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.

Question

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)

Answer 1

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.