8 Solar Thermal-Powered Adsorption Chiller
127
useful energy gain Q u , i.e. Q c–h = Q u . Eliminating T c and from Eqs. (8.4), (8.5) and
(8.18), we can write,
Q c−h =
h e /U L
h e /U L + 1
A C [G(τ α) e f f − U L (T h − T a )]
(8.19)
The steady state energy transfer from the heat-transfer fluid to the manifold fluid
can be expressed by,
Q h−m = h h−m A h−m
T h − T f
(8.20)
where, h h–m represents the heat transfer coefficient for this heat flow, A h–m is the area
of the heat pipe in contact with the manifold fluid and T f is the mean temperature of
the working fluid.
Again, since Q c–h = Q h–m , eliminating T h from Eqs. (8.19) and (8.20) we can
write,
Q h−m =
A C
(U L A C / h h−m A h−m ) + (U L / h e + 1)
[G(τ α) e f f − U L (T f − T a )]
⇒ Q h−m = F r A C [G(τ α) e f f − U L (T f − T a )]
(8.21)
where
F r =
1
(U L A C / h h−m A h−m ) + (U L / h e + 1)
(8.22)
F r is known as the heat removal factor and can be defined as the ratio of the actual
amount of heat transferred to the manifold fluid to the heat that would be transferred
if the entire collector were at the fluid inlet temperature. From Eq. (8.22), it can be
said that the value of F r is dependent on three ratios, U L /h e , U L /h h–m and A h–m /A c .
Since Q h–m = Q u , from Eqs. (8.3) and (8.21), collector efficiency can be written
as,
η = F r (τ α) e f f − F r U L
(T f − T a )
G
(8.23)
Thus the steady state efficiency of an ETC has a linear form; however, in real
applications, it may not be linear and may be difficult to obtain solving all the
parameters. To overcome this shortcoming, Cooper and Dunkle (1981) proposed a
second order efficiency equation with the assumption,
F r U L = a + b(T f − T a )
(8.24)
Substituting Eq. (8.24) into the Eq. (8.23), we obtain,
127
useful energy gain Q u , i.e. Q c–h = Q u . Eliminating T c and from Eqs. (8.4), (8.5) and
(8.18), we can write,
Q c−h =
h e /U L
h e /U L + 1
A C [G(τ α) e f f − U L (T h − T a )]
(8.19)
The steady state energy transfer from the heat-transfer fluid to the manifold fluid
can be expressed by,
Q h−m = h h−m A h−m
T h − T f
(8.20)
where, h h–m represents the heat transfer coefficient for this heat flow, A h–m is the area
of the heat pipe in contact with the manifold fluid and T f is the mean temperature of
the working fluid.
Again, since Q c–h = Q h–m , eliminating T h from Eqs. (8.19) and (8.20) we can
write,
Q h−m =
A C
(U L A C / h h−m A h−m ) + (U L / h e + 1)
[G(τ α) e f f − U L (T f − T a )]
⇒ Q h−m = F r A C [G(τ α) e f f − U L (T f − T a )]
(8.21)
where
F r =
1
(U L A C / h h−m A h−m ) + (U L / h e + 1)
(8.22)
F r is known as the heat removal factor and can be defined as the ratio of the actual
amount of heat transferred to the manifold fluid to the heat that would be transferred
if the entire collector were at the fluid inlet temperature. From Eq. (8.22), it can be
said that the value of F r is dependent on three ratios, U L /h e , U L /h h–m and A h–m /A c .
Since Q h–m = Q u , from Eqs. (8.3) and (8.21), collector efficiency can be written
as,
η = F r (τ α) e f f − F r U L
(T f − T a )
G
(8.23)
Thus the steady state efficiency of an ETC has a linear form; however, in real
applications, it may not be linear and may be difficult to obtain solving all the
parameters. To overcome this shortcoming, Cooper and Dunkle (1981) proposed a
second order efficiency equation with the assumption,
F r U L = a + b(T f − T a )
(8.24)
Substituting Eq. (8.24) into the Eq. (8.23), we obtain,