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revision 3369 by jfenwick, Tue Oct 26 03:24:54 2010 UTC revision 3370 by ahallam, Sun Nov 21 23:22:25 2010 UTC
# Line 11  Line 11 
11  %  %
12  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
13    
 \begin{figure}[h!]  
 \centerline{\includegraphics[width=4.in]{figures/onedheatdiff001}}  
 \caption{Example 1: Temperature differential along a single interface between  
 two granite blocks.}  
 \label{fig:onedgbmodel}  
 \end{figure}  
   
14  \section{Example 1: One Dimensional Heat Diffusion in Granite}  \section{Example 1: One Dimensional Heat Diffusion in Granite}
15  \label{Sec:1DHDv00}  \label{Sec:1DHDv00}
16    
17  The first model consists of two blocks of isotropic material, for instance  The first model consists of two blocks of isotropic material, for instance
18  granite, sitting next to each other.  granite, sitting next to each other (\autoref{fig:onedgbmodel}).
19  Initial temperature in \textit{Block 1} is \verb|T1| and in \textit{Block 2} is  Initial temperature in \textit{Block 1} is \verb|T1| and in \textit{Block 2} is
20  \verb|T2|.  \verb|T2|.
21  We assume that the system is insulated.  We assume that the system is insulated.
# Line 31  Intuition tells us that heat will be tra Line 24  Intuition tells us that heat will be tra
24  cooler one until both  cooler one until both
25  blocks have the same temperature.  blocks have the same temperature.
26    
27    \begin{figure}[ht]
28    \centerline{\includegraphics[width=4.in]{figures/onedheatdiff001}}
29    \caption{Example 1: Temperature differential along a single interface between
30    two granite blocks.}
31    \label{fig:onedgbmodel}
32    \end{figure}
33    
34  \subsection{1D Heat Diffusion Equation}  \subsection{1D Heat Diffusion Equation}
35  We can model the heat distribution of this problem over time using the one  We can model the heat distribution of this problem over time using the one
36  dimensional heat diffusion equation\footnote{A detailed discussion on how the  dimensional heat diffusion equation\footnote{A detailed discussion on how the
# Line 668  The last statement generates the plot an Line 668  The last statement generates the plot an
668  As expected the total energy is constant over time, see  As expected the total energy is constant over time, see
669  \reffig{fig:onedheatout1}.  \reffig{fig:onedheatout1}.
670    
671  \begin{figure}  \begin{figure}[ht]
672  \begin{center}  \begin{center}
673  \includegraphics[width=4in]{figures/ttblockspyplot150}  \includegraphics[width=4in]{figures/ttblockspyplot150}
674  \caption{Example 1b: Total Energy in the Blocks over Time (in seconds)}  \caption{Example 1b: Total Energy in the Blocks over Time (in seconds)}
# Line 723  want to substitute a value into the name Line 723  want to substitute a value into the name
723  and  and
724   \item \verb d  means that the value to substitute will be a decimal integer.   \item \verb d  means that the value to substitute will be a decimal integer.
725  \end{itemize}  \end{itemize}
726    
727  To actually substitute the value of \verb|i| into the name write \verb|%i| after  To actually substitute the value of \verb|i| into the name write \verb|%i| after
728  the string.  the string.
729  When done correctly, the output files from this command will be placed in the  When done correctly, the output files from this command will be placed in the

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