Insulation, Heat Loss and Troubleshooting
Wall and roof heat loss, pipe insulation economics, condensation, heating energy and a table of common thermal problems.
U-values and where the heat goes
The building envelope loses heat by conduction through walls, roofs, floors and glazing, and by air leakage and ventilation. The conduction loss through each element is Q̇ = U A (Tin − Tout), and the elements add. Typical U-values (W/m²·K):
| Element | Poorly insulated | Modern code level |
|---|---|---|
| Solid masonry wall | 1.5 to 2.1 | 0.15 to 0.30 |
| Cavity wall | 0.5 to 1.0 | 0.18 to 0.30 |
| Pitched roof, insulated at the rafters | 1.0 to 2.0 | 0.10 to 0.20 |
| Ground floor | 0.7 to 1.0 | 0.15 to 0.25 |
| Single glazing | 5 to 6 | — |
| Double glazing, low-e | 1.6 to 2.8 | 0.8 to 1.4 (triple 0.5 to 0.8) |
The shared wall of Conduction: Walls, Pipes and Insulation has U = 0.321 W/m²·K: a good cavity wall. Air leakage and ventilation lose heat at about 0.33 W per m³/h per K (ρ cp ÷ 3600), often as much as the conduction through the walls in a leaky building. Make it airtight, ventilate on purpose, and recover heat from the exhaust.
From heat loss to energy and cost
Heat loss changes with the weather. Heating degree-days (HDD, K·days) measure how much colder than a base temperature a place is over a season: the energy lost is E = U A × 24 × HDD ÷ 1 000 kWh.
Worked example: 100 m² of cavity wall in a 3 000 degree-day climate
- With U = 0.321: E = 0.321 × 100 × 24 × 3 000 ÷ 1 000 = 2 314 kWh a year. At 0.12 per kWh of electric heat that is $278; with a 90 percent efficient gas boiler at $0.04 per kWh, $103.
- Without the 100 mm of mineral wool, U would be 1.63 and the loss 11 771 kWh: the insulation saves 9 457 kWh a year.
- Add another 50 mm of insulation: R rises from 3.11 to 4.36, U falls to 0.229 and the annual loss to 1 651 kWh, a further saving of 663 kWh (about $80 with electric heat). The second layer saves less than the first: diminishing returns, because the saving is 1 ÷ R₁ − 1 ÷ R₂.
How much pipe insulation?
The best thickness balances the cost of the insulation against the value of the heat it saves. As more is added the saving per millimeter falls (see the 80 °C pipe of Conduction: Walls, Pipes and Insulation) while the cost keeps rising.
Worked example: 100 m of DN50 hot line, 8 000 hours a year
Heat at $0.05 per kWh, mineral wool k = 0.040, installed cost (illustrative) per meter as shown, spread over 10 years at 8 percent (a capital recovery factor of 0.149).
| Insulation | Heat loss | Heat cost per year | Insulation cost per year | Total per year |
|---|---|---|---|---|
| bare | 164 W/m | $6 547 | $820 | $7 367 |
The lowest total is at no insulation. The economic thickness rises with the price of energy and with the hours of operation and falls with the cost of installation. Insulation on steam and hot-water lines almost always pays back in under two years, and codes also limit surface temperatures for safety.
Condensation and cold pipes
If a surface is colder than the dew point of the surrounding air, water condenses on it: on cold pipes and ducts it drips and corrodes, and on walls it makes mold. Insulation raises the surface temperature above the dew point, and it must be sealed with a vapor barrier because moist air will otherwise reach the cold pipe through the joints and wet the insulation. (The dew point from the temperature and humidity is on the Psychrometric Calculator.)
Worked example: a chilled-water pipe and a cold wall
- Room air at 25 °C and 70 percent relative humidity has a dew point of 19.1 °C. A 22 mm copper pipe carrying 6 °C water has a surface at about 6.4 °C when bare (well below the dew point: it sweats).
- With 10 mm of insulation (k = 0.035) the surface is 20.4 °C, still too cold. To stay 0.5 K above the dew point (19.6 °C) needs 8 mm of insulation.
- The cavity wall: its inside surface is at 19.0 °C. In a room at 20 °C and 60 percent RH the dew point is 12.0 °C, so the wall is safe; an uninsulated solid wall with a surface at 12 °C would sit at the dew point and grow mold in the corners, where thermal bridges are coldest.
A hot water tank
A cylindrical 150 liter tank (0.50 m diameter, 1.1 m high, outside area 2.12 m²) holds water at 60 °C in a 20 °C room, with 50 mm of foam (k = 0.025) and an outside film of 5 W/m²K: U = 1 ÷ (0.050 ÷ 0.025 + 1 ÷ 5) = 0.45 W/m²K. The standing loss is 0.45 × 2.12 × 40 = 39 W, or 0.9 kWh a day: costing about $41 a year in electricity, and the reason a 200 mm jacket and insulated pipes are worth having.
Troubleshooting thermal problems
| Symptom | Likely cause | What to check or do |
|---|---|---|
| Component too hot, shuts down | thermal resistance too high, airflow blocked, power higher than designed | measure case and ambient; compute Tj = Ta + P Σθ; check the interface material, mounting torque, fan and filters |
| Heat sink hot but device hotter still | poor interface (dry joint, air gap, no grease) | remove, clean and re-apply a thin even layer of grease or a new pad; check flatness |
| Heat sink cooler than expected but device hot | heat not spreading: thin base or small contact | use a thicker base or a heat spreader; larger contact area |
| Enclosure too warm | sealed box with too little surface for the load, solar gain | compute ΔT = P ÷ (h A); add fans, a larger enclosure, shade or a heat exchanger |
| Hot pipe losing a lot of heat | missing or wet insulation, thermal bridges at supports and valves | infrared survey; insulate valves and flanges with removable jackets |
| Pipe or duct sweats | surface below the dew point | increase insulation and seal the vapor barrier; check the humidity |
| Cold spots, mold in corners | thermal bridges, poor insulation continuity | infrared camera; insulate continuous; ventilate and control humidity |
| Heat exchanger output falling | fouling, low flow, air or gas pocket, wrong flow direction | compare approach temperatures with the clean design; clean; vent; check valves for counterflow |
| Temperature takes too long to settle | large thermal mass, low h | compute τ = ρ c Lc ÷ h; add airflow or reduce mass |
Related
- Previous: Cooling Electronics and Thermal Design. Back to the start: Heat Transfer.
- Psychrometric Calculator (dew point).
- Heat Sink and Thermal Resistance Calculator.
- Workshop Safety (burns and hot surfaces).
FAQ
What is a thermal bridge?
A path through a wall or roof that conducts heat better than its surroundings (a steel beam, a concrete lintel, a metal fixing). Heat flows round the insulation through it, so the real U-value is higher than the simple calculation and the inside surface near it is cold.
Is more insulation always better?
For safety and energy yes up to a point, but with diminishing returns: the second 50 mm saves less than the first. The economic thickness depends on energy prices; for new buildings, code levels are usually near the optimum.
Do I need a vapor barrier on pipes?
On cold pipes, yes, on the warm side of the insulation: without it, moist air diffuses to the cold surface, condenses, and wets the insulation, which then loses its value. Hot pipes do not need one.
How accurate are heat-loss estimates?
For a simple wall, within 10 to 20 percent. The real uncertainty is air leakage, moisture, workmanship and the weather, so test a finished building (a blower-door test and an infrared survey).
References
- ISO 6946 (U-value of building components), ISO 13370 (heat transfer via the ground), ISO 13789 and EN 12831 (heat loss calculation).
- ASHRAE Handbook – Fundamentals (heat transfer, psychrometrics, thermal and water vapor transmission data).
- ASTM C680 and ISO 12241 (heat loss from insulated pipes and equipment); North American Insulation Manufacturers Association, 3E Plus (free insulation thickness software).
- Incropera, F. P., et al., Fundamentals of Heat and Mass Transfer, Wiley.
Last reviewed: October 2026. Prices, degree-days and U-values are illustrative: use your own.