Calculate the Nusselt number and the convection heat transfer coefficient for water at a bulk temperature of 32°C flowing at a velocity of 1.5 m/s through a 2.54-cm-ID duct with a wall temperature of 43°C. Use the Gnielinski correlation and two other correlations given in te text and cmpare the results.

Question

GIVEN

• Water flowing through a duct

• Bulk water temperature (Tb) = 32°C

• Water velocity (V) = 1.5 m/s

• Inside diameter of duct (D) = 2.54 cm = 0.0254 m

• Duct wall surface temperature (Ts) = 43°C

FIND Use three different methods to find (a) The Nusselt number (NuD)

(b) The convective heat transfer coefficient (hc)

ASSUMPTIONS

• Steady state

• Fully developed, incompressible flow

SKETCH



PROPERTIES AND CONSTANTS

for water at a reference temperature equal to the bulk temperature (Tref = 32°C)

Thermal conductivity (k) = 0.619 W/(m K)

Kinematic viscosity (?) = 0.773 × 10–6 m2/s

Prandtl number (Prb) = 5.16

Absolute viscosity (?b) = 763 × 10–6 (Ns)/m2

Prandtl number at surface temperatue(Prs) = 4.06 At the surface temperature of 43°C:

Absolute viscosity (?s) = 626.3 × 10–6 (Ns)/m2

Answer 1

The Reynolds number is



Therefore, the flow is turbulent.

(a) Therefore, the flow is turbulent. Three different correlations that can be used to calculate the

Nusselt number are contained in

1. The Gnielinski correlation

2. The Sieder and Tate

3. The Petukhov-Popov







(b) The heat transfer coefficient is given by



COMMENTS

The Nusselt numbers vary by about 8% around the average value of 266. This is within the accuracy

of empirical correlations.