Dry, compressed air at Tm$,$i $=75$C$,$ P$=10$atm, with a mass flow rate of m $=0\mathrm{.}001$ kg$/$s$,$ enters a $0\mathrm{.}03-$m$-$diameter, $5-$m$-$long tube whose surface is at Ts $=25$C$.$

a$.)$ Determine the thermal entry length, the mean temperature of the air at the tube outlet, and the total rate of heat transfer from the air to the tube wall. For this part, calculate h assuming fully developed laminar flow in the entire tube. Evaluate fluid properties using average of Tm$,$i and Ts$.$

b$.)$ Determine the thermal entry length, the mean temperature of the air at the tube outlet, and the total rate of heat transfer from the air to the tube

wall. For this part, treat the entry region and the fully developed regions separately to calculate h$.$ Evaluate fluid properties using average of Tm$,$i and Ts$.($Hint: for entry region, you will need to use eqns. $8\mathrm{.}56$ and $8\mathrm{.}57$ from $(8$th Ed$.)$

c$.)$ Compare the heat transfer rates from parts $($a$)$ and $($b$)$ and explain why they are different?

PLEASE ANSWER EVERY PART OF THE QUESTION SHOWING ALL WORK AND PROVIDING CORRECT NUMERICAL ANSWER.