Biot Number Calculator
Calculate Biot number for heat transfer analysis and thermal boundary layer characterization
Calculate Biot Number
Heat transfer coefficient at material surface
Material thermal conductivity
Characteristic length = Volume / Surface Area
Biot Number Results
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