Heat Transfer Calculation for Circular Floor with Enclosed Metal Dome

[mattyboson12]

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?

 

[Halo CX]

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.