Source: https://guthlabs.ai/docs/instruments/lmtd-heat-exchanger-calculator/

instrument / verified-clean

# LMTD Heat Exchanger 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/lmtd-heat-exchanger-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/lmtd-heat-exchanger-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/lmtd-heat-exchanger-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/lmtd-heat-exchanger-calculator/qualification/>)

## Ledger state

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

**Area**: Thermodynamics, Fluids & Aero

**Tranche**: tranche-4

**Evidence ID**: t4-168

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The core LMTD and corrected-duty formulas are standard under their stated assumptions, but the spec is not ready for an unqualified PASS. The exact ΔT1/ΔT2 mapping by arrangement, equal-terminal-difference behavior, F-factor source and validity range, and the additional inputs required for outlet-temperature calculations must be documented. The honest_label field is empty despite the outlet-temperature claim and the dependence of crossflow/multipass results on F-factor data.

### Formula and scope findings

- The LMTD formula is standard, but the specification does not define how ΔT1 and ΔT2 are assigned for counterflow, parallel-flow, crossflow, or multipass arrangements.

- The claimed outlet-temperature calculation is under-specified: outlet temperatures require a heat balance plus mass flow rates and specific heats, or equivalent heat-capacity rates; LMTD alone cannot determine them.

- Required-area calculation is claimed but its inverse formula is omitted. It should be A=q/(U·ΔTlm·F).

- The equal-terminal-difference case ΔT1=ΔT2 is not handled. The literal formula becomes 0/ln(1)=0/0, although its limiting value is ΔTlm=ΔT1=ΔT2.

- The formula requires ΔT1 and ΔT2 to be positive and nonzero for a real logarithm; temperature-crossing and zero-terminal-difference cases need explicit handling.

- F is not optional for crossflow or multipass calculations unless F=1 is explicitly justified. F must be supplied or obtained from a defined chart/correlation and normally satisfies 0<F≤1.

### Unit assumptions

- Temperature differences may be expressed in °C or K because their increments are equal, but absolute temperatures must not be substituted directly into the LMTD differences without applying the arrangement-specific terminal-temperature definitions.

- If U is in W/(m²·K), q is in W and A is in m². If U is in kW/(m²·K), q is in kW.

- F is dimensionless.

- For Fahrenheit inputs, temperature differences must be converted to K when U uses K-based SI units; a 1 °F difference is 5/9 K.

- The terminal temperature differences must use a consistent temperature scale and must be positive for the logarithm.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

A plain arithmetic implementation can fail at the removable 0/0 equal-terminal-difference case, produce undefined results or divide by zero when a terminal temperature difference is zero, and return materially different results when flow-arrangement or temperature-unit conventions are not explicit.

## 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": {
    "operation": "heat_duty",
    "arrangement": "counterflow",
    "hot_in_C": 150,
    "hot_out_C": 90,
    "cold_in_C": 30,
    "cold_out_C": 70,
    "U_W_m2K": 500,
    "area_m2": 10,
    "F": 1
  },
  "expected_outputs": {
    "deltaT1_K": 80,
    "deltaT2_K": 60,
    "deltaTlm_K": 69.5212,
    "q_W": 347605.95
  },
  "working": "Counterflow: ΔT1=Th,in−Tc,out=150−70=80 K; ΔT2=Th,out−Tc,in=90−30=60 K. ΔTlm=(80−60)/ln(80/60)=20/ln(4/3)=20/0.287682072=69.5212 K. q=U·A·ΔTlm·F=500·10·69.5212·1=347605.95 W."
}
````

## Related workflows

[Heat-Transfer Pathexchanger method 1](<https://guthlabs.ai/docs/instrument-workflows/heat-path/>)

## 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-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`