Modeling and Design of Net ZEBs as Integrated Energy Systems - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 27

(2.1h)
The transfer admittance has been multiplied by the area A to obtain its total
value. To obtain Y s we temporarily set T o = 0 and obtain the admittance as
seen from the interior surface, yielding (after multiplying by A ):
(2.1i)
If there is no thermal mass (zero thermal capacity) then we obtain the
simple equality Y s = − Y t = Au 0 . A similar result is obtained for windows by
eliminating all nodes exterior to the inner glazing. An important result is
obtained for an infinitely thick wall or a wall with no heat loss at the back
(adiabatic surface, or high amount of insulation u 0 ≈ 0); in this case Y s is
given by
(2.1j)
Walls with thick massive layers have admittance that is close to that given
by Eq. (2.1j) . When the penetration depth, given by
(2.1k)
is significantly less than the wall thickness then the wall behaves like a
semi-infinite solid. The magnitude and phase angle (and time lag/lead) of
a transfer function, such as Y s and Y t , are computed by means of complex
variables.
Substantial insight into wall and building thermal behavior may be gained
by studying the magnitude and phase angle of key transfer functions, such
as Y s and Y t . The time lead d s of Y s is the time difference between the peak
ofasinusoidal inputfunction, suchassolarradiation inthecaseoftheroom
interior surface, and the resulting peak of the interior surface temperature
T i . Now, we consider the variation of wall thermal admittance with thermal
mass thickness L for the fundamental frequency (one cycle per day, n = 1)
for unit wall area. Note that the diurnal ( n = 1) frequency is important in
the analysis of variables with a dominant diurnal harmonic, such as solar