Civil Engineering Reference
In-Depth Information
(2.9a)
The radiation conductances interconnecting room interior surface nodes
2-8 are given by:
(2.9b)
where
σ
is the Stefan-Boltzmann constant and is a linearization factor
which is based on an estimated mean temperature,
T
m
. The radiation
exchange factors between pairs of surfaces under consideration (
i
and
j
) are determined from the radiation view factors
F
ij
, and the radiative
properties of the room surfaces as follows:
where
m
=
M
−1
; the elements of matrix
M
are given by:
, with
if
i
=
j
; otherwise,
(
I
is the identity matrix).
Energy balances at the room interior nodes
are readily obtained after
replacing each wall by its Norton equivalent subnetwork consisting of an
equivalent heat source
Q
sc
(sc: short circuit) and a self-admittance
Y
eq
,
thereby eliminating all exterior nodes without discretizing the massive
elements. The equivalent source
Q
sc
is equal to the wall transfer admittance
times an external specified temperature. For the floor with self-admittance
Y
fs
and transfer admittance
Y
ft
we have
(the negative sign
follows the sign convention used).
Inclusion of a lumped thermal capacitance at the room air node is
represented by the constitutive equation
q
=
C
a
d
T/
d
t
where
q
represents
heat flow into the air capacitance
C
a
; the Laplace domain equation for this
is
q
(
s
) =
s
·
C
a
.
The energy balance for the model (with summations Σ
U
ij
over
j
= 1…8) is as
follows:
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