A long rod of 60-mm diameter and thermophysical properties rho = 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 Ti = 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.