A slab has a thermal diffusivity of (5 times 10^{-6} mathrm{~m}^{2} / mathrm{s}) and is fairly thick.

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A slab has a thermal diffusivity of \(5 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\) and is fairly thick. The initial temperature is \(300 \mathrm{~K}\) and the surface temperature is raised to \(600 \mathrm{~K}\) at time zero. Find the temperature \(0.5 \mathrm{~m}\) below the surface after one hour has elapsed.

Also find the depth to which the heat front has penetrated.

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