A spine attached to a wall maintained at a uniform temperature Tb has the shape of a circular cone with base diameter b, height L and a concave parabolic profile, and it is exposed to a fluid at a uniform temperature T?. 

(a) Assuming that the thermal conductivity k of the material of the spine and the heat transfer coefficient h are constants, and that the variation of the temperature in the r direction is negligible, develop an expression for the steady-state temperature distribution T(x) in the spine. 

(b) Obtain an expression for the rate of heat loss to the surrounding fluid.