Bare hot metal is not a wall, it is a radiator
Steel conducts about 1,600 times better than mineral wool. A 6 mm steel vessel wall at 250 °C has essentially no thermal resistance of its own — the outside face sits at very nearly the process temperature, and the only thing slowing the heat down is the air film against it.
Put 50 mm of rockwool on the same 10 m² wall and the picture changes completely:
| Bare 6 mm steel | + 50 mm rockwool | + 100 mm | |
|---|---|---|---|
| Outer surface temperature | 249.8 °C | 43.1 °C | 32.2 °C |
| Heat flux | 1,669 W/m² | 137 W/m² | 72 W/m² |
| Total loss | 16.7 kW | 1.4 kW | 0.7 kW |
A 92 % cut for the first 50 mm — and a surface someone can stand next to. Note the second 50 mm only halves it again: returns diminish fast, which is why economic thickness is a real question rather than "more is better".
The two answers this gives you
Heat flux, which turns into money. Multiply W/m² by your area and your operating hours and you have kWh; multiply by your fuel price and boiler efficiency and you have the annual cost of not insulating that surface.
Surface temperature, which is a safety answer. Above roughly 60 °C a touchable surface is a contact-burn risk, and the calculator flags it. Guarding a hot surface costs money and does nothing for your fuel bill; insulating it fixes both problems at once.
The physics behind it
Conduction through the layers is a resistance network in series:
Rtotal=k1AL1+k2AL2The interface temperature between two layers follows from continuity of heat flow:
T2=k1L2+k2L1k1L2T1+k2L1T3The outer surface temperature is not assumed — it is solved. The face has to shed exactly as much heat as arrives through the wall, by convection and radiation:
RtotalT1−Ts=hA(Ts−T∞)+εσA(Ts4−T∞4)That is solved by Newton iteration, with σ=5.67×10−8 W/m²K⁴ and the emissivity taken from the outer material. The radiation term is why a dull black surface runs cooler than a polished one at the same heat load, and why emissivity is worth getting right on a hot vessel.
That is solved by Newton iteration, and the heat rate follows from the solved surface: q=(T1−Ts)/Rtotal. Because both sides come from the same solve, what conducts through the wall is exactly what the face sheds — the model cannot report a wall losing more heat than its surface gives up.
The film coefficient uses a simple linear correlation, h=5+0.6v, with v the air speed across the face. It is a screening correlation, not a Nusselt solve — enough to separate still air in a plant room from a windy gantry, not enough to design to.
Pipes are not flat walls
Insulate a pipe and the heat spreads outwards through a steadily larger area, so resistance does not grow in proportion to thickness the way it does on a plane wall. Cylinders and spheres therefore use the radial forms:
Rcyl=2πkLln(r2/r1)Rsph=4πk1(r11−r21)The difference matters most exactly where insulation decisions get made — small pipes with thick lagging. On a 100 mm-radius pipe, 50 mm of rockwool over 10 m brings a 250 °C line down to 39.5 °C and 1.13 kW. Treat that as a flat wall and you will get the wrong answer, because the outer surface is half as much again as the inner one.
Materials
Eleven materials are built in, with conductivity and emissivity taken as an average of the typical range at around room temperature:
| Material | k (W/m·K) | ε |
|---|---|---|
| Pyrogel | 0.015 | 0.15 |
| Insulation foam | 0.02 | 0.95 |
| Rockwool | 0.033 | 0.05 |
| Polystyrene | 0.0365 | 0.85 |
| Drywall | 0.17 | 0.9 |
| Glass | 1.0 | 0.94 |
| Concrete | 1.33 | 0.9 |
| Stainless steel | 23 | 0.3 |
| Mild steel | 52 | 0.1 |
| Aluminium (oxidised) | 237 | 0.11 |
| Copper | 401 | 0.03 |
Note how little the metals differ from one another in practice: at these thicknesses, steel, aluminium and copper all behave as though they have no resistance at all. The insulation is the entire design. Choosing a better grade of steel for a vessel wall does nothing measurable for heat loss.
Conductivity also rises with temperature, and the values here are room-temperature averages — mineral wool at 400 °C conducts appreciably more than the 0.033 shown. For high-temperature work, use the manufacturer's hot-face data.
What this will not tell you
This is a one-dimensional steady-state model, and it is honest about the limits:
- Thermal bridging is ignored. Supports, brackets, nozzles, manways and flanges short-circuit insulation, and on a real vessel they can account for a large fraction of the total loss. Nothing here sees them.
- Wet insulation is not modelled. Mineral wool that has taken up water can lose most of its value, and corrosion under insulation is a far more expensive problem than the energy ever was.
- No cost, thickness optimisation or payback. The economic thickness depends on your fuel price, hours, cladding cost and installation access.
Every one of those makes a real surface worse than this calculator says. Treat the result as the best case, use it to find which surfaces are worth attention, and survey the ones that matter.