A furnace with a long, isothermal, graphite tube

Chapter 12, Problem 12.30

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A furnace with a long, isothermal, graphite tube ofdiameter D?12.5 mm is maintained at Tf?2000 Kand is used as a blackbody source to calibrate heat fluxgages. Traditional heat flux gages are constructed asblackened thin films with thermopiles to indicate thetemperature change caused by absorption of the inci-dent radiant power over the entire spectrum. The tradi-tional gage of interest has a sensitive area of 5 mm2and is mounted coaxial with the furnace centerline, butpositioned at a distance of L?60 mm from the begin-ning of the heated section. The cool extension tubeserves to shield the gage from extraneous radiationsources and to contain the inert gas required to preventrapid oxidation of the graphite tube.(a) Calculate the heat flux (W/m2) on the traditionalgage for this condition, assuming that the exten-sion tube is cold relative to the furnace.(b) The traditional gage is replaced by a solid- state(photoconductive) heat flux gage of the same area,but sensitive only to the spectral region between0.4 and 2.5?m. Calculate the radiant heat fluxincident on the solid-state gage within the pre- scribed spectral region.(c) Calculate and plot the total heat flux and the heatflux in the prescribed spectral region for the solid-state gage as a function of furnace temperature forthe range 2000Tf3000 K. Which gage willhave an output signal that is more sensitive tochanges in the furnace temperature?