--- title: "Heat loss from insulated steam pipe" subject: "Heat Transfer" chapter: 2 key: "semester_5/heat_transfer:insulated-steam-pipe-heat-loss" source: https://www.bctengineer.com/q/semester_5/heat_transfer/insulated-steam-pipe-heat-loss site: BCT Engineering --- # Heat loss from insulated steam pipe Heat Transfer · Chapter 2: Conduction Heat Transfer - Asked in: year not given, 8 marks - Video: [Heat Loss from a Steam Pipe | Insulation Thickness & Energy Cost | Heat Transfer Problem 3.78](https://www.youtube.com/watch?v=gagS3XQI66c) — Education Shop - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/heat_transfer/insulated-steam-pipe-heat-loss - Whole chapter: https://www.bctengineer.com/md/semester_5/heat_transfer/chapter-2 ## Question A steel steam pipe of inner diameter 80 mm and outer diameter 90 mm (k = 45 W/m K) is covered with 50 mm of insulation (k = 0.07 W/m K). Steam at 250 °C flows inside with h_i = 100 W/m^2 K. The outside air is at 25 °C with h_o = 10 W/m^2 K. Calculate (a) the heat loss per metre length of pipe, (b) the temperature at the pipe/insulation interface and at the outer surface of insulation, and (c) the critical radius of insulation for this pipe. ## Short answer Radial resistances: convection inside 0.0398, steel 0.00042, insulation 1.6989, air 0.1675 K/W per m. Total 1.9066 K/W gives Q/L = (250−25)/1.9066 = 118 W/m. Pipe/insulation interface ~245.3 °C, outer insulation surface 44.8 °C. Critical radius rc = k_ins/ho = 0.07/10 = 7 mm. ## Answer Data: $r_1 = 0.04$ m, $r_2 = 0.045$ m, $r_3 = 0.045+0.05 = 0.095$ m. For a cylinder, $R_{cond} = \dfrac{\ln(r_{o}/r_{i})}{2\pi kL}$ and $R_{conv} = \dfrac{1}{hA}$. Take $L = 1$ m. #### Resistances (K/W per metre) | Element | Expression | Value | |---|---|---| | Steam film | $1/(100\cdot 2\pi\cdot0.04)$ | 0.03979 | | Steel wall | $\ln(0.045/0.04)/(2\pi\cdot45)$ | 0.00042 | | Insulation | $\ln(0.095/0.045)/(2\pi\cdot0.07)$ | 1.69890 | | Outer air film | $1/(10\cdot2\pi\cdot0.095)$ | 0.16753 | | **Total** | | **1.90663** | #### (a) Heat loss $$ Q/L = \frac{250-25}{1.90663} = 118.0\ \text{W/m} $$ #### (b) Temperatures $$ \begin{aligned} T_{\text{inner steel}} &= 250 - 118.0(0.03979) = 245.3\ ^\circ\text{C}\\ T_{\text{pipe/insulation}} &= 245.3 - 118.0(0.00042) = 245.26\ ^\circ\text{C}\\ T_{\text{outer insulation}} &= 245.26 - 118.0(1.6989) = 44.8\ ^\circ\text{C} \end{aligned} $$ Check: $44.8 - 118.0(0.16753) = 25.0$ °C. #### (c) Critical radius $$ r_c = \frac{k_{ins}}{h_o} = \frac{0.07}{10} = 0.007\ \text{m} = 7\ \text{mm} $$ Since the pipe outer radius (45 mm) is already much greater than $r_c$, adding insulation always reduces heat loss here. **Answer:** $Q/L \approx 118\ \text{W/m}$; interface 245.3 °C; insulation outer surface 44.8 °C; $r_c = 7$ mm. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which is the conduction resistance of a cylindrical layer? A. ln(ro/ri)/(2 pi k L) B. (ro - ri)/(k A) C. ln(ro/ri)/(4 pi k) D. 1/(h 2 pi r L) Answer: A. Cylindrical conduction resistance is ln(ro/ri)/(2 pi k L). (Key point: Cylinder resistance) 2. Which element has by far the largest resistance in the pipe circuit? A. Steel wall B. Insulation C. Steam film D. Outer air film Answer: B. Insulation is 1.699 K/W of 1.907 total; steel is only 0.00042. (Key point: Dominant resistance) 3. What is the critical radius here and what does it mean? A. 95 mm; insulation never helps B. 7 mm; insulation increases loss for this pipe C. 7 mm; insulation always helps since pipe radius is larger D. 0.7 m; insulation helps only a little Answer: C. rc = k/ho = 0.07/10 = 7 mm, well below the 45 mm pipe radius. (Key point: Critical radius) 4. The heat loss per metre is about: A. 225 W/m B. 1036 W/m C. 12 W/m D. 118 W/m Answer: D. Q/L = (250-25)/1.9066 = 118 W/m. (Key point: Heat loss) ## Related in Heat Transfer - [Heat loss from a cylinder in cross flow](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Across-flow-air-cylinder-heat-loss) — Heat Transfer, chapter 3 - [Composite furnace wall heat loss](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Acomposite-furnace-wall-interface-temperatures) — Heat Transfer, chapter 2 - [Heat dissipation from a pin fin](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Apin-fin-aluminium-heat-dissipation) — Heat Transfer, chapter 6 - [Condensation of steam on a vertical plate](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Afilm-condensation-vertical-plate-numerical) — Heat Transfer, chapter 5 - [Diffusion of water vapour through stagnant air](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Aevaporation-water-test-tube-stagnant-air) — Heat Transfer, chapter 7 - [Water heating in a tube, Dittus-Boelter](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Adittus-boelter-water-heating-tube-length) — Heat Transfer, chapter 3 ## Related in other subjects - [Steam pipe with single insulation: heat loss rate](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Asteam-pipe-single-insulation-heat-loss) — Fundamental of Thermodynamics & Heat Transfer, chapter 7 - [Steam pipe asbestos insulation thickness](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Asteam-pipe-asbestos-thickness-2-1kw) — Fundamental of Thermodynamics & Heat Transfer, chapter 7 - [Pipe insulation: extra layer to cut heat 40%](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Apipe-insulation-additional-layer-40-percent) — Fundamental of Thermodynamics & Heat Transfer, chapter 7 - [Steel tube with asbestos: heat loss, interface temp](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Asteel-tube-asbestos-heat-loss) — Fundamental of Thermodynamics & Heat Transfer, chapter 7