Path: Thermal/ThermalAnalysis
% Model a thermal circuit from nodal masses
Creates a set of first order differential equations to model a thermal
circuit. Inputs are the nodal masses, a conductive node map, a radiative
node map, an input node map and an output node map. The output is a set
of first order differential equations in the form
.
T = aT + bq
y = cT
where T is the nodal temperature, q is the thermal input and y is the
vector of measurements.
A node map has one row for each node and as many columns as are necessary
to specify the connections. Each node map is accompanied by a coefficient
map that gives either the conductive or radiative heat transfer
coefficents for the node pair. Radiative heat transfer is of the form:
4 4
q = a(T - T )
ij i j
Thermnet linearizes about the nominal temperature. The result is
3 3
q = a(T T - T T )
ij ni i nj j
where the n indicates a nominal temperature. The radiative heat transfer
coefficient causes an asymmetry between nodes.
Thermnet will automatically make the a matrix symmetric for conduction.
Thermnet will warn you if you entered a coefficient twice and the two
were different. You only have to specify the connection in one direction.
If you want a node to conduct or radiate to infinity just input "inf" as
the node to which it is radiating or conducting.
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Form:
[a, b, c, ac, ar] = Thermnet( mn, cnm, cc, inm, onm, rnm, rc, tnom )
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Inputs
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mn (1,n) Thermal mass of each node
cnm (n,:) Conduction node map
cc (n,:) Conduction coefficients
inm (m,:) Input node map (nodes with inputs)
onm (p,1) Output node map (nodes with outputs)
rnm (n,:) Radiation node map
rc (n,:) Radiation coefficients
tnom (1,n) Nominal temperature for linearization
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Outputs
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a (n,n) Plant matrix
b (n,m) Input matrix
c (p,n) Output matrix
ac (n,n) Conduction part of the plant matrix
ar (n,n) Radiative (quartic) coefficient matrix
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