Question

Air compressors are sometimes installed in four-wheel drive vehicles to allow for maintaining tyre pressures whilst in the outback. One notable problem with this system is the increase in air temperature during compression, which leads to the heating up of metallic fittings on the compressor and hose, posing a thermal risk to operators. The compressor compresses air isentropically from atmospheric pressure to 300 kPa. The inlet air temperature is 300K.

(a) What is the temperature of the air at the exit of the compressor? [2]

(b) Assume the heat transfer from the air to a stainless steel fitting at the exit of the compressor produces a constant heat flux of 500 W/m² and a convective heat transfer coefficient of 50 W/m²K on the inner surface of the fitting at steady-state operating conditions. The fitting is in the shape of a hollow cylinder (through which the air flows), with inner diameter 10mm and outer diameter 20mm.

1. Draw a thermal circuit for the fitting. What is the total thermal resistance associated with heat transfer from the air to the outer surface of the fitting? [1+3]
2. What is the temperature of the outside surface of the fitting? [2]
3. Is the outside surface of the fitting safe to handle with bare hands? If not, what change would you make to the fitting to make it safe? [2]

Important properties for stainless steel: k = 16 W/mK, density = 7820 kg/m³, c_p = 0.466 kJ/kg.K

Important properties for air: c_p = 1.1 kJ/kg.K, c_v = 0.8 kJ/kg.K

Answer 1

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