Civil Engineering Reference
In-Depth Information
aligned with the force of gravity, thus the buoyancy force which originates the
natural convection process acts exclusively to induce the fluid motion in any
direction. However, the floor and the ceil of a room are horizontal surfaces,
and therefore, the buoyancy force is just normal to the surface. In this case,
flow patterns and heat transfer depend on whether the surface is cooled or
heated in reference with the fluid, and on surface orientation.
To estimate heat transfer by natural convection through the floor and the ceiling
The Horizontal Plate
empiric correlation has been used. More specifically,
two different cases have been taken into account: (i) A cold surface facing
upward and (ii) A hot surface facing downward. In these cases, air trend to
ascend/descend, respectively, is impeded by the plate. Therefore, the air flow
must move horizontally before it can ascend/descend from the edges of the
plate, which originated an ineffective heat transfer by convection (Incropera
and De Witt
2002
).
Therefore, the convection heat transfer coefficients for the floor and the ceil
can be estimated using Eq.
4.23
. However, in this case, Nusselt number is
calculated as a function of the Rayleigh number using the empiric correlation
known as
The Horizontal Plate
(Incropera and De Witt
2002
), see Eq.
4.27
.
In addition, the characteristic length of the surface in this empiric correlation
is equal to the quotient between the surface area and its perimeter.
0
Ra
1
/
4
L
10
4
10
7
.
54
×
,
≤
Ra
L
≤
Nu
L
=
(4.27)
Ra
1
/
3
L
10
7
10
11
0
.
15
×
,
≤
Ra
L
≤
2.
Heat Gain through the Glass of the Window
(
Q
glass
)
In general, heat transfer through the glass of a window can be defined as a com-
bination of convection, conduction and radiation processes, see Fig.
4.13
.More
specifically, it can be estimated as a combination of the heat gain by means of
beam solar irradiance (
Q
dr
) and diffuse solar irradiance (
Q
df
), and the heat gain
through conduction (
Q
c
). Hence, heat gain through the glass
(
Q
glass
)
is estimated
as shown in Eq.
4.28
(ASHRAE
2009
).
Q
glass
=
Q
dr
+
Q
df
+
Q
c
=
[
A
w
I
dr
SHGC
(θ)
IAC
(θ, Ω)
]
+
[
A
w
(
I
df
+
I
rf
)
SHGC
df
IAC
df
]
+
A
w
U
w
(
T
a
in
)
T
a
out
−
(4.28)
where:
A
w
is the window area (m
2
),
I
dr
and
I
rf
are the direct and reflected irradi-
ance (W/m
2
), respectively. IAC(
) and IAC
df
are the indoor solar attenuation
coefficient for beam and for diffuse solar heat gain coefficients (
θ,Ω
−
), respectively.
SHGC(
θ
) and SHGC
df
are the beam and diffuse solar heat gain coefficients
(
−
), respectively.
T
a
in
and
T
a
out
are the indoor and outdoor temperatures (
K
),
