IEEE Circuits and Systems Magazine - Q1 2023 - 48

Figure 4. Temperatures and flows in a heat pump.
Heat needs to first flow spontaneously-by conduction
or convection-from the cold environment (the one
to cool) at temperature Tce to the cold side of the pump
at Tc. Then, together with the absorbed energy, this heat
will be transported to the hot side at temperature Th,
from which it will flow here too spontaneously-to the
hot environment at The. The useful cooling effect obviously
occurs from Tce to The, but if the thermal conductance
relative to spontaneous flows is not large enough,
this effect can result in a pump ΔT significantly higher
than the effect itself, to the detriment of the COP.
VII. Applying the Presented Concepts Using EBM
In this section we show how to turn the principles and
equations described in Section VI into functional EBM
models for cooling system components. In this respect,
it must be noted that modeling can be applied either to
gain insight into existing systems, or to design entirely
new ones. In this work, compared to our previous papers
such as [9], we focus on presenting a modeling approach-also
in the form of a support library-that can
be applied to either case. Consequently, our library is
modularised in generic components, that can be validated
individually and then reused to compose models
for arbitrary cooling systems.
A. Defining Connectors
We already defined some connectors for the examples in
Section V; we here re-collect the definitions for the reader's
convenience, and add a few comments. From now on,
we assume Modelica.SIunits.* imported in all listings.
Vector and matrix heat ports serve when spatially
distributed phenomena come into play, for example to
represent the temperature profile along an exchanging
duct, or the power distribution over a surface; this matter
is addressed in Section VII-C.
B. Storage and Transfer Components
In this section, tightly related to the following Section
VII-C, we introduce an important distinction. Although
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IEEE CIRCUITS AND SYSTEMS MAGAZINE
Listing 4. Connectors useful for modeling cooling circuits.
Figure 5. Storage and transfer components and interconnections
thereof.
the storage and transfer of mass and energy take place
contextually in both time and space, for an effective
modularisation of models it is convenient to distinguish
" storage " and " transfer " components and to give them
a standardized structure, as depicted in Fig. 5 and explained
below.
Storage Components: These contain dynamic balances
of mass and energy, and correspond to a control volume
in which the properties of the contained fluid are considered
spatially uniform. Denoting by θ a vector containing
the required physical parameters such as geometric
dimensions and material constants, these components
have the structure reported below, and along which the
reader can build his/her new components.
At lest one pwh connector, see Section VII-A; we denote
by n the number of such connectors.
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