CVP verified calculation capability

Composite wall Calculation Capability

Plane composite wall from a layer list. R_i = L_i/(k_i A), optional films 1/(h A), R = R_in + ΣR_i + R_out. Optional Q=ΔT/R. Not Fourier/Newton Q, not lumped R-network, not heatsink θ, not steam, not cylindrical.

Physics · Thermo Capability ID physics.thermo.composite_wall version 1.0.0 CVP VERIFIED CURRENT Engineering

Model

Layer

Layer: R_i = L_i / (k_i A)
Film: R = 1 / (h A)
Wall: R = R_in + Σ R_i + R_out
Heat rate: Q = ΔT / R

Modes: plane

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`A`	Shared face area in m²	—	input / output
`k1`	Layer 1 conductivity in W/	—	input
`L1`	Layer 1 thickness in m	—	input
`k2`	Layer 2 conductivity in W/	—	input
`L2`	Layer 2 thickness in m	—	input
`layers`	Layer list {k, L}	—	input / output
`h_in`	Optional inner film coefficient in W/	—	input / output
`h_out`	Optional outer film coefficient in W/	—	input / output
`dT`	Optional temperature difference in K	—	input / output
`R`	—	—	output
`Q`	—	—	output
`n`	—	—	output
`R_in`	—	—	output
`R_out`	—	—	output
`model`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Plane composite wall; 1-D; shared A; R_i = L_i/(k_i A)
Optional films R = 1/(h A); series only; Q=ΔT/R
Not Fourier/Newton Q pages
Not lumped R-network, not heatsink θ, not steam, not cylindrical

Not supported

Fourier/Newton Q as the primary product
lumped R-network of already-computed R
heatsink θJC/θSA
steam
cylindrical/spherical walls
radiation
transient Zth
CFD

Example

One numerical check. The calculator page holds worked steps and FAQ.

k1=1 L1=0.5 k2=0.5 L2=0.2 A=2 → R=0.45 K/W

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Plane wall R = Σ L_i/(k_i A), optional films 1/(h A), optional Q = ΔT/R, + O3 mpmath tabulated resistance.. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Plane wall R = Σ L_i/(k_i A), optional films 1/(h A), optional Q = ΔT/R, + O3 mpmath tabulated resistance.· View Manifest · CVP overview · Specification
Verified scope: Plane wall R = Σ L_i/(k_i A), optional films 1/(h A), optional Q = ΔT/R, + O3 mpmath tabulated resistance.
Assurance: Engineering
Declared partition coverage: PASS · 7/7 declared partitions (films, alias, layers, heat, awkward, default, invalid-domain)
Deferred: Not a lumped R-network, not cylindrical, and not radiation.
Calculation version: 1.0.0
Verification: 14/14 calculation tests · 1/1 legacy golden · 8/8 legacy boundary · 5/5 legacy property
Production surface contract: 6/6
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-25.o2-o3
Verification revision: 2026-09-25.o2-o3 · 1/1 property · digest d63c309b6b4c
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: plane composite wall vs a separate-module identity (≤2 ULP). Not a lumped R-network and not cylindrical. ≤2 ULP vs O3 applies only to the published tabulated composite-wall vectors. Not radiation and not a heatsink.
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
CVP suite: 3/3 golden · 7/7 CVP boundary · 7/7 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.0 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 6/6.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/composite-wall' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"k1":1,"L1":0.5,"k2":0.5,"L2":0.2,"A":2},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "k1": 1,
    "L1": 0.5,
    "k2": 0.5,
    "L2": 0.2,
    "A": 2
  },
  "calculation_version": "1.0.0"
}

POST /api/v1/calc/composite-wall. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: composite-wall
Engine: composite-wall
REST: POST /api/v1/calc/composite-wall
MCP: execute_calculation with capability_id: "physics.thermo.composite_wall"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Incropera, F.P. and DeWitt, D.P. Fundamentals of Heat and Mass Transfer — Composite walls
ISO 80000-5 — Thermodynamics — Heat rate and temperature difference

Reference evidence classes: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"physics.thermo.composite_wall"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: execute_calculation' \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"physics.thermo.composite_wall","inputs":{"k1":1,"L1":0.5,"k2":0.5,"L2":0.2,"A":2},"calculation_version":"1.0.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.0.0) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.