Biot Number Calculator

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Choose which quantity to solve for. The corresponding input below becomes the output.
Characteristic length for the lumped-capacitance method is defined as Lc = V/A. Common geometry shortcuts are listed here.
The ratio of volume to surface area (V/A) for the object. For a sphere it is r/3; for an infinite cylinder r/2; for a slab the half-thickness.
m
Select a common material to auto-fill thermal conductivity. Choose "Custom" to enter k directly.
Thermal conductivity of the solid material. Auto-filled when a material is selected.
W/(m·K)
Convective heat transfer coefficient between the surface and the surrounding fluid. Typical values: natural air 5-25, forced air 25-250, water 500-10000 W/(m²·K).
W/(m²·K)
Biot Number (Bi)Transitional regime (0.1 - 1)
0.2

Dimensionless ratio of convective to conductive thermal resistance

Characteristic length (Lc)0.05m
Heat transfer regimeTransitional regime (0.1 - 1)
0.2
Lumped OK<0.1Transitional0.1-1Spatial needed1+

Biot number is 0.2000 - transitional regime.

  • Bi is between 0.1 and 1: internal conduction is faster than convection but temperature gradients inside the body cannot be fully ignored.
  • A simplified lumped model will introduce moderate error. For accurate results, use a one-term series solution or numerical analysis.
  • Material selected: Carbon steel (50 W/m·K).

Next stepUse the one-term series approximation or a finite-element solver for transient temperature distributions inside the body.

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