8 Solar Thermal-Powered Adsorption Chiller
137
Bed Equations During Adsorption-Desorption
Let us assume, at a certain point of time, Bed 1 is at the desorption phase, and
Bed 2 is at adsorption phase. The desorber bed, i.e., Bed 1, is then connected to
the condenser. Hot water flows through the tubes of the heat exchanger, providing
the necessary heat for the process of desorption. The hot water outlet temperature
depends on the rate of heat transfer between the tubes and the adsorbent bed. For the
desorber bed, Eq. (8.38) can be written as,
MC p
bed,des
dT bed,des
dt
= M bed h ads
dw
dt
des
+ ˙
m hot C p,hot (T in,hot − T bed,des )
1 − exp
−
(U A) bed
˙
m hot C p,hot
(8.43)
where, T bed,des is the temperature of the desorbing bed, ˙
m hot and C p,hot are the flow
rate and specific heat capacity of hot water.
dw
dt
des
is the rate of desorption and
can be calculated using Eq. (8.32). The equilibrium uptake w* at any time step can
be determined using Eq. (8.30). It needs mentioning that in the case of a desorber
bed, P sat (T ref ) is essentially the condenser pressure and P sat (T ads ) corresponds to the
saturation pressure of water at the bed temperature.
MC p
bed,des
can be obtained
from,
MC p
bed,des
=
MC p
bed
+ wM bed C p,des
where, C p,des is the specific heat capacity of water vapor at the desorber bed temperature. T in,hot is the inlet temperature of hot water, and the hot water outlet temperature
can be determined from,
T out,hot = T bed,des −
T bed,des − T in,hot
exp
−
(U A) bed
˙
m hot C p,hot
(8.44)
Similar to desorber bed, the model equation for adsorber bed, i.e., for Bed 2, can
be written as,
MC p
bed,ads
dT bed,ads
dt
= M bed h ads
dw
dt
ads
+ ˙
m cool C p,cool
T in,cool − T bed,ads
1 − exp
−
(U A) bed
˙
m cool C p,cool
(8.45)
where subscripts ads and cool represent adsorption and cooling water, respectively.
The outlet temperature of cooling water can be calculated from,