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Forced Convection

Six forced-convection calculators: flat plates, cylinders and square rods in cross-flow, developing and fully-developed tube flow, and PCB component arrays — average h and heat rate with real fluid properties.

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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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Forced-convection sizing comes down to one question: what is the heat transfer coefficient h? These six tools answer it for the classic external and internal geometries, using the standard engineering correlations with real fluid properties evaluated by an embedded CoolProp property database.

What's in this suite

  • Flat Plate — Isothermal — average h and heat rate for a plate in free-stream flow; switches automatically between laminar and mixed laminar–turbulent regimes at ReL=5×105.
  • Cylinder Cross-Flow — Isothermal — Hilpert's correlation with Reynolds-banded constants, from Re = 0.4 to 400 000.
  • Square Rod Cross-Flow — Isothermal — the square-prism variant (C = 0.102, n = 0.675, face normal to flow).
  • Fully-Developed Tube FlowNu=4.36 in laminar flow; the Gnielinski correlation for 2300Re<5×106.
  • Developing Tube Flow — combined-entry-length treatment from an abrupt square entry, bridging to the fully-developed limit.
  • PCB Component Array — case temperature of surface-mounted components in a forced-air channel, using Will's correlation (h=Gum0.8) with local air-temperature rise, fin efficiency and interface resistance.

Method

All external-flow tools follow the same chain. Fluid properties are evaluated at the film temperature

Tf=2Ts+T

then the Reynolds number fixes the regime, a Nusselt correlation of the form

Nu=CRenPr1/3

gives the dimensionless coefficient, and h=Nuk/L converts it back to W/m²·K. The heat rate is Q=hA(TsT). Internal-flow tools use the bulk-to-wall film temperature and, in the turbulent range, the friction-factor-based Gnielinski form, accurate to roughly ±10% over its stated range.

Assumptions

Uniform surface temperature, uniform free stream, smooth surfaces. Correlations are empirical fits — expect ±10–25% agreement with measurement depending on geometry and Reynolds range. Sources: Holman, Heat Transfer (1990); Incropera & DeWitt, Fundamentals of Heat and Mass Transfer.

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Frequently asked questions

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 tools do this automatically through the built-in property database.

Any fluid in the embedded CoolProp property database — air, water, CO₂ and other common industrial fluids — with density, viscosity, conductivity and Prandtl number evaluated at the film temperature and pressure you set.

The Gnielinski correlation, valid for Reynolds numbers between 2 300 and 5 million, built on the Petukhov friction factor. It is generally accurate to about ±10% and supersedes the older Dittus–Boelter form. Laminar flow uses the exact constant-heat-flux result Nu = 4.36.

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 CFD validated against operating data is the next step.