Quenching of a steel billet, a cylindrical steel billet 1 ft in diameter and 3 ft long, initially at 1000°F, is quenched in oil. Assume that the surface of the billet is at 200°F during the quenching process. The steel has the following properties, which may be assumed to be independent of the temperature: k = 25 Btu/hr ∙ ft ∙ F, p = 7.7g/cm³ and C_p = 0.12 cal/g ∙ C. Estimate the temperature of the hottest point in the billet after five minutes of quenching. Neglect end effects; that is, make the calculation for a cylinder of the given diameter but of infinite length. See Problem 12C.1 for the method for taking end effects into account.