A section of a long rotating shaft of radius is buried in a material of very low thermal conductivity. The length of the buried section is L. Frictional heat generated in the buried section can be modeled as surface heat flux. Along the buried surface the radial heat flux is or r qcc and the axial heat flux is qx. The exposed surface exchanges heat by convection with the ambient.
The heat transfer coefficient is h and the ambient temperature is Model the shaft as semiinfinite fin and assume that all frictional heat is conducted through the shaft. Determine the temperature distribution.
