Tools › Fluids and Heat Transfer › Conduction › Insulation and Pipe Heat Loss › Example
4 in steam line at 175 °C with 50 mm of mineral fiber: heat loss, surface temperature, economic thickness and freeze-up time
| Tool | Insulation and Pipe Heat Loss |
| Source | U.S. Departments of the Army and the Air Force (1987). Arctic and Subarctic Construction: Utilities. TM 5-852-5 / AFR 88-19, Volume 5, chapter 12 (Figure 12-4 and examples 12-9d, e, g, i, which the tool's test script reproduces); Churchill, S. W., and Chu, H. H. S. (1975). International Journal of Heat and Mass Transfer, Vol. 18, No. 9, pp. 1049–1053. |
| Level | Professional |
Problem
A horizontal 4 in steel steam line (114.3 mm outside diameter, 6.02 mm wall) at 175 °C runs 100 m through still air at 20 °C under 50 mm of mineral fiber with an oxidized aluminium jacket. Find the heat loss bare and insulated, the surface temperature against a 60 °C contact limit, the economic thickness for 8,000 h/yr with fuel at 0.03 per kWh burned at 80 % efficiency (5 % discount, 2 % escalation, 15 years), and the time for stagnant water at 10 °C in the same pipe to freeze in −20 °C air.
Inputs to Enter
- Pipe 114.3 mm OD, 6.02 mm wall, k 45 W/(m·K), bare emissivity 0.8; fluid 175 °C, ambient 20 °C, no wind, inside film neglected
- Layer 1: 50 mm mineral fiber, k = 0.02875 + 0.0001835 T W/(m·K) (T in °C, a line fitted to the DOE MEASUR polynomial); jacket emissivity 0.10
- Economics: 8,000 h/yr, 0.03 per kWh, efficiency 80 %, discount 5 %, escalation 2 %, 15 years, 0.182 kg CO2 per kWh; installed cost 30 / 42 / 58 / 78 / 102 / 130 per metre for 25 / 50 / 75 / 100 / 125 / 150 mm; run 100 m
- Line checks: 1 kg/s at 4.3 kJ/(kg·K); cold ambient −20 °C, water at 10 °C, 50 % frozen, maintain 5 °C, tracing factor 1.25
Answers
- Insulated: q = 65.30 W/m, surface 40.29 °C, k at the layer mean temperature 0.04850 W/(m·K), total resistance 2.374 m·K/W; film 4.146 (convection, Ra 1.78 × 10⁷) + 0.634 (radiation) = 4.780 W/(m²·K)
- Bare: q = 941.8 W/m at a surface of 174.6 °C; the insulation removes 93.1 % of the loss (6.530 kW against 94.18 kW over 100 m)
- Surface within the 60 °C limit; 21.16 mm would just meet it; critical radius k/h = 10.15 mm, well below the 57.15 mm pipe radius
- Present-worth factor 11.99; economic thickness 100 mm with a total present-worth cost of 23,132.17 (7,800.00 installed + 15,332.17 energy) for 100 m; annual saving against bare 26,974.23, payback 0.289 years, 163,600 kg CO2 avoided per year
- Fluid temperature after 100 m: 173.49 °C (single-phase fluid; condensing steam stays at saturation)
- Stagnant water in −20 °C air: 16.01 h to reach 0 °C, a further 78.37 h to freeze half of it; tracing 6.067 W/m, 7.584 W/m to install
Notes
The tool's default inputs are this case; press Submit. The case is illustrative, not a printed example: the numbers are checked against an independent numpy / scipy model, and the method against the worked examples of TM 5-852-5 chapter 12 (12.7 and 5.79 Btu/h per foot, 5.6 / 9.5 / 107 h, the economical-thickness table). The conductivity line and the costs are representative values, not a manufacturer's data.