Long cylindrical AISI stainless steel rods (k = 7.74 Btu/h·ft·°F and α = 0.135 ft2/h) of 4...

Long cylindrical AISI stainless steel rods (k = 7.74 Btu/h·ft·°F and α = 0.135 ft²/h) of 4-in-diameter are heat treated by drawing them at a velocity of 7 ft/min through a 21-ft-long oven maintained at 1700°F. The heat transfer coefficient in the oven is 20 Btu/h·ft²·°F. If the rods enter the oven at 70°F, determine their centerline temperature when they leave. Solve this problem using analytical one-term approximation method (not the Heisler charts).