The arrangement shown is to be used to calibrate a heat flux gage. The gage has a black surface that is \(8 \mathrm{~mm}\) in diameter and is maintained at \(10^{\circ} \mathrm{C}\) by means of a water-cooled backing plate. The heater, \(150 \mathrm{~mm}\) in diameter, has a black surface that is maintained at \(800 \mathrm{~K}\) and is located \(0.5 \mathrm{~m}\) from the gage. The surroundings and the air are at \(27^{\circ} \mathrm{C}\) and the convection heat transfer coefficient between the gage and the air is \(15 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\).

(a) Determine the net radiation exchange between the heater and the gage.

(b) Determine the net transfer of radiation to the gage per unit area of the gage.

(c) What is the net heat transfer rate to the gage per unit area of the gage?

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0.5 m * Heated plate, T Heat flux gage, T -Gage surface Cooling water