Transient Conduction (Lumped Capacitance) Calculator mechanism

Model scope

The core lumped-capacitance formula is correct, and the four numerical checks agree with it. Verdict is NEEDS_REVIEW because the specification claims validity only when Bi<0.1 but does not provide thermal conductivity or sufficient geometry/surface-area information to calculate Bi, and it does not state the inverse time-to-target formula or its domain constraints.

• The lumped-capacitance temperature relation is standard: T(t)=T∞+(Ti−T∞)exp(−t/τ), with τ=ρVc/(hA).
• For the advertised time-to-target output, the inverse formula is missing: t=−τ ln((Ttarget−T∞)/(Ti−T∞)). It is valid only when the ratio is positive and the target lies strictly between Ti and T∞; the target equal to T∞ is reached only asymptotically.
• A must be the convective heat-transfer surface area and must be consistent with the volume V. Using an arbitrary geometric or projected area gives an incorrect time constant.
• The honest-label condition Bi<0.1 cannot be verified from the listed inputs because thermal conductivity k and the characteristic length Lc=V/As are not listed. The instrument should either accept k and geometry/surface area explicitly or clearly state that Bi validation is external.

Units and conventions

• Use a consistent unit system; the vectors below use SI: h in W/(m²·K), A in m², V in m³, ρ in kg/m³, c in J/(kg·K), and time and τ in seconds.
• Temperature differences may be expressed in kelvins or degrees Celsius because both have the same increment; absolute temperatures are shown in °C or K consistently within each vector.
• The fluid temperature T∞ and h remain constant, material properties are constant, there is no internal heat generation, and the body starts at a uniform Ti.
• Bi=hLc/k, with Lc=V/As for the standard lumped-capacitance check and k in W/(m·K).

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "h_W_per_m2K": 25,
    "A_m2": 0.12,
    "V_m3": 0.002,
    "rho_kg_per_m3": 7800,
    "c_J_per_kgK": 500,
    "Ti_C": 100,
    "Tinf_C": 20,
    "time_s": 100,
    "k_W_per_mK": 45,
    "Lc_m": 0.0166666667
  },
  "expected_outputs": {
    "tau_s": 2600,
    "sampled_points": [
      {
        "time_s": 100,
        "T_C": 96.9815
      }
    ],
    "key_curve_features": {
      "initial_temperature_C": 100,
      "long_time_asymptote_C": 20,
      "behavior": "monotonic cooling"
    },
    "Bi": 0.00925926
  },
  "working": "ρVc=7800×0.002×500=7800 J/K. hA=25×0.12=3 W/K. τ=7800/3=2600 s. t/τ=100/2600=0.0384615385. exp(−t/τ)=exp(−0.0384615385)=0.962268715. T=20+(100−20)×0.962268715=20+80×0.962268715=96.9814972 °C≈96.9815 °C. Bi=25×0.0166666667/45=0.00925926."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The instrument can produce an undefined 0/0 result when Ti equals Tinf unless it special-cases equilibrium. It can also return a numerically plausible temperature for Bi >= 0.1 even though the stated lumped-capacitance validity condition is violated. Unlabeled temperature units create an additional convention hazard.

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-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json