A long rod of 60-mm diameter and thermo physical properties P = 8000 kg/m³, c = 500 J/kg ∙ K, and k = 50 W/m ∙ K is initially at a uniform temperature and is heated in a forced convection furnace maintained at 750 K. The convection coefficient is estimated to be 1000 W/m² ∙ K.

(a) What is the centerline temperature of the rod when the surface temperature is 550 K?

(b) In a heat -treating process, the centerline temperature of the rod must be increased from T_j = 300 K to T = 500 K. Compute and plot the centerline temperature histories for h = 100, 500 and 1000 W/m² ∙ K. In each case the calculation may be terminated when T = 500 K.