Biot Number Calculator

Calculate Biot number for heat transfer analysis and thermal boundary layer characterization

Calculate Biot Number

W/(m²·K)

Heat transfer coefficient at material surface

W/(m·K)

Material thermal conductivity

m

Characteristic length = Volume / Surface Area

Biot Number Results

0.0000
Biot Number (Bi)
0.000000 m
Characteristic Length

Formula: Bi = h × L_c / k

Calculation: 0 × 0.000000 / 0 = 0.0000

Example: Water in Copper Pan

Material: Water

Thermal conductivity (k): 0.7 W/(m·K)

Heat transfer coefficient (h): 13.1 W/(m²·K)

Characteristic length (L_c): 0.15 m

Calculation: Bi = 13.1 × 0.15 / 0.7 = 2.807

Result: Significant temperature gradient

Common Materials

Water

k = 0.7 W/(m·K)

h = 13.1 W/(m²·K)

Water in copper pan

Steel

k = 45 W/(m·K)

h = 25 W/(m²·K)

Steel in air

Aluminum

k = 237 W/(m·K)

h = 25 W/(m²·K)

Aluminum in air

Concrete

k = 1.7 W/(m·K)

h = 10 W/(m²·K)

Concrete structure

Wood

k = 0.15 W/(m·K)

h = 8 W/(m²·K)

Wood in air

Glass

k = 1.4 W/(m·K)

h = 10 W/(m²·K)

Glass in air

Biot Number Significance

Bi << 1 (< 0.1)

Lumped analysis valid

Uniform temperature

Bi ≤ 1

Low temperature gradients

Modified lumped analysis

1 < Bi ≤ 10

Moderate gradients

Distributed analysis needed

Bi >> 1 (> 10)

Large temperature gradients

Surface controls heat transfer

Understanding the Biot Number

What is the Biot Number?

The Biot number (Bi) is a dimensionless number that compares the internal thermal resistance of a body to its external thermal resistance. It determines whether temperature gradients within the body can be ignored during heat transfer analysis.

Physical Significance

  • Determines if lumped parameter analysis is valid
  • Predicts temperature distribution within objects
  • Critical for thermal system design
  • Essential for heat treatment processes

Formula and Variables

Bi = h × L_c / k

  • Bi: Biot number (dimensionless)
  • h: Heat transfer coefficient [W/(m²·K)]
  • L_c: Characteristic length [m]
  • k: Thermal conductivity [W/(m·K)]

Characteristic Length: L_c = Volume / Surface Area

For simple geometries: sphere (R/3), cylinder (R/2), plate (thickness/2)

Applications in Heat Transfer

Thermal Processing

Heat treatment of metals, food processing, and sterilization operations

Electronic Cooling

Design of heat sinks, thermal management of electronic components

Building Design

Thermal analysis of walls, windows, and building materials