8 Solar Thermal-Powered Adsorption Chiller
129
G(τα)
T c
T f
Glass cover
Absorber
T sky
T a
T g
Convection
Radiation
x
Water flow direction
Fig. 8.6 Assumed model of ETC
Now, the governing equation that explains the time dependence of the temperature
of the glass cover is,
C p g δ g ρ g
dT g
dt
= ε g σ (T
4
sky − T
4
g ) + h g,a (T a − T g )
+
ε c ε g
ε c + ε g − ε c ε g
σ (T
4
c − T
4
g )
(8.27)
where subscripts g, a, c and sky stand for glass cover, ambient, absorber plate and the
sky, respectively. Cp represents the specific heat capacity, T is the temperature in K;
δ stands for the thickness, and ρ represents the density. Using Swinbank’s formula
(Swinbank 1963) T sky = pT
1.5
a where p = 0.0552 K
−1/2 , the sky temperature can be
obtained from the ambient temperature.
Now, for the absorber plate, the governing equation can be expressed as,
C p c δ c ρ c
dT c
dt
= G(τ α) +
ε c ε g
ε c + ε g − ε c ε g
σ (T
4
g − T
4
c ) + h f,c (T f − T c ) (8.28)
where subscript f stands for fluid (water). The plate receives radiative heat from the
glass cover and transfers it to the working fluid predominantly in convective mode.
Finally, the temperature of the fluid, having a velocity of u along the positive x
axis, depends on time and its position in the flow channel. The governing equation
to describe the change in fluid temperature with time and position is,
C p f ρ f
π d
2
in
4
dT f
dt
+ u
dT f
dx
= π d in h f,c (T c − T f )
(8.29)