$327$MAE$/4$

Question $1$

a$)$ A cylindrical bar $20$ mm in diameter projects $150$ mm into an air stream which has a velocity of $40\frac{m}{s}$ and is at a temperature of $427C,$ and a pressure of $1$ atmosphere. If the root of the bar is cooled to $210C,$ calculate the heat transfer through the root if the thermal conductivity $(k)$ of the bar is $80{10}^{-3}k\frac{W}{m}K.$ The heat transfer coefficient between the bar and the air may be obtained from

${}_d=0\mathrm{.}2R_{de}^{0\mathrm{.}8}$

$(24$ marks$)$