$(30$ points$)$ see Figure $1$ below $-$ In support of disaster relief following a hurricane, you seek to

retrofit a first responder vehicle with enhanced air conditioning. In doing so$,$ you must route the

air conditioning ductwork through a section of the powerplant compartment where it is exposed

to high external ambient temperatures. This exposed section of duct heats the cooled air and

reduces the overall effectiveness of the passenger compartment cooling system. Due to space

restrictions, the galvanized steel duct is not insulated. Assume the surface temperature of the

duct is that of the external ambient air in the engine compartment, and use properties for air at

$300$ K

a$.$ Calculate the hydraulic diameter for the ductwork $m.$

b$.$ Is the flow is laminar or turbulent? Explain.

c$.$ Find the air temperature $C$ as it enters the crew compartment $($exiting the ductwork$).$

d$.$ Calculate the rate of heating $W$ to the section of duct.