The flames in an industrial furnace burn at 800°C on average and the convection coefficient between the hot gas and the inside wall of the furnace is h₁ = 30 W/m² K. The wall of the furnace is made of steel (k, = 20 W/m-K) and is L = 10 cm thick. To ensure nobody will burn themself on the exterior surface of the furnace, the steel is to be covered by an insulating material with a low thermal conductivity (k = 0.05 W/m-K). The air surrounding the furnace is at 27°C and free convection on the exterior wall of the furnace is expected to produce a convection coefficient of h = 5 W/m²-K. Any radiation effects are expected to be negligible in this analysis. a) If safety standards require that the outer surface of the furnace not exceed 65°C, how thick should the insulation layer be? This problem is most straightforward if you leverage the concept of thermal resistance. b) Using your result from part (a), calculate the overall heat transfer coefficient (U) from the furnace gas to the ambient air. c) Your analysis did not include the effects of contact resistance between the furnace wall and the insulation-did you therefore overestimate or underestimate the required insulation thickness? Explain in a few sentences.

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The flames in an industrial furnace burn at 800°C on average and the convection coefficient
between the hot gas and the inside wall of the furnace is ℎ1 = 30 W m2–K⁄ . The wall of the
furnace is made of steel (?? = 20 W m–K⁄ ) and is ? = 10 cm thick. To ensure nobody will
burn themself on the exterior surface of the furnace, the steel is to be covered by an
insulating material with a low thermal conductivity (?? = 0.05 W m–K⁄ ). The air
surrounding the furnace is at 27°C and free convection on the exterior wall of the furnace
is expected to produce a convection coefficient of ℎ = 5 W/m2–K. Any radiation effects are
expected to be negligible in this analysis.
a) If safety standards require that the outer surface of the furnace not exceed 65°C, how
thick should the insulation layer be? This problem is most straightforward if you
leverage the concept of thermal resistance.
b) Using your result from part (a), calculate the overall heat transfer coefficient (?)
from the furnace gas to the ambient air.
c) Your analysis did not include the effects of contact resistance between the furnace
wall and the insulation—did you therefore overestimate or underestimate the
required insulation thickness? Explain in a few sentences.

The flames in an industrial furnace burn at 800°C on average and the convection coefficient
between the hot gas and the inside wall of the furnace is h₁ = 30 W/m²-K. The wall of the
furnace is made of steel (k = 20 W/m-K) and is L = 10 cm thick. To ensure nobody will
burn themself on the exterior surface of the furnace, the steel is to be covered by an
insulating material with a low thermal conductivity (k₂ = 0.05 W/m-K). The air
surrounding the furnace is at 27°C and free convection on the exterior wall of the furnace
is expected to produce a convection coefficient of h = 5 W/m²-K. Any radiation effects are
expected to be negligible in this analysis.
a) If safety standards require that the outer surface of the furnace not exceed 65°C, how
thick should the insulation layer be? This problem is most straightforward if you
leverage the concept of thermal resistance.
b) Using your result from part (a), calculate the overall heat transfer coefficient (U)
from the furnace gas to the ambient air.
c) Your analysis did not include the effects of contact resistance between the furnace
wall and the insulation did you therefore overestimate or underestimate the
required insulation thickness? Explain in a few sentences.
Transcribed Image Text:The flames in an industrial furnace burn at 800°C on average and the convection coefficient between the hot gas and the inside wall of the furnace is h₁ = 30 W/m²-K. The wall of the furnace is made of steel (k = 20 W/m-K) and is L = 10 cm thick. To ensure nobody will burn themself on the exterior surface of the furnace, the steel is to be covered by an insulating material with a low thermal conductivity (k₂ = 0.05 W/m-K). The air surrounding the furnace is at 27°C and free convection on the exterior wall of the furnace is expected to produce a convection coefficient of h = 5 W/m²-K. Any radiation effects are expected to be negligible in this analysis. a) If safety standards require that the outer surface of the furnace not exceed 65°C, how thick should the insulation layer be? This problem is most straightforward if you leverage the concept of thermal resistance. b) Using your result from part (a), calculate the overall heat transfer coefficient (U) from the furnace gas to the ambient air. c) Your analysis did not include the effects of contact resistance between the furnace wall and the insulation did you therefore overestimate or underestimate the required insulation thickness? Explain in a few sentences.
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