = (5.20)

The mass transfer of water vapour from the return air to the surface of the liquid
desiccant d m s /dy can be calculated from Equation 5.19, whereby the water vapour
pressure p H 2 O is calculated at the inlet temperature of the return air and the water
vapour saturation pressure is calculated at the inlet temperature of the salt solution.
The mass transfer coefficient β R is obtained fromEquation 5.20, using the heat transfer
coefficient h c,R between the return air and liquid desiccant film.
Since the water vapour pressure p S ( T S,in , ξ S,in ) above the salt solution film depends
on the concentration of the salt solution at the solution/return air interface, the con-
centration gradient across the desiccant film thickness in the absorber unit has to be
known. The resistance to water vapour transport from the surface of the solution film
into the solution is described by a diffusion coefficient D ( ξ S )(m 2 s − 1 ) for water trans-
port in salt solutions, which can be calculated as a function of the salt concentration
and temperature (Conde, 2003):

√ ξ s
τ 1

τ 2 τ 3

D ( ξ S ) = D H 2 O 1 − 1 + (5.21)