Source: https://guthlabs.ai/docs/instruments/convection-coefficient-nu-correlation-estimator/mechanism/

instrument mechanism / verified-clean

# Convection Coefficient (Nu Correlation) Estimator mechanism

The inspectable method record for Convection Coefficient (Nu Correlation) Estimator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The supplied correlations are standard but the instrument is not fully specified for all advertised geometries. Verdict is NEEDS_REVIEW because local-versus-average flat-plate output, Dittus-Boelter heating/cooling exponent, property-reference temperature, and cylinder/sphere correlations are ambiguous or missing. The requested honest label of correlation-dependent accuracy of approximately plus or minus 10-25 percent is reasonable only within each correlation's applicability range; it should not imply validity outside those ranges.

- Nu=hL/k is the standard definition of the Nusselt number, provided L is the same characteristic length used by the selected correlation and k is evaluated at a stated reference temperature.

- Nu=0.664 Re_L^0.5 Pr^(1/3) is the standard local laminar flat-plate correlation for a smooth plate with constant properties and zero pressure gradient; the average-from-leading-edge laminar correlation is instead Nu_L=1.328 Re_L^0.5 Pr^(1/3). The instrument must state whether local or average h is intended.

- The flat-plate laminar correlation requires an applicable laminar Reynolds-number range, commonly Re_L less than approximately 5.0e5 for a smooth plate. Transition, roughness, pressure gradient, and leading-edge effects are not specified.

- Dittus-Boelter Nu=0.023 Re_D^0.8 Pr^n is an approximate correlation for fully developed turbulent flow in a smooth circular tube with approximately constant properties. It generally requires Re_D above about 1.0e4 and an appropriate Prandtl-number range.

- The Dittus-Boelter exponent n is not specified: n=0.4 is conventionally used for heating the fluid and n=0.3 for cooling the fluid. The heat-transfer direction must be an explicit input.

- The geometry picker lists cylinders and spheres, but no cylinder or sphere correlation is supplied. Those selections cannot produce a verified result from this specification.

## Units and conventions

- Velocity is converted to m/s, characteristic length to m, k to W/(m*K), and kinematic viscosity nu to m^2/s.

- Re=VL/nu for the flat plate and Re=VD/nu for the circular pipe.

- Pr is dimensionless and supplied directly by the fluid-property table; equivalently Pr=nu/alpha when thermal diffusivity is available.

- For the flat plate, L is the distance from the leading edge and the reported value uses the local correlation Nu_x=0.664 Re_x^0.5 Pr^(1/3).

- For the pipe, D is the inside diameter and h is based on Nu_D=0.023 Re_D^0.8 Pr^0.4, assuming fluid heating.

- The tabulated properties are treated as exact inputs for these test calculations, although real-property uncertainty and interpolation uncertainty remain.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "geometry": "flat_plate",
    "fluid": "air",
    "temperature_C": 20,
    "velocity_m_per_s": 10,
    "characteristic_length_m": 0.5,
    "correlation": "local laminar flat plate",
    "property_reference_temperature": "20 C"
  },
  "expected_outputs": {
    "Re": 332005.31,
    "Pr": 0.707,
    "Nu": 340.84,
    "h_W_per_m2_K": 17.52
  },
  "reference_data": {
    "temperature_C": 20,
    "air_kinematic_viscosity_m2_per_s": 0.00001506,
    "air_thermal_conductivity_W_per_m_K": 0.0257,
    "air_Prandtl_number": 0.707,
    "source_convention": "widely tabulated standard value; Incropera heat-transfer textbook air-properties table"
  },
  "working": "Re=VL/nu=(10 m/s)(0.5 m)/(1.506e-5 m^2/s)=5/(1.506e-5)=332005.31. sqrt(Re)=sqrt(332005.31)=576.20. Pr^(1/3)=0.707^(1/3)=0.89085. Nu=0.664(576.20)(0.89085)=340.84. h=Nu*k/L=(340.84)(0.0257 W/(m*K))/(0.5 m)=17.52 W/(m^2*K)."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The zero-characteristic-length input produces h=0/0 and must be rejected. The signed-velocity probe also exposes an implementation hazard: directly raising negative Re to the fractional power 0.8 produces an undefined real-valued result, so velocity magnitude handling must be explicit.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/convection-coefficient-nu-correlation-estimator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/convection-coefficient-nu-correlation-estimator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/convection-coefficient-nu-correlation-estimator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche7/tranche7-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`