Air at 16°C and atmospheric pressure enters a 1.25-cm-ID tube at 30 m/s. For an average wall temperature of 100°C, determine the discharge temperature of the air and the pressure drop if the pipe is (a) 10-cm-long and (b) 102-cm-long.

Question

GIVEN

• Atmospheric air flowing through a tube

• Entering air temperature (Tb,in) = 16°C

• Tube inside diameter (D) = 1.25 cm = 0.0125 m

• Air velocity (V) = 30 m/s

• Average wall surface temperature (Ts) = 100°C

FIND

The discharge temperature (Tb,out) and the pressure drop (?p) if the pipe length (L) is

(a) 10 cm (0.1 m) (b) 102 cm (1.02 m)

ASSUMPTIONS

• Steady state

• The tube is smooth

SKETCH



for dry air at the entering bulk temperature of 16°C

Density (?) = 1.182 kg/m3

Thermal conductivity (k) = 0.0248 W/(m K)

Kinematic viscosity (?) = 15.3 × 10–6 m2/s

Prandtl number (Pr) = 0.71

Specific heat (c) = 1012 J/(kg K)

Answer 1

The discharge temperature will first be calculated using air properties evaluated at the entering

temperature and will then be recalculated using the average bulk air temperature of the first iteration

to evaluate the air properties.

The Reynolds number is



(a) L/D = 0.1 m/0.0125 m = 8 < 20. The Dittus-Boelter correlation will be used to

calculate the fully developed Nusselt number





The outlet temperature is given be



Performing another iteration



(b) The friction factor,



The pressure drop is given



Pa

For L = 1.02 m, L/D = 1.02m/0.0125 m = 81.6 > 60. Therefore, the analysis is the same as above.

From the first iteration, the heat transfer coefficient (hc,fd) = 129.2 W/(m2 K).





Performing another iteration





COMMENTS

Note that by increasing the length of the pipe by a factor of 10 leads to a temperature rise increase of

about 350% and a pressure drop increase of about 875%