--- title: "Insulation layer: minimum outside heat transfer coefficient" subject: "Fundamental of Thermodynamics & Heat Transfer" chapter: 7 key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:insulation-min-outside-h-270c-70c" source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/insulation-min-outside-h-270c-70c site: BCT Engineering --- # Insulation layer: minimum outside heat transfer coefficient Fundamental of Thermodynamics & Heat Transfer · Chapter 7: Introduction to Heat Transfer - Asked in: 2067 Mangsir, 6 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/insulation-min-outside-h-270c-70c - Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-7 ## Question The inside surface of an insulating layer is at 270°C, and the outside surface is dissipating heat by convection in to air at 20°C. The insulation layer is 4 cm thick and has thermal conductivity of 1.2W/m.K. What is the minimum value of the heat transfer coefficient at the outside surface if the outside temperature is not to exceed 70°C? ## Short answer Conduction flux: q = 1.2 × (270−70)/0.04 = 6000 W/m². Convection: q = h × (70−20) = 50h. Equating yields h = 6000/50 = 120 W/m²·K, the minimum outside heat transfer coefficient. ## Answer **Given:** inside surface T₁ = 270 °C, outside surface T₂ ≤ 70 °C, air T_∞ = 20 °C, thickness L = 4 cm = 0.04 m, k = 1.2 W/m·K. Steady, one-dimensional flow. #### Conduction through the layer q = k (T₁ − T₂)/L = 1.2 × (270 − 70)/0.04 = 240/0.04 = 6000 W/m² #### Convection from the outside surface q = h (T₂ − T_∞) = h (70 − 20) = 50 h #### Equate 50 h = 6000, so h = 6000/50 = 120 W/m²·K **Answer: the minimum outside heat transfer coefficient is h = 120 W/m²·K.** If h were smaller, the surface would have to run hotter than 70 °C to lose the same heat. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the heat flux conducted through the 4 cm insulation? A. 1.2 x 250/0.04 = 7500 W/m2 B. 1.2 x 200/0.04 = 6000 W/m2 C. 1.2 x 200 x 0.04 = 9.6 W/m2 D. 1.2 x 50/0.04 = 1500 W/m2 Answer: B. q = k(T1 - T2)/L = 1.2 x (270 - 70)/0.04 = 6000 W/m2. (Key point: Conduction flux) 2. Which temperature difference is used in q = h(...) at the outer surface? A. 270 - 20 B. 270 - 70 C. 70 - 20 = 50 K D. 70 + 20 Answer: C. Convection is driven by surface minus air temperature: 70 - 20 = 50 K. (Key point: Convection temperature difference) 3. Equating fluxes gives h = 120 W/m2K. What does this represent? A. The maximum allowable h B. The h needed only if surface is at 20 °C C. An h independent of the surface temperature limit D. The minimum h to keep the outer surface at or below 70 °C Answer: D. A smaller h would force the surface above 70 °C to reject the same 6000 W/m2. (Key point: Result and meaning) ## Close variants set in other exams - [Insulating layer: minimum outside heat transfer coefficient](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Ainsulating-layer-min-outside-h-300c) — Fundamental of Thermodynamics & Heat Transfer, chapter 7, asked 2× ## Related in Fundamental of Thermodynamics & Heat Transfer - [Plate with convection and radiation: inside temperature](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aplate-convection-radiation-inside-temp) — Fundamental of Thermodynamics & Heat Transfer, chapter 7 - [Temperature difference across insulating layer, 1600 W](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Ainsulating-layer-temp-difference-1600w) — Fundamental of Thermodynamics & Heat Transfer, chapter 7 - [Hollow cylinder: heat transfer; temperature at 10 cm](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Ahollow-cylinder-8-12cm-radial-10cm) — Fundamental of Thermodynamics & Heat Transfer, chapter 7, asked 2× - [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 - [Overall heat transfer coefficient: two-layer plane wall](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Acomposite-plane-wall-two-layers-overall-u) — Fundamental of Thermodynamics & Heat Transfer, chapter 7, asked 2×