IEA Solar Heating and Cooling Programm - NachhaltigWirtschaften.at

IEA SHC Task 38 Solar Air Conditioning and Refrigeration Subtask C2-A, November 9, 2009
The partial derivative of a variable x with respect to time t can be thus written with respect to
the angular position θ following:
This yields the following system:
∂x
∂t
π ∂x
=
τ ∂θ
ro
Mass conservation equation
M
d
π ∂W
+ m
τ ∂θ
ro
a
⎛
⎜
⎝
π
τ
ro
Mass transfer equation:
M
d
π ∂W
= h
τ ∂θ
ro
m
S
∂wa
∂w
+ u
∂θ
∂z
( w − w )
Heat conservation equation
a
eq
a
⎞
⎟ = 0
⎠
(31)
(32)
M
d
π ∂H
+ m
τ ∂θ
ro
a
⎛
⎜
⎝
π
τ
ro
Heat transfer equation
M
d
π ∂H
= h
τ ∂θ
ro
m
S
∂ha
∂ha
+ u
∂θ
∂z
⎞
⎟ = 0
⎠
( w − w )( h + c T ) + h S( T − T )
a
eq
fg
pv
a
t
The obtained equation system is coupled non linear hyperbolic, since the enthalpy of the
moist air and of the desiccant depend on the water content and on the temperature.
In the bibliography the equations were solved by Macalaine-cross, [17] and Stabat, [11] by
neglecting the terms
∂w a
∂h
and a
∂θ ∂θ
a
d
(33)
(34)
in front of transport term which yields a simplification of
the equations and of the matrix to be solved. In this work we conserved these terms.
Transformation to a discrete problem and restriction to 2 dimensions
The wheel is divided into elementary domains following the figure below
R
∆z
∆θ
Figure 20 : discretisation of the desiccant wheel
page 48