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Insulation: economic thickness

Calculate heat loss from pipes or walls with and without insulation, the surface temperature and the thickness with the lowest total cost, combining annualized investment and heat lost.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

Pre-sizing
Surface
Insulation

Typical catalog values; use the manufacturer’s conductivity curve.

Costs

Cost of heat = fuel price per GJ ÷ boiler efficiency. The steam cost calculator gives this value.

Economic analysis
—Annual savings with the proposed thickness
—

Total yearly cost by thickness

Bars: investment annualized at the MARR and service life, plus the cost of the heat lost. The shortest bar is the economic thickness.

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Surface temperature and heat loss

The dashed line marks 60 °C (140 °F), the usual personnel-protection limit.

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Results by thickness

Project payback

Cash flow of the improvement: investment in year 0 and annual savings escalated at the rate entered, discounted at the MARR.

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The report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. In the print dialog, choose Save as PDF.

Method, assumptions and references

Equations used

Pipe: q = (Tf − Ts) × 2πk ÷ ln(r2/r1) = h × 2πr2 × (Ts − Ta) [W/m]
Wall: q = (Tf − Ts) × k ÷ t = h × (Ts − Ta) [W/m²]
k = k50 + (k200 − k50) × (Tm − 50) ÷ 150, with Tm = (Tf + Ts) ÷ 2
h = hc + hr; hr = ε σ (Ts⁴ − Ta⁴) ÷ (Ts − Ta)
Natural convection (Churchill–Chu): horizontal cylinder Nu = [0.60 + 0.387 Ra^(1/6) ÷ (1 + (0.559/Pr)^(9/16))^(8/27)]²; vertical wall Nu = [0.825 + 0.387 Ra^(1/6) ÷ (1 + (0.492/Pr)^(9/16))^(8/27)]²
Forced convection: cylinder (Churchill–Bernstein) and flat plate; combined Nu = (Nu_nat³ + Nu_forced³)^(1/3)
Total yearly cost = investment × CRF(i, n) + q × L × hours × 3600 ÷ 10⁹ × cost of heat; CRF = i(1+i)ⁿ ÷ ((1+i)ⁿ − 1)

Assumptions and limits

  • Inner face of the insulation at process temperature: inside film and pipe wall resistances neglected (conservative).
  • Steel pipe outside diameter per ASME B36.10M; bare pipe emissivity 0.8.
  • Air properties at film temperature (Sutherland), sea-level atmospheric pressure.
  • Conductivity linear between 50 °C and 200 °C, extrapolated outside that range; defaults are typical catalog values.
  • Does not account for thermal bridges at supports, flanges and valves, nor insulation degradation from moisture.

Standards and technical documents

  • ASTM C680-23: Standard Practice for Estimate of the Heat Gain or Loss and the Surface Temperatures of Insulated Flat, Cylindrical, and Spherical Systems
  • ISO 12241:2022: Thermal insulation for building equipment and industrial installations — Calculation rules
  • ASTM C1055: Standard Guide for Heated System Surface Conditions that Produce Contact Burn Injuries; ISO 13732-1:2006: Ergonomics of the thermal environment — Hot surfaces
  • ASTM C335 / ISO 8497: medição da condutividade térmica de isolamento de tubulações / thermal transmission of pipe insulation
  • Churchill, S. W.; Chu, H. H. S. (1975); Churchill, S. W.; Bernstein, M. (1977): correlações de convecção / convection correlations (Incropera, Fundamentals of Heat and Mass Transfer)
  • VDI 2055 Part 1: Thermal insulation of heated and refrigerated operational installations — Calculation rules (economic thickness)

U.S. regulations

  • OSHA General Duty Clause (Section 5(a)(1)): hot surfaces that can cause burns must be addressed; ASTM C1055 is the usual engineering basis
  • ASHRAE Standard 90.1 and the IECC: minimum pipe insulation for building service systems, adopted by state and local energy codes
  • DOE / NAIMA 3E Plus: reference tool for insulation thickness under energy assessments

Frequently asked questions

What is the economic insulation thickness?

The thickness with the lowest total yearly cost: the insulation investment, annualized at your MARR and service life, plus the cost of the heat still lost. The calculator tests commercial thicknesses from 1 to 6 in and shows the lowest total.

Why does an aluminum jacket make the surface hotter?

Bright aluminum has low emissivity (about 0.1), so it radiates little heat. The heat crossing the insulation leaves mostly by convection, and the outer face runs hotter than a painted or mastic finish.

What surface temperature is safe?

Common practice limits touchable surfaces to 60 °C (140 °F), based on ASTM C1055 and ISO 13732-1. The calculator shows the minimum thickness to reach it.