Type a line (steam pipe 60.3 mm 180 °C insulation 50 mm k 0.04 h 10 ambient 35 °C 20 m) or fill in the fields: the line and the fields stay in step.
Enter the outside diameter of the pipe, the temperature of the fluid in it (steam, thermal oil or hot water), the insulation thickness and its conductivity k, the surface coefficient h and the air temperature, and the calculator gives the heat loss in watts per metre, for the whole run and, with the operating hours, in MWh per year, together with the surface temperature of the insulation and the loss of the same pipe bare. It shows the working with your numbers, draws the temperature through the insulation, and gives a line you can copy or add to a request.
There are no default figures for k or h: the calculator asks for them and assumes none. The pipe wall and the inside film are left out, and the result says so. Surface temperature limits follow SOLAS II-2 and the rules for the space: the calculator gives the temperature, but puts no limit figure next to it.
The resistance of the insulation layer per metre of pipe is ln(r2 / r1) / (2 pi k), with r1 half the outside diameter, r2 the outer radius of the insulation and k its conductivity. A 60.3 mm steam pipe with 50 mm of insulation and k 0.04 W/(m K): ln(80.15 / 30.15) / (2 pi x 0.04) = 3.890 m K/W.
The resistance from the surface to the air is 1 / (2 pi r2 h), with h the surface coefficient. With h 10 W/(m2 K): 1 / (2 pi x 0.08015 x 10) = 0.1986 m K/W. The loss is q = (180 - 35) / (3.890 + 0.1986) = 35.5 W/m, or 709 W over 20 m, and the surface temperature 35 + 35.5 x 0.1986 = 42.0 °C.
A bare pipe loses q = h pi D (Tf - Ta): 10 x pi x 0.0603 x 145 = 274.7 W/m, so the insulation cuts the loss by 87.1 %. Over 8000 h a year, 709 W is 5.67 MWh; at a boiler efficiency of 85 % that is 6.68 MWh of fuel, and at 60 per MWh, 400.52 per year.
| Quantity | Relation | Note |
|---|---|---|
| Insulation layer | R insulation = ln(r2 / r1) / (2 pi k) | m K/W per metre; r1 = outside diameter / 2, r2 = r1 + insulation thickness |
| Outer surface | R surface = 1 / (2 pi r2 h) | h covers convection and radiation from the surface together |
| Loss, insulated | q = (Tf - Ta) / (R insulation + R surface) | W per metre |
| Surface temperature | Ts = Ta + q x R surface | °C |
| Loss, bare pipe | q = h x pi x D x (Tf - Ta) | W per metre; D the outside diameter in m |
| Critical radius | r = k / h | below it, added insulation can raise the loss |
| Energy per year | E = q x L x hours / 1 000 000 | MWh; per metre without a length |
| Fuel cost | E / boiler efficiency x price per MWh | in the currency of the price |
The pipe wall and the inside film are left out: the inner face of the insulation, or the surface of a bare pipe, is taken at the fluid temperature. The conductivity k and the surface coefficient h are used as entered.
The resistance of a cylindrical layer ln(r2 / r1) / (2 pi k), the resistance from the outer surface 1 / (2 pi r2 h), their sum in series, the surface temperature from the heat flow and the critical radius k / h are standard heat transfer relations, checked against several independent course notes and worked problems. That the pipe wall and the inside film are small against the insulation shows in worked problems that set their resistances next to the insulation, or call them negligible outright. The bare pipe loss, the surface coefficient as convection and radiation together, and the yearly loss through the boiler efficiency come from open methods for pipe heat loss. Requirements for hot surfaces in machinery spaces are in SOLAS chapter II-2.
As two thermal resistances in series, per metre of pipe. The insulation layer: ln(r2 / r1) / (2 pi k), with r1 half the outside diameter of the pipe, r2 = r1 + the insulation thickness and k the conductivity of the insulation. The outer surface: 1 / (2 pi r2 h), with h the surface coefficient. The loss is q = (Tf - Ta) divided by the sum of the two. A steam pipe of 60.3 mm with 50 mm of insulation, k 0.04 W/(m K), h 10 W/(m2 K), steam at 180 °C and air at 35 °C: ln(80.15 / 30.15) / (2 pi x 0.04) = 3.890 m K/W and 1 / (2 pi x 0.08015 x 10) = 0.1986 m K/W, so q = 145 / 4.089 = 35.5 W/m, or 709 W over 20 m.
Because with insulation they are usually small: a steel wall and the film of the fluid inside each add a small fraction of the resistance of the insulation layer. The calculator takes the inner face of the insulation at the fluid temperature and says so with the result. Leaving them out can only make the loss come out higher, never lower, since each resistance left out would reduce it; the bare pipe figure is an upper estimate for the same reason.
The outside diameter of the pipe and the insulation thickness in mm; the fluid and the air temperatures in °C (K and °F are read too); the conductivity k of the insulation in W/(m K) and the surface coefficient h in W/(m2 K); and, if wanted, the length in m, the operating hours per year, a price per MWh and the boiler efficiency. The calculator holds no default k or h and does not assume one: k comes from the data sheet of the insulation fitted, and h is the figure for the outer surface and the air around it, convection and radiation together. A line without k or h is answered with a request for the missing figure.
A bare pipe loses q = h pi D (Tf - Ta) per metre: the same 60.3 mm pipe at 180 °C in air at 35 °C with h 10 loses 274.7 W/m, so 50 mm of insulation cuts the loss by 87.1 %. Without a separate bare surface h the comparison uses the same h; a bare surface is hotter and gives off more by radiation, so enter bare h for a closer figure. Insulation can raise the loss only while its outer radius is below k / h, the critical radius: with k 0.04 and h 10 that is a radius of 4 mm, and the calculator says so whenever the insulation entered is that thin.
As plain arithmetic. The energy per year in MWh is the loss in W times the operating hours per year, divided by 1 000 000. The fuel burnt for it is that energy divided by the boiler efficiency, and the cost is the fuel energy times the price per MWh. A thermal oil line of 114.3 mm at 250 °C with 80 mm of insulation, k 0.045 W/(m K), h 9 W/(m2 K) and air at 40 °C loses 65.1 W/m; over 8000 h that is 0.521 MWh per metre per year; with a boiler efficiency of 85 % that is 0.613 MWh of fuel, and at 60 per MWh, 36.77 per metre per year. Bare, the same metre would cost 383.25.
No. It gives the outer surface temperature, Ts = Ta + q / (2 pi r2 h): 42.0 °C for the steam pipe above. Surface temperature limits follow SOLAS II-2 and the rules for the space, and the calculator puts no limit figure next to the result.
The calculator gives the heat loss of the line. When insulation material, cladding or pipe parts are needed, send the line from the calculator with the details of the pipe run and the space, and Vessel Core checks the details before an offer goes back.
