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- 2067 Mangsir · 6 marks
Insulation layer: minimum outside heat transfer coefficient
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.
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?
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.
✓ Answer checked by Claude Opus 5.5 (high effort)
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