The equation has been proposed by Hausen for the transition range (2300 < Re < 8000) as well as for higher Reynolds numbers. Compare the values of Nu predicated by Hausen’s equation for Re = 3000 and Re = 20,000 at D/L = 0.1 and 0.01 with those obtained from Gnielinski correlation. Assume the fluid is water at 15°C flowing through a pipe at 100°C.

Question

GIVEN

• Water flowing through a pipe

• The Hausen correlation given above

• Water temperature = 15°C

• Pipe temperature = 100°C

FIND

• The Nusselt number using the Hausen correlation and appropriate equations and charts in the text for Re = 3000 and 20,000 and D/L = 0.1 and 0.01

ASSUMPTIONS

• Steady state

• Constant and uniform pipe temperature

SKETCH



PROPERTIES AND CONSTANTS

for water at 15°C

Absolute viscosity (?b) = 1136 × 10–6 (Ns)/m2

Prandtl number (Pr) = 8.1 At 100°C ?s = 277.5 × 10–6 (Ns)/m2

Prs= 1.75

Answer 1

For Re = 3000, D/L = 0.1 the flow is in the transition region. In addition, L/D = 10. Therefore, the flow is not fully developed. The “short duct approximation” curve in the text will be used to estimate the Nusselt number



NuD= 23.

For Re = 3000, D/L = 0.01, the flow is fully developed and the Nusselt number will be estimated by

Gnielinski correlation,



NuD

is calculated for other Re and L/D ratio as per above equation and tabulated below.

For Re = 20,000, D/L = 0.1, the flow is turbulent, not fully developed. The fully developed Nusselt

number can be estimated



Correcting this for the entrance effect



Applying the Hausen correlation to the remaining cases and comparing them to the results from the

text yields the following



COMMENTS

Note that the large difference in Case 2 is probably due to the use of a laminar correlation from the

text when the flow is transitional. There are large variations in flow and heat transfer in this regime

and it is usually avoided by good designers.