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Developing Tube Flow

Mean h for combined-entry-length (developing) laminar or turbulent flow in a smooth tube.

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In turbulent flow h scales with velocity to the power 0.8 — doubling the air speed buys you roughly 75% more heat transfer, not double.

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Developing Tube Flow (Combined Entry Length)

Calculates the mean heat transfer coefficient along the length of a tube from an abrupt square entry, where both the velocity and temperature profiles are still developing.

Film Temperature

Tf=2Tw+Tb

Reynolds Number

ReD=μρumD

Laminar Developing Flow (Re < 2 300)

Define the entry-length parameter:

ξ=(L/DRePr)1/3
  • If ξ ≥ 2 (thermally developing): Num=1.86ξ(μ/μw1)
  • If ξ < 2 (effectively fully developed): Num=3.66

The viscosity ratio μ/μ_w is assumed unity (appropriate for gases and near-ambient liquids).

Turbulent Developing Flow (Re ≥ 2 300)

Gnielinski fully-developed Nu:

f=(0.79lnRe1.64)2 Nudev=1+12.7f/8(Pr2/31)(f/8)(Re1000)Pr

Entry-length correction (Incropera eq. 8.57):

Num=Nudev(1+(L/D)0.6762.4254)

The entry factor is validated for Pr ≈ 0.7 (air).

Heat Transfer Coefficient and Heat Rate

h=DNumk,Q=h(πDL)(TwTb)

Validity

  • Laminar: 0.48 < Pr < 16 700
  • Turbulent: 0.5 < Pr < 2 000, Re < 5 × 10⁶
  • Entry correction for turbulent regime validated for Pr ≈ 0.7 (air); apply with caution for other fluids

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. 8.57, 8.63a & 8.63b, 1990.
  • Rohsenow, W.R., Hartnett, J.P. and Cho, Y.I., Handbook of Heat Transfer, 3rd ed., McGraw-Hill, 1998, p. 5.29.
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Frequently asked questions

Mean h for combined-entry-length (developing) laminar or turbulent flow in a smooth tube. Enter your inputs and press Calculate — the worked solution shows every step of the method with your numbers substituted in.

Fluid properties like viscosity and conductivity change strongly with temperature, so correlations specify evaluating them at the film temperature — the average of the surface and free-stream (or wall and bulk) temperatures. The calculator does this automatically through its built-in property database.

The underlying correlations are empirical fits to experimental data; ±10–25% is typical depending on geometry and Reynolds range. Treat the outputs as sizing estimates — for guaranteed numbers on a specific piece of plant, measurement or validated CFD is the next step.