A large truck drives down the highway at 10 m/s hauling a rectangular trailer that is 6 m long, 2 m wide, and 2 m tall. The trai
ler contains frozen food and is therefore temperature-controlled. Its external surface can be approximated to be a consistent 15°C, while the outside air is at 20°C. Assume the heat transfer on the front, back, and bottom of the trailer is negligible.
a) How much cooling power must be provided to maintain the temperature controlled trailer? (i.e. What is the total heat transfer rate from the air to the trailer)?b) What is the minimum local heat transfer coefficient on the surface of the trailer? Where does the minimum occur?c) What percentage of the total heat transfer is occuring over a laminar boundary layer?d) If the cooling system can only provide 5 KW of cooling, what is the fastest speed that this truck can drive while still adequately maintaining the temperature within the trailer?
a) How much cooling power must be provided to maintain the temperature controlled trailer? (i.e. What is the total heat transfer rate from the air to the trailer)?b) What is the minimum local heat transfer coefficient on the surface of the trailer? Where does the minimum occur?c) What percentage of the total heat transfer is occuring over a laminar boundary layer?d) If the cooling system can only provide 5 KW of cooling, what is the fastest speed that this truck can drive while still adequately maintaining the temperature within the trailer?
1 answer:
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Answer:
a) Irreversible, b) Reversible, c) Irreversible, d) Impossible.
Explanation:
Maximum theoretical efficiency for a power cycle (), no unit, is modelled after the Carnot Cycle, which represents a reversible thermodynamic process:
(1)
Where:
- Temperature of the cold reservoir, in Kelvin.
- Temperature of the hot reservoir, in Kelvin.
The maximum theoretical efficiency associated with this power cycle is: (,
)
In exchange, real efficiency for a power cycle (), no unit, is defined by this expression:
(2)
Where:
- Heat released to cold reservoir, in kilojoules.
- Heat gained from hot reservoir, in kilojoules.
- Power generated within power cycle, in kilojoules.
A power cycle operates irreversibly for , reversibily for
and it is impossible for
.
Now we proceed to solve for each case:
a) ,
Since , the power cycle operates irreversibly.
b) ,
Since , the power cycle operates reversibly.
c) ,
Since , the power cycle operates irreversibly.
d) Since , the power cycle is impossible.