A cylindrical aluminium rod 002 m in diameter and 1 m

Question

A cylindrical aluminium rod 0.02 m in diameter and 1 m length is taken out of an oven at 150^oC and cooled in a 3 m/s cross flow of air at 23^oC.

a. Calculate the average convective heat transfer coefficient. Use a correlation that uses properties at film temperature. The properties at the assumed film temperature are given as: v=1.9x10-5 m2/s, k=0.0286 w/(mK), Pr=0.707.

b. We want to know how long it will take for the rod to cool to 50^oC so that it can be handled. Assuming that h=37 W/(m2K), can this problem be solved using lumped capacitance technique? Aluminium properties are given as: k=237 W/(mK), p=2702 Kg/m3, Cp= 903 J/(KgK). Using lumped capacitance technique, calculate how long it will take the rod to cool to 50^oC.