
377Solar Heating and Cooling of Buildings
© 2008 Taylor & Francis Group, LLC
Then, for a given air temperature, the differentiation of Equation 7.49 gives
dT t
Ud
p
()
=
∞
(7.50)
Adding Equations 7.48 through 7.50 gives a single differential equation for the plate
temperature:
() ()
()
()mc
U
U
mc
dT t
dt
IUTt
p
c
R
p
cs cp
+
=− −
∞
α
(7.51)
Equation 7.51 can be solved directly for given values of I
s
and T
a
. The solution to Equation
7.51 then gives the plate temperature as a function of time, for an initial plate temperature
T
p,0
, in the form
Tt T
I
U
I
U
TT
UAt
mc UU
pa
ss
c
ss
c
pa
cc
p
c
() ()exp
(/
,
−= −−−
−
()
+
αα
0
∞∞
)( )
mc
(7.52)
Collecto