A rigid and long cylindrical object is rotating around its axis at a constant rotational speed, in an otherwise quiescent and infinitely large fluid. The cylinder only has rotational motion, without...

A rigid and long cylindrical object is rotating around its axis at a constant rotational speed, in an otherwise quiescent and infinitely large fluid. The cylinder only has rotational motion, without any translational motion. The surface temperature of the object is higher than the temperature of the ambient fluid. The motion can be assumed laminar everywhere.

 a. Write the complete mass, momentum, and energy conservation equations and their boundary conditions assuming an incompressible, Newtonian, and constant-property fluid, in polar cylindrical coordinates.

b. Simplify the equations for steady-state conditions.