Temperature Distribution for FDF of Newtonian Fluids in Tubes — Lesson 1

This lesson covers the topic of Transport Phenomena of Non-Newtonian Fluids, focusing on the temperature distribution for a fully developed flow of Newtonian fluids in tubes. The lesson explains the constraints of the problem, the velocity profiles for power law fluids, and the energy equation. It also discusses the conditions for fully developed flow, the effects of temperature on velocity, and the process of solving the energy equation. The lesson further delves into the assumptions of the problem, the equation of motion, and the equation of energy. It concludes with the final solution for the temperature distribution of a Newtonian fluid under fully developed flow conditions.

Video Highlights

01:25 - Explanation of the velocity profile and the energy equation.
07:44 - Explanation of the process to obtain the temperature distribution by simplifying the energy equation.
14:59 - Discussion on the solution of the problem and the steps to obtain the final temperature distribution.
43:23 - Conclusion of the lecture with references for further reading.

Key Takeaways

• The flow is fully developed when the L/D ratio is very large, generally more than 150.
• The temperature profile is only applicable for the region of the tube where the flow is fully developed.
• The velocity profile is not a function of temperature, but the temperature is a function of velocity.
• The velocity profile for Newtonian fluids is parabolic.
• The temperature is a function of both r and z, making the problem more complicated to solve mathematically.
• The final solution for the temperature distribution of a Newtonian fluid under fully developed flow conditions is obtained through a series of mathematical steps and assumptions.