What is the Nusselt number? Please explain in detail its significance. Is the average Nusselt number associated with flow through a tube larger than, equal to, or less than the Nusselt number for fully developed conditions? Why?
The Correct Answer and Explanation is:
The Nusselt number (Nu) is a dimensionless quantity that represents the ratio of convective heat transfer to conductive heat transfer in a fluid flow. It is commonly used to describe heat transfer in both laminar and turbulent flow systems. The Nusselt number is defined as: Nu=hLkNu = \frac{hL}{k}Nu=khL
Where:
- hhh is the convective heat transfer coefficient (W/m²·K),
- LLL is the characteristic length (m) (e.g., the diameter of a tube),
- kkk is the thermal conductivity of the fluid (W/m·K).
Significance of the Nusselt Number
The Nusselt number provides a measure of the effectiveness of convective heat transfer compared to pure conduction. A higher Nusselt number indicates that convection is dominant in the heat transfer process, meaning heat is being transferred more effectively through the fluid. Conversely, a lower Nusselt number indicates a smaller contribution of convection relative to conduction.
In practical applications, the Nusselt number is used to calculate the heat transfer rate for a given flow configuration (like inside a pipe or around a heat exchanger). It’s particularly important in designing systems where efficient heat exchange is needed, such as in chemical reactors, power plants, and HVAC systems.
Average Nusselt Number vs Fully Developed Conditions
For flow through a tube, the average Nusselt number under typical conditions (e.g., for fully developed, laminar flow) is larger than the Nusselt number for fully developed conditions, for the following reasons:
- Fully Developed Flow: In fully developed flow, the temperature and velocity profiles do not change along the length of the tube. This means the convective heat transfer is at a steady state, and the Nusselt number is constant along the flow direction. However, in the entrance region (before the flow becomes fully developed), the temperature gradient is steeper, and thus the heat transfer is more effective.
- Developing Flow: In the developing flow region (before the flow becomes fully developed), the temperature profile and velocity profile are still evolving. This increases the heat transfer in this region, meaning that the average Nusselt number for the entire flow will be higher than in the fully developed region, where the flow characteristics are established.
In summary, the average Nusselt number for flow through a tube is generally larger than the Nusselt number for fully developed conditions, primarily because the flow’s heat transfer ability is enhanced in the developing flow regions.
