Write the steady state heat equation and boundary conditions

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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, or , r qcc is assumed uniform. However, at the flat end the axial heat flux, qcc varies with radius according to

83_Figure 9.jpg

q"z = βr,

Where ß is constant. The exposed surface exchanges heat by convection with the ambient. The heat transfer coefficient is h and the ambient temperature is Treat the shaft as semi-infinite and assume that all frictional heat is conducted through the shaft. Write the steady state heat equation and boundary conditions.

Reference no: EM131284351

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