Transient Plane Couette Flow — Lesson 3

This lesson covers the concept of solving tangent problems, specifically focusing on tangent plane Couette flow and tangent plane Poiseuille flow. The lesson begins with an explanation of the steady plane Couette flow, where the velocity distribution is linear. The instructor then discusses the concept of a Newtonian liquid bounded by two parallel plates and the changes in velocity profile over time. The lesson further delves into the governing differential equation and the use of the separation of variables method to solve the partial differential equation. The instructor also explains the conditions under which this method can be used. The lesson concludes with the application of these concepts to solve the tangent plane Couette flow and tangent plane Poiseuille flow problems.

Video Highlights

00:30 - Introduction to the tangent problem and the concept of tangent plane Couette flow.
08:36 - Explanation of the concept of orthogonal property and how it is used in solving the problem.
12:30 - Discussion on the superposition technique used to make the boundary conditions homogeneous.
25:13 - Discussion on using the method of separation of variables to solve the differential equation.
35:02 - Explanation of the final velocity distribution for the tangent plane Couette flow.
49:26 - Discussion on the solution for the tangent plane Poiseuille flow.

Key Takeaways

- The steady plane Couette flow results in a linear velocity distribution.
- The separation of variables method can be used to solve partial differential equations when the governing equation is linear and homogeneous.
- The method of separation of variables is applicable to steady two-dimensional problems or one-dimensional tangent problems.
- The solution of the tangent plane Couette flow and tangent plane Poiseuille flow problems can be obtained by applying the separation of variables method and using the appropriate boundary conditions.