A long stainless-steel rod of 50-mm diameter is heated to a uniform temperature of = 727 before being exposed to a fluid flowing with = 1.5 m/s at = 527 in a large room whose walls are also at = = 527 . (a) The average Nusselt number for the circular cylinder in cross flow is = 0.193 0.6181/3 . Properties of the fluid are = 0.02 W/mK, = 0.7 and = 1.5 105 m2 /s. Determine the average convection coefficient, , at the start of the cooling process. (b) If the stainless steel is black, examine if it is valid to linearize the radiation heat transfer. If valid, what is the effective radiation heat transfer coefficient, , at the start of the process? (c) Assuming a constant cumulative (radiation plus convection) heat transfer coefficient corresponding to the results of parts (a) and (b), i.e., = + , how many hours will it take for the center-line temperature of the rod reach 627 ? Properties of the steel are = 25 W/mK and = 5.2 106 m2 /s