Source: https://guthlabs.ai/docs/instruments/transient-conduction-lumped-capacitance-calculator/implementation/

instrument implementation / implementation-contract

# Transient Conduction (Lumped Capacitance) Calculator implementation

A source-bound implementation contract for Transient Conduction (Lumped Capacitance) Calculator; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t6-025

**Effect**: Computation or source lookup only

## Input and validation requirements

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.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "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."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/transient-conduction-lumped-capacitance-calculator/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/transient-conduction-lumped-capacitance-calculator/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/transient-conduction-lumped-capacitance-calculator/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-tranche6/tranche6-results.json`