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\sslist{example02.py} |
\sslist{example02.py} |
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\label{Sec:1DHDv0} |
\label{Sec:1DHDv0} |
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Our second example is a cold iron bar at a constant temperature of $T\hackscore{ref}=20^{\circ} C$, see \reffig{fig:onedhdmodel}. The bar is perfectly insulated on all sides with a heating element at one end keeping the the temperature at a constant level $T\hackscore0=100^{\circ} C$. as heat is applied; energy will disperse along the bar via conduction. With time the bar will reach a constant temperature equivalent to that of the heat source. |
Our second example is a cold iron bar at a constant temperature of $T\hackscore{ref}=20^{\circ} C$, see \reffig{fig:onedhdmodel}. The bar is perfectly insulated on all sides with a heating element at one end keeping the the temperature at a constant level $T\hackscore0=100^{\circ} C$. As heat is applied; energy will disperse along the bar via conduction. With time the bar will reach a constant temperature equivalent to that of the heat source. |
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This problem is very similar to the example of temperature diffusion in granite blocks presented in the previous section~\ref{Sec:1DHDv00}. So we will modify the script we have already developed for the granite blocks to adjust |
This problem is very similar to the example of temperature diffusion in granite blocks presented in the previous section~\ref{Sec:1DHDv00}. So we modify the script we have already developed for the granite blocks to adjust |
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it to the iron bar problem. |
it to the iron bar problem. |
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The obvious difference between the two problems are the dimensions of the domain and different materials involved. This will change the time scale of the model from years to hours. |
The obvious difference between the two problems are the dimensions of the domain and different materials involved. This will change the time scale of the model from years to hours. |
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The new settings are; |
The new settings are; |
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Besides some cosmetic modification this all we need to change. The total energy over time is shown in \reffig{fig:onedheatout1 002}. As heat |
Besides some cosmetic modification this all we need to change. The total energy over time is shown in \reffig{fig:onedheatout1 002}. As heat |
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is transfered into the rod by the heater the total energy is growing over time but reaches a plateau |
is transfered into the rod by the heater the total energy is growing over time but reaches a plateau |
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when the temperature is constant is the rod, see \reffig{fig:onedheatout 002}. |
when the temperature is constant is the rod, see \reffig{fig:onedheatout 002}. |
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YOu will notice that the time scale of this model is several order of magnitudes faster than |
You will notice that the time scale of this model is several order of magnitudes faster than |
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for the granite rock problem due to the different length scale and material parameters. |
for the granite rock problem due to the different length scale and material parameters. |
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In practice it can take a few models run before the right time scale has been chosen\footnote{An estimate of the |
In practice it can take a few models run before the right time scale has been chosen\footnote{An estimate of the |
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time scale for a diffusion problem is given by the formula $\frac{\rho c\hackscore{p} L\hackscore{0}^2}{4 \kappa}$, see |
time scale for a diffusion problem is given by the formula $\frac{\rho c\hackscore{p} L\hackscore{0}^2}{4 \kappa}$, see |
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