Problem 4: Uniform internal heat generation at q = 6 x 107 W/m is occurring in a cylindrical nuclear reactor fuel rod of 60-mm diameter, and under steady-state conditions the temperature distribution is of the form T(r) = a + br, where T is in degrees Celsius and r is in meters, while a = 900 C and b = -5.26 x 105 C/m. The fuel rod properties are k = 30 W/mK, p = 1100 kg/m, and cp = 800 J/kg-K. a) What is the rate of heat transfer per unit length of the rod at r = 0 (the centerline) and at r = 30 mm (the surface)? b) If the reactor power level is suddenly increased to q = 108 W/m, what is the initial time rate of temperature change at r = 0 and r = 30 mm?