Temperature Distribution in Fluids Confined Between Co-axial Cylinders — Lesson 3

This lesson covers the transport phenomena of non-Newtonian fluids, focusing on the temperature distribution in fluids confined between coaxial cylinders. It discusses the impact of the confinement gap size on the velocity profile and temperature distribution. The lesson explains how the curvature effect can be neglected when the cylinders are very close, resulting in a linear velocity profile. However, when the gap is moderate, the velocity profile becomes non-linear, and the temperature distribution changes significantly. The lesson also provides a detailed walkthrough of the mathematical calculations involved in determining the velocity profile and temperature distribution.

Video Highlights

02:28 - Discussion on the impact of the curvature effects on the velocity profile and temperature distribution.
20:25 - Explanation of the energy equation in cylindrical coordinates and the use of scaling parameters to write the equation in a dimensionless form.
29:28 - Final temperature distribution in dimensionless form and in dimensional form.
30:17 -Comparison of the current problem with the previous lecture's problem, highlighting the importance of curvature effects.

Key Takeaways

• The size of the confinement gap between coaxial cylinders significantly impacts the velocity profile and temperature distribution of non-Newtonian fluids.
• When the gap is very small, the curvature effect can be neglected, resulting in a linear velocity profile.
• When the gap is moderate, the velocity profile becomes non-linear, and the temperature distribution changes significantly.
• The mathematical calculations involved in determining the velocity profile and temperature distribution are complex and require a thorough understanding of the transport phenomena of non-Newtonian fluids.