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...

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 Tj = 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.