A manufacturing process calls for heating long copper rod which are coated with a thin film having ε = 1, by placing them in a large evacuated oven whose surface is maintained at 1650 K. The rods are of 10-mm diameter and are placed in the oven with an initial temperature of 300 K.

(a) What is the initial rate of change of the rod temperature?

(b) How long must the rods remain in the oven to achieve a temperature of 1000 K?

(c) The heating process may be accelerated by routing combustion gases also at J 650 K, through the oven. For convection coefficients of 10, 100 and 500 W/m² · K. determine the time required for the rods to reach 1000 K.