Question: 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.