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  "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"
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  "limitations": [
    "Plane wall; 1-D; shared A; SI K/W",
    "R_i = L_i/(k_i A); optional films 1/(h A); Q=ΔT/R when ΔT is given",
    "Not Fourier/Newton Q (see /calc/physics/heat-transfer)",
    "Not lumped R-network (see /calc/physics/thermal-resistance)",
    "Not heatsink θJC/θSA, not steam, not cylindrical"
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  "boundary_conditions": [
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    "k, L, A, or h ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "layers[] with k1/L1, or k/L, or R1, or h → MIXED_INPUT_ENCODING",
    "heat-transfer, heatsink, radiation, steam, series, or cylindrical as mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "Incropera, F.P. and DeWitt, D.P. Fundamentals of Heat and Mass Transfer",
      "section": "Composite walls",
      "supports": "Plane multilayer wall; R_i = L_i/(k_i A); film resistances 1/(h A); series combination; Q = ΔT/R",
      "kind": "reference"
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    {
      "title": "ISO 80000-5 — Thermodynamics",
      "section": "Heat rate and temperature difference",
      "url": "https://www.iso.org/standard/30675.html",
      "supports": "Q is heat rate; R relates ΔT to Q",
      "kind": "standard"
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        "L1": 0.5,
        "k2": 0.5,
        "L2": 0.2,
        "A": 2
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        "mode": "plane",
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        "n": 2
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      "actual": {
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        "R": 0.45,
        "A": 2,
        "layers": [
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            "k": 1,
            "L": 0.5,
            "R": 0.25
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            "R": 0.2
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        "A": 2,
        "dT": 10
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        "Q": 22.22222222222222
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      "actual": {
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        "R": 0.45,
        "A": 2,
        "layers": [
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            "L": 0.5,
            "R": 0.25
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            "L": 0.2,
            "R": 0.2
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        "dT": 10,
        "Q": 22.22222222222222
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        "k2": 0.5,
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        "A": 2,
        "h_in": 10,
        "h_out": 20
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        "R_in": 0.05,
        "R_out": 0.025
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      "actual": {
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        "A": 2,
        "layers": [
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            "L": 0.5,
            "R": 0.25
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            "L": 0.2,
            "R": 0.2
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        "model": "composite_wall",
        "h_in": 10,
        "R_in": 0.05,
        "h_out": 20,
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      "tol": 1e-12
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    {
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      "inputs": {
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        "A": 2
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        "R": 0.45,
        "A": 2,
        "layers": [
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            "R": 0.25
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            "R": 0.2
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        "n": 2,
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      "tol": 1e-12
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    {
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      "ok": true,
      "kind": "boundary",
      "inputs": {
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        "A": 2
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      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "composite wall needs at least two layers (k, L). A single slab is thermal-resistance"
    },
    {
      "id": "boundary-cw-k0",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "k1": 0,
        "L1": 0.5,
        "k2": 0.5,
        "L2": 0.2,
        "A": 2
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "k1 must be greater than zero"
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      "ok": true,
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        "L1": 0.5,
        "k2": 0.5,
        "L2": 0.2,
        "A": 2,
        "k": 1,
        "L": 0.5
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      "expectError": "MIXED_INPUT_ENCODING",
      "code": "MIXED_INPUT_ENCODING",
      "error": "Use k1/L1 layer list. A single slab is thermal-resistance"
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    {
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        "k2": 0.5,
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        "R1": 0.25,
        "R2": 0.2
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