Modeling and Design of Net ZEBs as Integrated Energy Systems - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 35

(2.7)
Thus, at a specific time t , the heat gain per unit area through a wall or
a roof can be calculated using a simple, recursive equation with constant
coefficients; the sol-air temperature T sol-air can be used to represent the
outdoor conditions. Assuming that the internal temperature T i = T indoor is
constant, the indoor heat flux through a multilayered wall at the current
time is calculated by means of the following (ASHRAE, 2009a):
(2.8)
where q ( t ) is the indoor heat flux at the current time ;A is the indoor surface
area ofawall ;n isthesummation index; N MAX isthenumber ofcoefficients
used; Δ t is the time step; T sol-air is the sol-air temperature representing
outdoor conditions; T indoor is the constant indoor temperature.
The maximum number of coefficients that can be obtained from the
polynomial transfer function depends on the number of poles P .
Therefore the calculation of CTFs has two degrees of freedom. One is due to
thechoiceofthenumberofpoles P whiletheotherisduetothechoiceofthe
number N of coefficients, which cannot be greater than P − 1.
2.1.4 Detailed Zone Model and Building Transfer Functions
We have seen various techniques for representing heat transfer through
multilayered walls. Now we consider thermal zone models using thermal
network techniques, followed by solutions in the frequency and time
domains.
Thethermalnetworkmodelforatypicalzone overabasement( Figure2.6 ) ,
with one window and convective auxiliary heating can vary in level of detail
according to how convection and radiation heat transfer are modeled in the
room interior. Two common choices are followed: