Transient Conduction (Lumped Capacitance) Calculator

Inspectable records

Ledger state

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

Area

Thermodynamics, Fluids & Aero

Tranche

tranche-6

Evidence ID

t6-025

Ledger rows

1

No ledger note is attached.

Review findings

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.

Formula and scope findings

• 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.

Unit assumptions

• 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).

Boundary hardening

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.

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": {
    "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."
}

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