Fully-Developed Tube Flow
Calculates the convective heat transfer coefficient for hydrodynamically and thermally fully-developed flow inside a smooth circular tube.
Film Temperature
Fluid properties are evaluated at the film temperature (average of wall and bulk):
Tf=2Tw+TbReynolds Number
ReD=μρumDNusselt Number
Laminar flow (Re < 2 300) — uniform heat flux boundary:
Nu=4.36Turbulent flow (2 300 ≤ Re < 5 × 10⁶):
f=(0.79lnRe−1.64)−2 Nu=1+12.7f/8(Pr2/3−1)(f/8)(Re−1000)PrThis is the Gnielinski correlation, valid for 0.5 < Pr < 2 000.
Heat Transfer Coefficient and Heat Rate
h=DNu⋅k Q=h⋅(πDL)⋅(Tw−Tb)Validity
- Reynolds number: laminar < 2 300; turbulent 2 300 – 5 × 10⁶
- Prandtl number: 0.5 – 2 000
- Smooth tube; fully-developed both hydrodynamically and thermally
- Transition region (2 300 < Re < 10 000) predictions are approximate
References
- Gnielinski, V., Int. Chem. Eng., 16, 359, 1976.
- Incropera, F.P. and DeWitt, D.P., Fundamentals of Heat and Mass Transfer, 3rd ed., John Wiley & Sons, eq. 8.53, 8.63a & 8.63b, 1990.