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1D Transient Heat Conduction CDF Tool

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1	=== Analytic Solution for 1D Transient Heat Conduction ===
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3	The problem geometry and boundary conditions are shown below. An initially isothermal (T,,initial,,) semi-infinite medium is suddenly subject to a surface temperature T,,h,,.
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5	[[Image(semi_inf.png, 200px)]]
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7	The temperature field can be non-dimensionalized as:
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9	$\theta (x,t)=\frac{T(x,t)-T_{\text{initial}}}{T_h-T_{\text{initial}}}$
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11	The governing differential equation (with spatially one-dimensional heat flow) is
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13	$\frac{\partial \theta (x,t)}{\partial t} = \alpha \frac{\partial^2 \theta (x,t)}{\partial x^2}$
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15	The solution for all locations ''x'' and times ''t'' is:
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17	$\theta(x,t) = 1-\text{erf}\left[\frac{x}{2\sqrt{\alpha t}}\right]$
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19	where $\alpha$ is the material's thermal diffusivity.
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22	=== Graphical CDF Tool ===
23	The following is an embedded, active Mathematica CDF tool. The units for $\alpha$ are cm^2^/sec, with corresponding units of cm and sec for ''x'' and ''t'', respectively.
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25	[[File(1Dtransientheat.cdf)]]