Engine oil flows at a rate of 0.5 kg/s through a 2.5-cm-ID tube. The oil enters 25°C while the tube wall is at 100°C. (a) If the tube is 4-m-long. Determine whether the flow is fully developed. (b) Calculate the heat transfer coefficient.

Question

GIVEN

• Engine oil flows through a tube

• Mass flow rate (m

) = 0.5 kg/s

• Inside diameter (D) = 2.5 cm = 0.025 m

• Oil temperature at entrance (Ti) = 25°C

• Tube surface temperature (Ts) = 100°C

• Tube length (L) = 4 m

FIND

(a) Is flow fully developed? (b) The heat transfer coefficient (hc) ASSUMPTIONS

• Steady state

SKETCH

Answer 1

The Reynolds number is



Therefore, the flow is laminar.

(a) The entrance length at which the velocity profile approaches its fully developed shape is given



Therefore, the velocity profile is fully developed for 98.8% of the tube length.

The entrance length at which the temperature profile approaches its fully developed shape is given by



Therefore, the temperature profile is not fully developed.

(b) Since the velocity profile is fully developed but the temperature profile is not, will be

used to estimate the Nusselt number



Using the ‘parabolic velocity’ curve NuD k= 4.8



COMMENTS

The rate of heat transfer calculated with the heat transfer coefficient at the inlet is



The outer temperature (To) is given by



This small temperature change does not warrant another iteration. If the temperature change was

larger, the fluid properties would need to be re-evaluated at the average bulk temperature and a new

heat transfer coefficient calculate.