A cylindrical mild steel billet, 3 cm OD by 10 cm long, initially at 500 °C, is plunged into a large container filled with oil at 100 °C. The average heat transfer coefficient between the steel and oil is 500 W/m2 ∙K. Find the time required to cool (a) the center and (b) the surface of the billet to 250 °C. Assume that (i) the billet is lumped, (ii) the billet is not lumped, and (iii) the billet is very long. Comment on the comparison of these results.

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