Cylindrical/Spherical Conduction Resistance Calculator mechanism

Model scope

The two single-layer resistance formulas are standard under the stated steady radial-conduction assumptions, but the specification is incomplete for the claimed multi-layer interface-temperature output. The exact ambiguity requiring review is how layers are ordered and summed, which boundary temperatures are supplied for interface temperatures, and what sign convention is used for q. The empty honest_label field should be populated with these assumptions and limitations before release.

• The cylindrical formula R=ln(r2/r1)/(2πkL) is standard for steady, one-dimensional radial conduction through a cylindrical wall with constant k and no contact resistance.
• The spherical formula R=(1/r1−1/r2)/(4πk) is standard for steady, one-dimensional radial conduction through a spherical shell with constant k and no contact resistance; spherical resistance correctly has no L term.
• The specification does not explicitly provide q=ΔT/R, although that is the standard heat-rate relation once total resistance is known.
• For multiple layers, the required total-resistance formula R_total=ΣR_i is not stated.
• Interface-temperature calculation is claimed but no formula, layer ordering convention, or required boundary temperatures are specified. ΔT alone determines temperature differences, not absolute interface temperatures.
• Required geometric and material constraints are not stated: r2>r1>0, k>0, and L>0 for cylindrical conduction; r2>r1>0 and k>0 for spherical conduction.

Units and conventions

• Use a fully consistent unit system: radii and cylindrical length L in metres, k in W/(m·K), ΔT in K, R in K/W, and q in W.
• Temperature differences in kelvin and degrees Celsius are numerically equivalent.
• For a cylindrical wall, L is the axial conduction length and the radii are inner and outer radii.
• For a spherical shell, r1 and r2 are inner and outer radii.
• For multilayer calculations, adjacent layers share the same interface radius, each layer resistance is calculated with its own k, and all layer resistances are in series.
• Interface temperatures in the multilayer vector use T_hot=120 K at r=0.05 m and T_cold=0 K at r=0.08 m, with heat flowing outward.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "geometry": "cyl",
    "r1_m": 0.05,
    "r2_m": 0.06,
    "k_W_per_mK": 0.5,
    "L_m": 1,
    "deltaT_K": 100
  },
  "expected_outputs": {
    "R_total_K_per_W": 0.0580348,
    "q_W": 1723.1054
  },
  "working": "R=ln(0.06/0.05)/(2π·0.5·1)=ln(1.2)/π=0.1823215568/3.141592654=0.0580348 K/W. q=ΔT/R=100/0.0580348=1723.1054 W."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specified formulas expose unhandled invalid-input hazards: equal radii produce zero resistance and an undefined heat-rate division, zero conductivity produces a division-by-zero resistance, and an unstated sign convention can reverse the heat-rate sign.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json