Table of Contents
What is the Biot Number?
The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations. It represents the ratio of internal conductive resistance within a body to the external convective resistance at its surface. This ratio determines whether temperature gradients within the object are significant during transient heating or cooling.
When the Biot number is less than 0.1, the internal resistance is so small compared to external resistance that the object's temperature can be considered uniform throughout. This simplification, known as the lumped capacitance method, greatly simplifies transient heat transfer analysis and is widely used in engineering practice for quick thermal calculations.
Biot Number Formula
Where h is the convective heat transfer coefficient (W/m²K), Lc is the characteristic length (volume divided by surface area), and k is the thermal conductivity of the solid (W/mK). For a sphere, Lc = r/3; for a cylinder, Lc = r/2; for a flat plate, Lc = thickness/2.
Typical Values
| Material | k (W/mK) | Bi (h=100, Lc=0.01m) |
|---|---|---|
| Copper | 385 | 0.0026 |
| Aluminum | 205 | 0.0049 |
| Steel | 50 | 0.020 |
| Glass | 1.0 | 1.000 |
| Wood | 0.15 | 6.667 |
Frequently Asked Questions
What happens when Bi is much greater than 1?
When the Biot number is much greater than 1, the internal conductive resistance dominates. The surface temperature quickly approaches the ambient temperature while the interior remains at its initial temperature for a significant time. The temperature distribution within the object must be calculated using more complex methods such as Heisler charts or numerical solutions to the heat equation.
How is characteristic length determined?
The characteristic length is the ratio of the object's volume to its surface area (V/A). For a sphere of radius r, this equals r/3. For an infinitely long cylinder of radius r, it equals r/2. For a plane wall of thickness 2L, it equals L. Using V/A ensures the Biot number criterion (Bi less than 0.1) is consistent across different geometries.
Can the Biot number apply to mass transfer?
Yes, an analogous Biot number for mass transfer can be defined using the mass transfer coefficient, characteristic length, and diffusion coefficient. When the mass transfer Biot number is less than 0.1, the concentration within the object can be assumed uniform, analogous to the thermal lumped capacitance assumption.