190
S. Sangwan and P. R. Chakraborty
C O P =
SC E
Q de + Q sh
(10.11)
Heat recovery cycle (analysis)
The thermodynamic cycle of the heat recovery process is shown in Fig. 10.2. The
heat recovery can be attained till thermal equilibrium is established between the beds
so that both the beds reach a common temperature (described by sates e and f on
the thermodynamic cycle in Fig. 10.2). The estimation of equilibrium temperature of
the two beds T e and T f (T e = T f = T eq ) is be based on two alternative formulations
based on relative values of T b and T d . If the condition T b ≥ T d is satisfied, then T eq
can be estimated from the following formulation.
Q sh |
T eq
T a
=
Q sc |
T eq
T c
(10.12)
On the other hand if the condition T b < T d is satisfied, then T eq needs to be estimated
from the following formulation.
Q sh + Q de |
T eq
T b
=
Qsc + Q ad |
T eq
T d
(10.13)
Q sh |
T eq
T a
, Q de |
T eq
T b
, Q sc |
T eq
T c
, and Q ad |
T eq
T d
can be obtained from Eqs. 10.2–10.5 by changing the upper limits of integrations to e and f respectively. Although the temperatures
T e and T f are equal at state points e and f, the concentrations of refrigerant at desorbing and adsorbing beds are not equal, i.e. x e (T e , T csat ) = x f (T f , T esat ); and one
should be careful while calculating Q de |
T eq
T b
and Q ad |
T eq
T d
from Eqs. 10.3 and 10.5.
By substituting appropriate expressions of Q sh |
T eq
T a
, Q sc |
T eq
T c
, Q sh , Q sc , Q de |
T eq
T b
, and
Q ad |
T eq
T d
in Eq. 10.12 or 10.13, we obtain an equation with a single unknown T eq and
Eq. 10.12 or 10.13 can be rewritten as:
F(T eq ) = 0
(10.14)
where, F(T eq ) is a nonlinear function of T eq . Equation 10.14 can be solved by using
iterative secant method to determine the value of T eq in the following manner.
T
(i)
eq = T
(i−1)
eq
− F
(i−1)
T
(i−1)
eq
− T
(i−2)
eq
F (i−1) − F (i−2)
(10.15)
where, i represents the iteration step. The two initial guesses to initiate the iteration
has been considered to be T b , and T d .
If T b ≥ T d , regenerated or recovered heat per kg of adsorbent Q reg can be simply
estimated as:
Q reg = Q sh |
T eq
T a
=
Q sc |
T eq
T c
(10.16)
S. Sangwan and P. R. Chakraborty
C O P =
SC E
Q de + Q sh
(10.11)
Heat recovery cycle (analysis)
The thermodynamic cycle of the heat recovery process is shown in Fig. 10.2. The
heat recovery can be attained till thermal equilibrium is established between the beds
so that both the beds reach a common temperature (described by sates e and f on
the thermodynamic cycle in Fig. 10.2). The estimation of equilibrium temperature of
the two beds T e and T f (T e = T f = T eq ) is be based on two alternative formulations
based on relative values of T b and T d . If the condition T b ≥ T d is satisfied, then T eq
can be estimated from the following formulation.
Q sh |
T eq
T a
=
Q sc |
T eq
T c
(10.12)
On the other hand if the condition T b < T d is satisfied, then T eq needs to be estimated
from the following formulation.
Q sh + Q de |
T eq
T b
=
Qsc + Q ad |
T eq
T d
(10.13)
Q sh |
T eq
T a
, Q de |
T eq
T b
, Q sc |
T eq
T c
, and Q ad |
T eq
T d
can be obtained from Eqs. 10.2–10.5 by changing the upper limits of integrations to e and f respectively. Although the temperatures
T e and T f are equal at state points e and f, the concentrations of refrigerant at desorbing and adsorbing beds are not equal, i.e. x e (T e , T csat ) = x f (T f , T esat ); and one
should be careful while calculating Q de |
T eq
T b
and Q ad |
T eq
T d
from Eqs. 10.3 and 10.5.
By substituting appropriate expressions of Q sh |
T eq
T a
, Q sc |
T eq
T c
, Q sh , Q sc , Q de |
T eq
T b
, and
Q ad |
T eq
T d
in Eq. 10.12 or 10.13, we obtain an equation with a single unknown T eq and
Eq. 10.12 or 10.13 can be rewritten as:
F(T eq ) = 0
(10.14)
where, F(T eq ) is a nonlinear function of T eq . Equation 10.14 can be solved by using
iterative secant method to determine the value of T eq in the following manner.
T
(i)
eq = T
(i−1)
eq
− F
(i−1)
T
(i−1)
eq
− T
(i−2)
eq
F (i−1) − F (i−2)
(10.15)
where, i represents the iteration step. The two initial guesses to initiate the iteration
has been considered to be T b , and T d .
If T b ≥ T d , regenerated or recovered heat per kg of adsorbent Q reg can be simply
estimated as:
Q reg = Q sh |
T eq
T a
=
Q sc |
T eq
T c
(10.16)