The Nusselt number and the Biot number are both dimensionless parameters used in heat transfer analysis, but they represent different physical phenomena and have different physical significances.
Nusselt Number (Nu): The Nusselt number characterizes the convective heat transfer between a solid surface and a fluid. It is defined as the ratio of convective heat transfer to conductive heat transfer across a boundary layer. Mathematically, the Nusselt number is expressed as:
Nu = (hL) / k
Where:
- h is the convective heat transfer coefficient between the fluid and the solid surface.
- L is a characteristic length of the system (such as the length of the surface in the flow direction).
- k is the thermal conductivity of the fluid.
The Nusselt number indicates the enhancement or reduction of heat transfer due to convection compared to conduction alone. A high Nusselt number implies that convection dominates, resulting in efficient heat transfer. It is commonly used in forced convection, natural convection, and boiling/condensation heat transfer analyses.
Biot Number (Bi): The Biot number characterizes the relative importance of conduction within a solid compared to convection at its surface. It is defined as the ratio of the internal thermal resistance to the external thermal resistance. Mathematically, the Biot number is expressed as:
Bi = hL / k_s
Where:
- h is the convective heat transfer coefficient between the fluid and the solid surface.
- L is a characteristic length of the system (such as the length of the solid object).
- k_s is the thermal conductivity of the solid.
The Biot number indicates the significance of conduction within the solid compared to the convective heat transfer at its surface. A low Biot number implies that conduction is dominant, meaning that the temperature distribution within the solid is relatively uniform. On the other hand, a high Biot number suggests that convection is significant, resulting in a non-uniform temperature distribution within the solid.
In summary, the Nusselt number focuses on the heat transfer between a solid surface and a fluid, indicating the degree of convective heat transfer enhancement, while the Biot number characterizes the importance of conduction within a solid compared to the convective heat transfer at its surface.