Heat Transfer from a Rotating Cylinder in Simple Shear Flow

Heat Transfer from a Rotating Cylinder in Simple Shear Flow 

To begin our analysis of the cylinder problem, it is necessary to consider briefly the velocity field. The fluid mechanics solution for a circular cylinder rotating with an imposed angular velocity il in a simple shear flow was given originally by Bretherton26 for the creeping-flow limit. In this case, the velocity field can be specified in terms of a stream-function (see Chap. 7) such that 

A sketch of the physical problem and a definition of the cylindrical polar coordinates (r, p) are given in Fig. 9-17. For the creeping-flow limit, the governing equations and boundary conditions are 

the velocities are nondimensionalized with respect to (la, where G is the shear rate of the undisturbed flow and a is the cylinder radius. The Bretherton solution of (9 300) and (9 301) is 

In the present case, there is no externally applied torque on the cylinder (i.e., it is free to rotate in the flow). Thus the hydrodynamic torque must also vanish at steady state and 

---

Problem 9-19. Heat Transfer From a Rotating Cylinder in Simple Shear Flow. We... 

---