Page 161 - Design of Solar Thermal Power Plants

146 3. GENERAL DESIGN OF A SOLAR THERMAL POWER PLANT

convection thermal radiation. The mean Nusselt number of receiver
exterior wall surface is calculated through Eq. (3.27) [52]
2
8 9
> >
1
> >
0:387Ra
> 6 >
< =
Nu wb ¼ 0:6 þ wb ; 10 5 < Ra wb < 10 12 (3.27)
9
h
> 0:559 10 i 8 >
> 27>
1 þ
> >
: ;
PR
3
gbðT wb T a Þðr AP þ dÞ
Ra wb ¼
va
(3.27a)
3
gðT wb T a Þðr AP þ dÞ
¼
vaT a
92
8
> >
> >
> >
> >
> 1 >
> 6 >
lNu wb l < 0:387Ra wb =
h wb ¼ ¼ 0:6 þ # 8 (3.28)
H H > " 9 27>
0:559
> 16 >
> >
> >
1 þ
> >
> >
: P r ;
in which b is the volumetric expansion coefficient of the air, 1/ C, as

2
b ¼ 1/T a ; v is the kinematic viscosity of the air, m /s; a is temperature
2
diffusion coefficient, m /s; P r is the Prandtl number of the air; T wb
is the mean temperature of absorber exterior wall surface, C.

We substitute Eqs. (3.26e3.28) into (3.25)
2 3
2pkH
P COND ¼ 4 þ pðr AP þ dÞHh wb ðT w T a Þ
5
r AP þ d
ln
r AP
2 92 3
8
> >
> >
6 > > 7
> >
6 > 1 > 7
2pkH 0:387Ra
>
>
6 < 6 = 7
6 wb 7
þ dl 0:6 þ
r AP þ d " 9
¼ 6 # 8 ðr AP þ dÞ7
6ln > 0:559 16 27> 7
6
>
>
>
7
>
> >
4 r AP > 1 þ > 5
>
>
P r
: ;
ðT w T a Þ
(3.29)
In the case that the reference temperature is the ambient air
temperature, P r ¼ 0.71, we substitute it into Eq. (3.29)
2 3
2pkH 1 2
P COND ¼ 4 þ pl 0:6 þ 0:32Ra 6 wb ðr AP þ dÞ ðT w T a Þ
5
r AP þ d
ln
r AP
(3.30)