A large block of steel with a thermal conductivity of (40 mathrm{~W} / mathrm{m}^{circ} mathrm{C}) and a

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A large block of steel with a thermal conductivity of \(40 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}\) and a thermal diffusivity of \(1.5 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s}\) is initially at a uniform temperature of \(25^{\circ} \mathrm{C}\). The surface is exposed to

(a) A heat flux of \(3 \times 10^{5} \mathrm{~W} / \mathrm{m}^{2}\);

(b) Sudden rise in surface temperature of \(200^{\circ} \mathrm{C}\) Calculate the temperature at a depth of \(1 \mathrm{~cm}\) after a time of 10 seconds for both cases. Verify the results with analytical results.

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