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Flat Plate — Isothermal

Average h and heat rate from an isothermal flat plate in free-stream flow.

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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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Results are indicative

Figures assume typical conditions and the stated method. For measured, guaranteed numbers on your plant, our engineers run site surveys, heat loss audits, and full process models.

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Flat Plate in Forced Convection — Isothermal

Calculates the average convective heat transfer coefficient and total heat rate for a flat plate held at a uniform surface temperature in a uniform free-stream flow. The correlation automatically switches between laminar and mixed (laminar–turbulent) regimes based on the Reynolds number.

Film Temperature

Fluid properties are evaluated at the film temperature:

Tf=2Ts+T

Reynolds Number

ReL=μρUL=νUL

Nusselt Number

For laminar flow (Re_L < 5 × 10⁵):

Nu=0.664ReL0.5Pr1/3

For mixed (laminar–turbulent) flow (Re_L ≥ 5 × 10⁵):

Nu=(0.037ReL0.8871)Pr1/3

The constant 871 accounts for the laminar leading-edge section before the turbulent boundary layer develops.

Heat Transfer Coefficient and Heat Rate

h=LNuk Q=hA(TsT),A=L×W

Validity

  • Prandtl number range: 0.6 – 50 (gases and light liquids).
  • Not suitable for liquid metals (Pr ≪ 1) or heavy oils / silicones (Pr ≫ 50).

References

  • Schlichting, H., Boundary Layer Theory, 7th ed., McGraw-Hill, 1979.
  • Schultz-Grunow, F., Luftfahrtforschung, vol. 17, p. 239, 1940.
  • Holman, J.P., Heat Transfer, 7th ed., McGraw-Hill, 1990.
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Frequently asked questions

Average h and heat rate from an isothermal flat plate in free-stream flow. 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.