Heated systems · one-dimensional reference model
Documented Insulation Thickness Calculator
Calculate thickness for a target external surface temperature using separate convection and radiation terms. Supply design apparent thermal conductivity, jacket emissivity, boundary temperatures and the controlling personnel/process criterion.
Reference-model result
Implemented reference model
qᵣ = εσ[(Tₛ+273.15)⁴−(Tᵣ+273.15)⁴]
q″ = q꜀+qᵣ
flat: δ = k(Tₕ−Tₛ)/q″
cylinder: r₂ ln(r₂/r₁) = k(Tₕ−Tₛ)/q″
cylinder heat loss: Q′ = 2πr₂q″
σ=5.670374419×10⁻⁸ W/(m²·K⁴), the NIST 2022 CODATA Stefan–Boltzmann constant. The cylinder equation is strictly increasing for r₂>r₁ and is solved by a bracketed bisection with a reported closure residual; the former fixed 0.5/0.1 mm stepping could stop after 500 iterations without meeting its temperature tolerance.
Published heat-loss check
A University of California, Santa Barbara heat-transfer example gives a 50 mm diameter surface at 50 °C in 20 °C air/surroundings, h꜀=6.5 W/(m²·K) and ε=0.8: convection 30.63 W/m, radiation 25.04 W/m and total 55.67 W/m. The surface-loss submodel here reproduces those rounded values (minor difference from the newer CODATA σ).
ISO and ASTM scope/status
ISO 12241:2022, edition 3, corrected November 2022, is Published and gives calculation rules for heat-transfer-related properties of building equipment and industrial installations, mainly under steady state. Exact methods and clauses remain NEEDS_LICENSED_SOURCE; this page’s single-layer model is not labelled an ISO 12241 conformity calculation. ISO 13787:2003 treats declared thermal conductivity as a function of temperature. ASTM C680-23a warns that performance depends on wind, jacket emittance, ambient conditions, temperature-dependent properties and input-data quality.
No universal “safe surface temperature”
ISO 13732-1:2006, edition 1 and confirmed, provides burn-threshold/risk-assessment methods for contact periods of 0.5 s and longer but explicitly does not set surface-temperature limits. ASTM C1055-20 states that it is outside its scope to determine one temperature that is “safe”; contact time, surface material/configuration, injury criterion and exposed population matter. Therefore the former universal 50/60 °C personnel limits were removed.
Design use
Use a design apparent k covering the actual mean-temperature range, ageing and moisture condition; obtain h꜀ from the applicable orientation/airflow correlation or controlled procedure; use the installed jacket emissivity and credible radiant surroundings. Round-up, available product thicknesses, dimensional tolerances, compression, seams, cladding, corrosion-under-insulation control, supports and verification measurements belong to the qualified system design, not this algebraic result.
