The intake manifold of an automobile engine can be approximated as a 4-cm-ID tube, 30 cm in length. Air at a bulk temperature of 20°C enters the manifold at a flow rate of 0.01 kg/s. The manifold is a heavy aluminum casting and is at a uniform temperature of 40°C. Determine the temperature of the air at the end of the manifold.
GIVEN
• Air flow through a tube
• Tube inside diameter (D) = 4 cm = 0.04 m
• Tube length (L) = 30 cm = 0.30 m
• Inlet bulk temperature (Tb,in) = 20°C
• Air flow rate (m ) = 0.01 kg/s
• Tube surface temperature (Ts) = 40°C
FIND
• Outlet bulk temperature (Tb,out)
ASSUMPTIONS
• Steady state
• Constant and uniform tube surface temperature
SKETCH
PROPERTIES AND CONSTANTS
for dry air at the inlet bulk temperature of 20°C
Thermal conductivity (k) = 0.0251 W/(m K)
Absolute viscosity (?) = 18,240 × 10–6 (Ns)/m2
Prandtl number (Pr) = 0.71
Specific heat (c) = 1012 J/(kg K)
The Reynolds number is
The Nusselt number for fully developed flow can be estimated from the Dittus-Boelter correlation
Since L/D = 30cm/4 cm = 7.5 < 60, the flow is not fully developed and the fully developed heat
transfer coefficient must be
to determine the outlet air temperature
COMMENTS
The rise in air temperature is not large enough to require another iteration using new air properties at
the average bulk air temperature.
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