Uniform internal heat generation at q˙⁢ = 2.75 × 107 W/m3 is occurring in a cylindrical nuclear reactor fuel rod of 40-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. Find the steady state temperature gradient, d⁢T/d⁢r, at the outer surface of the rod, in °C/m. What is the steady state rate of heat transfer at the outer surface, in W/m?Immediately after the sudden increase in reactor power level (at t= 0 sec), what is the temperature at the centerline?Immediately after the sudden increase in reactor power level (at t= 0 sec), what is the time rate of temperature change, d⁢T/d⁢t, at the centerline, in °C/s?