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How It Works
The Biot number (Bi) is a dimensionless quantity used in heat transfer analysis. It compares the internal thermal resistance within a body to the external convective thermal resistance at its surface. The formula is Bi = hL / kₛ, where h is the heat transfer coefficient, L is a characteristic length, and kₛ is the thermal conductivity of the solid.
When Bi < 0.1, the temperature gradient inside the body is negligible, allowing the simpler lumped capacitance method. When Bi >> 1, significant internal temperature gradients exist and a detailed conduction analysis is required.
Example Problem
A sphere with a diameter of 0.1 m has a heat transfer coefficient of h = 50 W/m²·K and thermal conductivity kₛ = 200 W/m·K. The characteristic length (radius) is L = 0.05 m. What is the Biot number?
- Bi = hL / kₛ = 50 × 0.05 / 200
- Bi = 2.5 / 200 = 0.0125
Because Bi < 0.1, the lumped capacitance model applies and the temperature within the sphere can be assumed uniform during transient cooling or heating.
Frequently Asked Questions
What does a high Biot number mean?
A high Biot number (Bi >> 1) indicates that internal conduction resistance is much larger than external convection resistance. This means large temperature gradients develop inside the body, and the lumped capacitance approach is not valid.
When can the lumped capacitance method be applied?
The lumped capacitance method is valid when Bi < 0.1. In this regime the internal conduction resistance is so small compared to surface convection resistance that the body's temperature is essentially uniform throughout the transient process.
How is characteristic length determined?
The characteristic length is typically the body's volume divided by its surface area (L = V/A). For a sphere this equals r/3, for a long cylinder r/2, and for a flat plate half the thickness. Using V/A provides a consistent basis for comparing different geometries.
What does a Biot number of 1 signify?
A Biot number of 1 means that the internal conduction resistance and external convection resistance are equal. Neither dominates, so a full conduction-convection analysis is needed to accurately predict the temperature distribution.
Can the Biot number be negative?
No. The Biot number is always a non-negative value because it is a ratio of positive thermal resistances. All three quantities in the formula (h, L, and kₛ) are positive physical properties.
Related Calculators
- Nusselt Number Calculator — ratio of convective to conductive heat transfer across a boundary.
- Fourier Number Calculator — dimensionless time for transient heat conduction analysis.
- Prandtl Number Calculator — ratio of momentum diffusivity to thermal diffusivity.
- Thermal Conductivity Calculator — compute heat conduction through materials.