Consider a very long, slender rod. One end of the rod is attached to a base surface maintained at Tb, while the surface of the rod is exposed to an air temperature of 400°C. Thermocouples imbedded in the rod at locations 25 mm and 120 mm from the base surface register temperatures of 335°C and 375°C, respectively.

(a) Calculate the rod base temperature (°C).
(b) Determine the rod length (mm) for the case where the ratio of the heat transfer from a finite length fin to the heat transfer from a very long fin under the same conditions is 99 percent.