Natural Convection (Rayleigh/Grashof) Calculator mechanism

Model scope

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.

• 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.

Units and conventions

• 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.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

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.

Other records

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