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In this section we will consider unsteady heat conduction in
a uniform bar, as shown in figure 1. We will assume
that the temperature T depends only on the position
x along the bar and the time t. In other words, we assume
that the temperature variations over the cross sections are
negligible. We also assume that the heat conduction satisfies
Fourier's law, so that the heat flux in the x-direction
is given by the
| |
(1) |
where we assume that k is a constant.
Figure 1:
Heat conduction in a bar.
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