In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation

Question:

where qg = local rate of heat generation per unit volume at rro = outside radiusq1 = rate of heat generation per unit volume at the centerlineCalculate the temperature drop from the center line to the surface for a 1 in. OD rod having a thermal conductivity of 15 Btu/(h ft ?F) if the rate of heat removal from its surface is 500,000 Btu/(h ft2).GIVENA cylindrical rod with internal generation and heat removal from its surfaceOutside diameter (Do) = 1 inRate of heat generation is as given aboveThermal conductivity (k) = 15 Btu/(h ft ?F)Heat removal rate (q/A) = 500,000 Btu/(h ft2)ASSUMPTIONSThe heat flow has reached steady stateThe thermal conductivity of the fuel rod is constantOne dimensional conduction in the radial direction