Heat Transfer Calculation for Circular Floor with Enclosed Metal Dome

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SUMMARY

The discussion focuses on calculating the temperature of the inner surface of a hemispherical metal dome enclosing a circular floor with a diameter of 9.15 m, an emissivity of 0.8, and a temperature of 29.4°C. The net rate of heat transfer between the floor and the dome is established at 660 W, despite confusion regarding the application of the Stefan-Boltzmann law. Participants clarify that the view factor must be considered to accurately determine the heat exchange, as the dome's emissivity is significantly lower at 0.1, affecting the equilibrium state.

PREREQUISITES
  • Understanding of the Stefan-Boltzmann law
  • Knowledge of emissivity and its impact on thermal radiation
  • Familiarity with view factors in radiative heat transfer
  • Basic principles of heat transfer in enclosed systems
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  • Study the calculation of view factors in thermal radiation
  • Learn about the application of the Stefan-Boltzmann law in non-equilibrium systems
  • Explore emissivity values and their significance in heat transfer calculations
  • Investigate methods for measuring and calculating heat transfer rates in enclosed spaces
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Students in thermal engineering, mechanical engineers, and professionals involved in heat transfer analysis and design of thermal systems.

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Homework Statement


A circular floor 9.15 m in diameter has an emissivity of 0.8 and is at a temperature of 29.4C. The floor is enclosed by a hemispherical metal dome which has an emissivity of 0.1. If the net rate of heat transfer between the floor and the dome is 660 W, calculate the temperature of the inner surface of the dome.

How do you work out the view factor between the two surfaces?
 
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I ran into a confusion here. With the given values of diameter, emissivity and temperature for the floor how could it emit or absorb radiation at a rate of 660 W if it is in equilibrium with the dome? Because using the Stefan-Boltzmann law, I calculated a much higher value of emission or absorption rate for the floor.
 

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