Question

Uniform internal heat generation at  q˙⁢ = 2.00 × 10⁷ W/m³ is occurring in a cylindrical nuclear reactor fuel rod of 50-mm diameter, and under steady-state conditions the temperature distribution is of the form T(r)=a+br^2, 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, ρ= 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?

Answer 1