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.

a. find the steady state temperature gradient, d⁢t/d⁢r, at the outer surface of the rod, in °c/m.

b. what is the steady state rate of heat transfer at the outer surface, in w/m?

c. immediately after the sudden increase in reactor power level (at t= 0 sec), what is the temperature at the centerline?

d. 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?