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#: ../../source/components/subsystems/heat_transfer.rst:4
msgid "Spatially Distributed Heat Transfer"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:6
msgid ""
"Our next example of creating reusable subsystems will introduce a slight "
"twist.  In this section we will not only demonstrate how to create a "
"reusable subsystem model, as in the previous examples from this chapter, but"
" that subsystem model will use an array of **component** instances where the"
" size of that array can be used to control the spatial resolution of the "
"results."
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:14
msgid "Flat System"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:16
msgid ""
"Let's start, as usual, with a flat system level model like the one shown "
"below:"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:24
msgid ""
"This model consists of a collection of thermal capacitances with thermal "
"conductors in between them.  In this case, there are 3 thermal capacitances "
"and 5 thermal conductors.  On the left side, heat is applied to the system "
"and on the right side a temperature sensor measures how the temperature of "
"the rightmost thermal capacitance changes."
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:31
msgid "When implemented in Modelica, the model looks like this:"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:36
msgid ""
"Simulating this system, we can see the temperature response of the rightmost"
" thermal capacitance in the following plot:"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:43
msgid "Segmented Rod Subsystem"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:47
msgid ""
"In our flat system model, we have 3 thermal capacitances and 5 conductances."
"  This configuration represents a rod that has been divided into 3 equal "
"segments and the conductance that occurs between those segments as well as "
"between each segment and some ambient conditions.  In theory, we can divide "
"a rod into :math:`N` equal segments with :math:`N-1` conduction paths "
"between them and :math:`N` conduction paths between each segment and the "
"ambient conditions."
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:55
msgid ""
"Our particular configuration was for :math:`N=3`.  But we can create a "
"subsystem model where :math:`N` is a parameter of the subsystem.  In other "
"words, we can create a subsystem model that is divided into :math:`N` equal "
"segments.  But to do so, we cannot simply drag and drop the capacitances "
"into the model and connect them with conductances because we don't know the "
"exact number."
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:62
msgid ""
"Instead, we'll use an array **of components** to represent this collection "
"of capacitances and conductances.  The resulting ``Rod`` model can be "
"written in Modelica as follows:"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:70
msgid ""
"There are several interesting things to note about this model.  First, the "
"number of segments the rod will be divided into is represented by the ``n`` "
"parameter:"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:78
msgid ""
"The parameter ``n`` is then used in the following declarations to specify "
"the number of capacitance and conductance elements in the rod:"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:85
msgid ""
"Note that if we wish to apply a modification, *e.g.,* ``G=G_rod`` to every "
"component in an array of components, we can use the ``each`` qualifier on "
"the modification.  We'll discuss the ``each`` qualifier and how to apply "
"modifications to arrays of components later in this chapter in the section "
"on :ref:`sub-modifications`."
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:91
msgid ""
"Now that we've declared our component arrays, we can then wire together the "
"capacitances and conductances using ``for`` loops in an ``equation`` "
"section:"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:99
msgid ""
"We also need to connect the ends of the rod to the external connectors so "
"that the rod can be connected to other models:"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:106
msgid ""
"In this way, we are able to create a segmented rod model with an arbitrary "
"number of equally divided segments."
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:110
msgid "Spatial Resolution"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:112
msgid ""
"Now that we have our parameterized ``Rod`` model, we can look at how the "
"number of segments in the rod impacts the response we see. Ultimately, what "
"we should see is that as the number of segments gets larger (or, as the size"
" of the segments gets smaller), we should converge on a solution."
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:118
msgid "We'll start by considering a model where ``n=3``, *i.e.,*"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:124
msgid ""
"We can then extend this model to create additional models with more "
"segments, *e.g.,*"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:139
msgid ""
"If we simulate all of these cases, we see that as ``n`` gets larger, they "
"appear to converge to a common solution and that ``n=10`` seems to provide a"
" reasonable solution without the need to introduce a large number of "
"superfluous components:"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:153
msgid "Conclusion"
msgstr ""

#: ../../source/components/subsystems/heat_transfer.rst:155
msgid ""
"In this section, we've seen how we can build assemblies of arbitrary size "
"using arrays of components and ``for`` loops to connect them together."
msgstr ""
