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IEA SHC Task 38 Solar Air Conditioning and Refrigeration Subtask C2-A, November 9, 2009
Equations (7), (8), (9) and (10) are coupled, hyperbolic and non-linear. With the assumption
of the Lewis number (Le), equal unity and the desiccant matrix in equilibrium with air means
that (T d = T eq and w eq = w a ). Banks [8] used matrix algebra and demonstrated that these
equations (7 to 10) can be reduced by applying the potential function Fi(T,w) to the following
system:
∂Fi
, eq ∂F
, a
∂F
, a
γ iµ + u
+
= 0 i=1;2
∂t
∂t
∂z
(11)
∂Fi
, d
γ
iµ
+ J
m
( Fi
, eq
− Fi
, a
) = 0 i=1;2
∂t
(12)
These equations are similar to those for the sensible regenerator (Equations 1 and 2), with
the potential function F i replacing the temperature and the parameters γ i replacing the
specific heat ratio, and they can be solved using analogy with heat transfer alone as
suggested by Maclaine-cross and Banks [7] and Close and Banks [9]. There are many
expressions for the potential functions of moist air-silica gel; we chose those proposed by
Jurinak [10] and Stabat [11].
F = h
1
(13)
1.5
( 273.15 + T ) 0. 8
2
1. 1
F = + w
(14)
6360
The solution sequence for the desiccant wheel is then:
. j
i
C j
= m a
C
C
M
=
* d i(
moy)
ri
. min j
*
i
=
m
C
C
a
i
min
i
max
N
γ
NUT
0
1
=
C
min
⎛
⎜
⎝
1
+
1
( h A) ( h A)
m
s
m
r
⎞
⎟
⎠
−1
⎡
( )
( ) ⎥ ⎥ ⎤
=
m 1
⎢ −
*
ε
i
ε
cc
NUT0
, Ci
1
or ε
* 1. 93 i
= C ri
( C
* ri
≤ 0. 4 ) for very low rotation speed
⎢⎣
9 Cri
⎦
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