Problem 1. (6 pts)

A nuclear reactor has spherical fuel elements that produce heat according to the relationship

à -à-[¹-(3)]

where is the volumetric heat generation rate, kW/m³, and ro is the radius of the sphere.

(a) Use the shell-balance approach and derive the differential equation that governs the

temperature profile within the sphere. (3 pts)

(b) Using this differential equation solve the expression for the temperature difference

between the center and surface of the sphere (i.e., Tecenter-Tsurface). (3 pts)