A medical investigator is proposing to use radioactive spheres for thermal ablation of tumors. The idea is that the radioactivity will generate heat at a constant, uniform rate, G (J m-3 s-1), that will raise the temperature of the sphere relative to its surroundings.
a) Develop an equation for the heat flux at the surface of the sphere (macroscopic balance).
b) Determine the temperature distribution in the sphere (microscopic balance).
c) Estimate the heat generation rate in the sphere given
Core temperature = 60 °C
Surface temperature = 45 °C
Sphere radius = 0.5 mm
Sphere thermal conductivity = 27.5 W m-1 K-1