Source: https://guthlabs.ai/docs/instruments/natural-convection-rayleigh-grashof-calculator/

instrument / verified-clean

# Natural Convection (Rayleigh/Grashof) Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/natural-convection-rayleigh-grashof-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/natural-convection-rayleigh-grashof-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/natural-convection-rayleigh-grashof-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/natural-convection-rayleigh-grashof-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Thermodynamics, Fluids & Aero

**Tranche**: tranche-7

**Evidence ID**: t7-062

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The Grashof and Rayleigh algorithms are standard, but the instrument specification is incomplete because it does not define geometry/orientation, the exact Nusselt correlation, validity range, boundary condition, property reference temperature, or the sign convention for ΔT. The vectors use SI units, a vertical isothermal plate, and the all-range Churchill–Chu correlation. The honest label 'correlation-based estimate' is appropriate but should be expanded to disclose these assumptions.

### Formula and scope findings

- The Grashof and Rayleigh formulas are standard for natural convection: Gr = gβΔTL^3/ν^2 and Ra = Gr·Pr.

- The specification does not identify which Nusselt correlation is used. The test vectors assume the all-range Churchill–Chu correlation for an isothermal vertical plate: Nu_L = [0.825 + 0.387Ra_L^(1/6)/(1 + (0.492/Pr)^(9/16))^(8/27)]^2.

- Geometry and orientation are underspecified. Churchill–Chu in this form applies to a vertical isothermal plate with characteristic length measured vertically; cylinders, horizontal plates, enclosures, and other geometries require different correlations.

- The applicable Rayleigh-number range and flow-regime constraints are not stated. Correlation validity depends on geometry, surface boundary condition, and Ra range.

- The property-evaluation temperature is not specified. Fluid properties should normally be evaluated at the film temperature T_f = (T_surface + T_bulk)/2, or at a clearly documented alternative.

- The meaning of ΔT is not stated as an absolute temperature difference. ΔT must be nonnegative for the magnitude-based Grashof/Rayleigh calculation; signed ΔT requires an explicitly defined buoyancy-direction convention.

### Unit assumptions

- All calculations use SI units: g in m/s^2, β in 1/K, ΔT in K, L in m, ν in m^2/s, k in W/(m·K), and h in W/(m^2·K).

- A temperature difference of 1 K equals a temperature difference of 1 °C.

- Pr is dimensionless and is supplied by the fluid-property table.

- The characteristic length L is the vertical plate height.

- The heat-transfer coefficient is calculated from h = Nu_L·k/L.

- The tabulated properties in the vectors are treated as already evaluated at the appropriate film temperature.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The specification does not define invalid-input handling for zero viscosity, and the signed-temperature convention can produce a negative Rayleigh number that is invalid for fractional-power correlations unless an absolute-value convention is explicitly applied. The piecewise branch assumption also creates a discontinuous Nu result at Ra=10^9.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "geometry": "vertical isothermal plate",
    "correlation": "all-range Churchill-Chu",
    "fluid": "water",
    "delta_T_K": 0,
    "L_m": 1,
    "g_m_per_s2": 9.80665,
    "beta_per_K": 0.000207,
    "nu_m2_per_s": 0.000001004,
    "Pr": 7.02,
    "k_W_per_mK": 0.598
  },
  "expected_outputs": {
    "Gr": 0,
    "Ra": 0,
    "Nu": 0.68,
    "h_W_per_m2K": 0.40664
  },
  "reference_data": {
    "g_m_per_s2": 9.80665,
    "g_source_convention": "CODATA standard gravity",
    "water_beta_per_K_at_20C": 0.000207,
    "water_beta_source_convention": "widely tabulated standard value",
    "water_kinematic_viscosity_m2_per_s_at_20C": 0.000001004,
    "water_kinematic_viscosity_source_convention": "widely tabulated standard value",
    "water_Pr_at_20C": 7.02,
    "water_Pr_source_convention": "widely tabulated standard value",
    "water_k_W_per_mK_at_20C": 0.598,
    "water_k_source_convention": "widely tabulated standard value"
  },
  "working": "Gr = (9.80665 × 0.000207 × 0 × 1.0^3)/(1.004×10^-6)^2 = 0. Ra = 0 × 7.02 = 0. Churchill–Chu: Nu = [0.825 + 0.387×0^(1/6)/(1 + (0.492/7.02)^(9/16))^(8/27)]^2 = 0.825^2 = 0.680625, reported as 0.68. h = Nu×k/L = 0.68×0.598/1.0 = 0.40664 W/(m^2·K). This is an edge case: the correlation returns a finite conduction-like Nu at Ra = 0, although there is no buoyancy-driven convection."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

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

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

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

- `BOUNDARY_HAZARD_CATALOG.json`