Suppose an engineer suggests that air instead of water could flow through the tube and the velocity of the air could be increased until the heat transfer coefficient with the air equals that obtained with water at 1.5 m/s. Determine the velocity required and comment on the feasibility of the engineer’s suggestion. Note that the speed of sound in air at 100°C is 387 m/s.

Question

GIVEN

• Air flow through a tube

• Bulk inlet air temperature (Tb,in) = 93°C

• Tube diameter (D) = 0.015 m

• Tube length (L) = 0.3 m

• Tube surface temperature (Ts) = 204°C

• From Problem 7.32: h ,c L = 13,037 W/(m2 K)

FIND

• The velocity (V) required to obtain h ,c L = 13,037 W/(m2 K)

ASSUMPTIONS

• Steady state

• Constant and uniform tube temperature

SKETCH



PROPERTIES AND CONSTANTS

for dry air at the inlet bulk temperature of 93°C

Thermal conductivity (k) = 0.0302 W/(m K)

Kinematic viscosity (?) = 22.9 × 10–6 m2/s

Prandtl number (Pr) = 0.71

Answer 1

The flow must be turbulent, therefore, the heat transfer coefficient of the fully developed case must be

13,037 W/(m2 K) Therefore, the Nusselt number is



Applying the Dittus-Boelter correlation



Solving for the Reynolds number



Solving for the velocity



This velocity is obviously unrealistic because it corresponds to a Mach number of 30. Under such

conditions when the speed of sound is reached, a shock wave will form and choke the flow.