Short Answer:

The Nusselt number is a dimensionless number used in heat transfer to describe the ratio of convective heat transfer to conductive heat transfer across a fluid boundary. It helps in understanding how effectively heat is being transferred by convection compared to conduction. A higher Nusselt number indicates better convective heat transfer performance.

In simple terms, the Nusselt number measures how efficiently a fluid carries heat away from a surface compared to heat that would be transferred by pure conduction. It plays an important role in the design of heat exchangers, cooling systems, and thermal analysis of engineering components.

Detailed Explanation:

Nusselt Number

The Nusselt number (Nu) is one of the most important dimensionless numbers in the study of heat transfer. It is named after the German engineer Wilhelm Nusselt, who contributed greatly to the understanding of convective heat transfer. The Nusselt number is used to compare the rate of heat transfer through convection to that through conduction in a fluid layer near a surface.

Mathematically, it is expressed as:

Where:

• Nu = Nusselt number (dimensionless)
• h = Convective heat transfer coefficient (W/m²·K)
• L = Characteristic length (m)
• k = Thermal conductivity of the fluid (W/m·K)

In this formula, the numerator represents the convective heat transfer and the denominator represents the conductive heat transfer. The ratio gives a clear idea of how much more effective convection is compared to conduction.

If Nu = 1, it means heat is transferred only by conduction, without any convection effects.
If Nu > 1, it indicates that convection is enhancing the overall heat transfer rate.

Physical Meaning of Nusselt Number

The Nusselt number shows the enhancement of heat transfer due to fluid motion. In fluids, heat can be transferred in two main ways — conduction, which occurs due to molecular interaction, and convection, which occurs when the fluid moves and carries heat along with it.

When a fluid flows over a hot surface, a thermal boundary layer forms where the temperature changes from that of the surface to that of the fluid. The movement of fluid within this layer causes heat to be transferred more effectively. The Nusselt number represents this increase in heat transfer.

In simpler terms, the Nusselt number tells us how much more effective convective heat transfer is compared to simple conduction.

Types of Nusselt Number

The Nusselt number can be defined for different flow conditions, mainly:

1. Local Nusselt Number (Nuₓ):
   It represents the Nusselt number at a specific location on the surface.

where  is the local heat transfer coefficient at distance .

1. Average Nusselt Number (Nuₐᵥg):
   It represents the average heat transfer performance over the entire surface.

The average value is mostly used in engineering calculations to determine the overall convective heat transfer from surfaces like plates, pipes, or fins.

Applications of Nusselt Number

1. Heat Exchanger Design:
   The Nusselt number is used to calculate the heat transfer coefficient, which is essential in designing efficient heat exchangers.
2. Cooling of Electronic Devices:
   It helps in analyzing the cooling of circuit boards and processors where forced convection is applied.
3. Boiling and Condensation Studies:
   In phase change heat transfer processes, such as boiling and condensation, the Nusselt number helps predict heat flux.
4. Flow over Plates and Tubes:
   It is used to evaluate the heat transfer performance in systems like radiators, condensers, and evaporators.
5. Turbulent and Laminar Flow Analysis:
   The Nusselt number helps in distinguishing between laminar and turbulent flow heat transfer effects.

Typical Ranges of Nusselt Number

• For pure conduction, .
• For laminar flow over a flat plate,  ranges between 10 and 50.
• For turbulent flow,  can reach values up to several hundred or thousand, depending on fluid velocity and surface conditions.

These values show how much convection enhances heat transfer efficiency compared to conduction.

Correlation of Nusselt Number

Engineers often use empirical correlations that relate Nusselt number to other dimensionless numbers like the Reynolds number (Re) and the Prandtl number (Pr).

For example, for turbulent flow in a pipe:

Such correlations make it possible to predict heat transfer rates in practical systems without performing detailed experiments every time.

Conclusion

The Nusselt number is a key parameter in the study of convective heat transfer. It helps engineers and scientists compare the effectiveness of convective and conductive heat transfer processes. A higher Nusselt number means that convection is dominating and that heat is being transferred more efficiently. Understanding the Nusselt number is essential in designing and analyzing heat exchangers, boilers, and cooling systems in mechanical engineering applications.