Physics

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Biot Number Calculator.

Calculate the dimensionless Biot number for heat transfer.

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biotNumber: 0.833333

biotNumber

0.000000

Use Cases

Lumped Capacitance Analysis

Engineers use the Biot number to check if the lumped capacitance method is valid for transient heat transfer problems. If Bi < 0.1, the assumption of uniform temperature is reasonable.

Example: Cooling a small metal sphere in air: Bi = 0.05, so lumped capacitance applies.

Heat Exchanger Design

In designing heat exchangers, the Biot number helps evaluate the relative importance of internal conduction versus surface convection, guiding material selection and fin design.

Example: Comparing Bi for a copper fin vs. a stainless steel fin of the same geometry.

Frequently Asked Questions

What is the Biot number and why is it important?
The Biot number (Bi) is a dimensionless quantity used in heat transfer to compare the resistance to heat conduction within a solid to the resistance to heat convection at its surface. It helps determine whether a body can be treated as having a uniform temperature (lumped capacitance) or if temperature gradients are significant.
How is the Biot number calculated?
The Biot number is calculated by multiplying the convection heat transfer coefficient (h) by the characteristic length (L) and dividing by the thermal conductivity (k) of the solid: Bi = h * L / k. This calculator uses the inputs you provide for these three parameters.
What does a high or low Biot number indicate?
A Biot number much less than 1 (typically < 0.1) indicates that conduction inside the solid is much faster than convection at the surface, so the temperature can be assumed uniform. A Biot number greater than 1 suggests significant temperature gradients within the solid, requiring a more detailed analysis.

Tips & Common Mistakes

Tips

  • Ensure consistent units: convection coefficient in W/(m²·K), length in meters, and thermal conductivity in W/(m·K) to get a dimensionless Biot number.
  • For non-uniform shapes, use the characteristic length defined as volume divided by surface area (V/A) for lumped capacitance analysis.
  • A Biot number below 0.1 is the common threshold for neglecting internal temperature gradients.
  • Double-check your thermal conductivity value: it should be for the solid material, not the fluid.

Common Mistakes to Avoid

  • Using the wrong characteristic length: for a slab, it's half-thickness; for a cylinder, it's radius; for a sphere, it's radius. Using the full thickness can skew results.
  • Forgetting that the Biot number is dimensionless: if your result has units, you've likely made an error in input or calculation.

Last updated: August 13, 2026