Environmental Engineering Reference
In-Depth Information
case). When there is wind, the convection heat transfer from the glass envelope to the
atmosphere gives a much bigger heat loss. This is estimated from Newton's law of
cooling:
q
go-a,conv
=
h
go
−
a
π
D
go
(T
go
−
T
a
)
(6.2.22)
and
k
air
D
go
h
go-a
=
Nu
D
go
(6.2.23)
glass envelope outside surface temperature (
◦
C); T
a
=
where: T
go
=
ambient air temper-
ature (
◦
C); h
go-a
=
T
a
)/2 (W/m
2
-
◦
C);
convection heat transfer coefficient for air at (T
go
−
T
a
)/2 (W/m-
◦
C); D
go
=
k
air
=
thermal conductivity of air at (T
go
−
glass envelope out-
side diameter (m); and Nu
Dgo
=
average Nusselt number based on the glass envelope
outside diameter D
go
.
a)
No wind
When there is no wind, the convection heat transfer from the glass enve-
lope to the environment occurs by natural convection and the correlation developed
by Churchill and Chu is used to estimate the Nusselt number (Cengel, 2006):
⎡
⎤
2
0387R
1
/
6
D
go-a
⎣
⎦
10
5
<
Ra
Dgo
<
10
12
Nu
D
go
=
0
.
60
+
(6.2.24)
1
+
0
.
559
/
Pr
go-a
9
/
16
8
/
27
g
β
(T
go
−
T
a
)D
go
ν
go-a
Ra
D
go
=
Pr
go-a
(6.2.25)
1
T
go-a
β =
(6.2.26)
ν
go-a
α
Pr
go-a
=
(6.2.27)
go-a
where: Ra
Dgo
=
Rayleigh number for air based on the glass envelope outside diameter,
9.81 m/s
2
);
D
go
;g
=
gravitational constant (
=
α
go-a
=
thermal diffusivity for air at T
go-a
(m
2
/s);
β =
volumetric thermal expansion coefficient (ideal gas) (1/K); Pr
go-a
=
Prandtl
kinematic viscosity for air at T
go-a
(m
2
/s);
number for air at T
go-a
;
ν
go-a
=
and
T
go-a
T
a
)/2 (K).
This correlation assumes a long isothermal horizontal cylinder. Also, all the fluid
properties are determined at the mean film temperature, (T
go
=
film temperature (T
go
+
T
a
)/2.
b)
Wind
When there is wind, the convection heat transfer from the glass envelope
to the environment occurs by forced convection. The Nusselt number in this case is
estimated with Zhukauskas' correlation for external forced convection flow normal
to an isothermal cylinder (Incropera et al., 2007):
+
CRe
D
go
Pr
a
Pr
a
1
/
4
1
<
ReD
go
<
10
6
Nu
D
go
=
0
.
7
<
Pr
a
<
500
and
Pr
go
(6.2.28)
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