/[escript]/trunk/doc/cookbook/onedheatdiff002.tex
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revision 2619 by ahallam, Thu Aug 13 04:32:23 2009 UTC revision 2620 by gross, Thu Aug 20 06:24:00 2009 UTC
# Line 16  Line 16 
16   It is quite simple to now expand upon the 1D heat diffusion problem we just tackled. Suppose we have two blocks of isotropic material which are very large in all directions to the point that the interface between the two blocks appears infinite in length compared to the distance we are modelling perpendicular to the interface and accross the two blocks. If \textit{Block 1} is of a temperature \verb 0  and \textit{Block 2} is at a temperature \verb T  what would happen to the temperature distribution in each block if we placed them next to each other. This problem is very similar to our Iron Rod but instead of a constant heat source we instead have a heat disparity with a fixed amount of energy. In such a situation it is common knowledge that the heat energy in the warmer block will gradually conduct into the cooler block until the temperature between the blocks is balanced.   It is quite simple to now expand upon the 1D heat diffusion problem we just tackled. Suppose we have two blocks of isotropic material which are very large in all directions to the point that the interface between the two blocks appears infinite in length compared to the distance we are modelling perpendicular to the interface and accross the two blocks. If \textit{Block 1} is of a temperature \verb 0  and \textit{Block 2} is at a temperature \verb T  what would happen to the temperature distribution in each block if we placed them next to each other. This problem is very similar to our Iron Rod but instead of a constant heat source we instead have a heat disparity with a fixed amount of energy. In such a situation it is common knowledge that the heat energy in the warmer block will gradually conduct into the cooler block until the temperature between the blocks is balanced.
17    
18  \begin{figure}[h!]  \begin{figure}[h!]
19  \centerline{\includegraphics[width=4.in]{figures/onedheatdiff002}}  %\centerline{\includegraphics[width=4.in]{figures/onedheatdiff002}}
20  \caption{Temperature differential along a single interface between two granite blocks.}  \caption{Temperature differential along a single interface between two granite blocks.}
21  \label{fig:onedgbmodel}  \label{fig:onedgbmodel}
22  \end{figure}  \end{figure}

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