% Verbal description for system HeatedRod (HeatedRod_desc.tex)
% Generated by MTT on Thu Sep 4 18:05:09 BST 1997.
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% %% Revision 1.1 1997/09/11 16:16:50 peterg
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\begin{table}[htbp]
\begin{center}
\leavevmode
\begin{tabular}{l l l}
\hline
Parameter & Symbol & Value \\
\hline
Length & $L_r$ & 1m \\
Diameter & $D_r$ & 1mm \\
Resistivity & $\rho$ & $1.68\times10^{-9} \Omega$m \\
Thermal conductivity & $\sigma$ & 390 W$\text{m}^{-1}$\\
Thermal capacity & $\kappa$ & 380 J$\text{m}^{-3}$\\
\hline
\end{tabular}
\caption{Heated rod parameters}
\label{tab:rod}
\end{center}
\end{table}
System \textbf{HeatedRod} is a model of a well-insulated rod of copper with an
electric current passing through it which warms it up. The two ends of
the rod are fixed at ambient temperature; this is where all the heat
loss occurs.
This example introduces the idea of the {\bf FP}, \textbf{RT} and
\textbf{CT} components in the context of thermal conduction.
The model is similar to that described in chapter 8 of \citeN{Cel91}.
However, instead of representing the thermal resistance by {\bf RS}
components and reinserting the entropy flow, the {\bf RT} component
uses two {\bf FP} components to convert from true to pseudo bonds and
back again. Similary, the thermal capacity is modelled by the {\bf
CT} component.
This distributed system (which strictly speaking has a partial
differential equation model) is approximated by an ordinary
diffferential equation model by modelling the system by a number of
discrete segments of length $\Delta x$. Each segment model consists
of two conceptual parts.
\begin{itemize}
\item An ideal lump of copper with no thermal resistance but with the
normal attributes of electrical resistance (modelled by the
\textbf{RS} component and thermal capacity (modelled by the
\textbf{CF} component).
\item A thin lump wtih thermal resistance but no thermal capacity or
electrical resistance (modeled by the \textbf{RT} component).
\end{itemize}
At this level of the hierarchy, all bonds are true energy bonds and
thus energy conservation is assured. Note that the \textbf{RS}
component correctely transforms electrical to thermal energy.
The system was simulated with a total of nine lumps whilst passing a
current of 1A though the rod for a total of 10s. The initial
temperature and the end temperatures were all set at 300K.