Dear teacher, thanks for your help. I may not express my meaning clearly. I have looked at the Couette example provided in examples/flow. I need two kinds of walls, one is insulated wall and the other is heat conducting wall.

The temperature distribution of the first insulating wall is recorded in the Chinese fluid mechanics book. See Fig.1.



In many literatures about couette flow, first, give the system a constant temperature; second , only keep the wall temperature and give both wall a opposite direction velocity, remove the fluid temperature control. A temperature distribution in the form of an approximate parabola can be obtained, see Fig.2.



Finally, I would like to ask how to control the velocity and temperature about the wall at the same time and get a similar temperature distribution.