The radiation heat gage shown in the diagram is made from constantan metal foil, which is coated black and is in the form of a circular disk of radius R and thickness t. The gage is located in an evacuated enclosure. The incident radiation flux absorbed by the foil, qi diffuses toward the outer circumference and into the larger copper ring, which acts as a heat sink at the constant temperature T(R). Two copper lead wires are attached to the center of the foil and to the ring to complete a thermocouple circuit that allows for measurement of the temperature difference between the foil center and the foil edge, ∆T = T(O) - T(R).

Obtain the differential equation that determines T(r), the temperature distribution in the foil, under steady-state conditions. Solve this equation to obtain an expression relating ∆T to qi. You may neglect radiation exchange between the foil and its surroundings.

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Evacuated enclosure TIR) T(0) Foil Copper ring Copper wires