Uniform internal heat generation at q˙⁢ = 5.00 × 107 w/m3 is occurring in a cylindrical nuclear reactor fuel rod of 43-mm diameter, and under steady-state conditions the temperature distribution is of the form t(r)=a+br2 , where t is in degrees celsius and r is in meters, while a= 800 °c and b= -4.167 × 105 °c/m2. the fuel rod properties are k= 30 w/m·k, rho= 1100 kg/m3, and cp= 800 j/kg·k. what is the rate of heat transfer per unit length of the rod at r = 0 (the centerline) and at r = 25 mm (the surface)? if the reactor power level is suddenly increased to q2 = 108 w/m3, what is the initial time rate of temperature change at r = 0 and r = 25 mm?