Biot Number Calculator for Heat Transfer Analysis

Calculator Inputs

Case Name

Geometry Option

Convection Coefficient, h (W/m²·K)

Thermal Conductivity, k (W/m·K)

Characteristic Length, Lc (m)

Total Slab Thickness (m)

Cylinder Radius (m)

Sphere Radius (m)

Prism Length (m)

Prism Width (m)

Prism Height (m)

Density, ρ (kg/m³) — Optional

Specific Heat, cp (J/kg·K) — Optional

Tip: For transient lumped analysis, Bi ≤ 0.1 is the usual acceptance rule. This tool also compares resistance scales and can estimate a lumped time constant.

Biot Number Sensitivity Plot

The graph shows how the Biot number changes with the convection coefficient while holding your current geometry and conductivity fixed.

Formula Used

Bi = hLc / k

Where:

Bi = Biot number
h = convection heat transfer coefficient (W/m²·K)
Lc = characteristic length (m)
k = thermal conductivity (W/m·K)

Characteristic length options:

Custom: Lc = given value
Slab: Lc = thickness / 2
Long cylinder: Lc = radius / 2
Sphere: Lc = radius / 3
Rectangular prism: Lc = V / As = abc / [2(ab + ac + bc)]

Optional time constant: τ = ρcpLc / h. This is useful only when a lumped temperature model is physically reasonable.

How to Use This Calculator

Select a geometry option or enter a custom characteristic length.
Enter the convection coefficient and thermal conductivity.
Provide geometry dimensions only for the selected body type.
Optionally enter density and specific heat to estimate a lumped time constant.
Press Calculate Biot Number to show results above the form.
Read the classification, resistance comparison, and sensitivity plot.
Use the export buttons to save a CSV or PDF summary.

Example Data Table

Case	Geometry	h (W/m²·K)	k (W/m·K)	Lc (m)	Bi	Interpretation
Aluminum fin base	Custom	35	205	0.012	0.00205	Lumped approach is excellent.
Polymer sphere	Sphere, r = 0.03 m	120	0.20	0.010	6.0	Strong internal gradients expected.
Steel wall	Slab, t = 0.01 m	60	45	0.005	0.00667	Uniform temperature is a good approximation.
Food block	Rectangular prism	18	0.45	0.00833	0.333	Use caution with lumped assumptions.

These examples are illustrative and help compare geometry effects, conductivity contrast, and convection strength.

FAQs

1) What does the Biot number measure?

It compares internal conduction resistance to external convection resistance. Small values mean the solid temperature stays relatively uniform. Large values mean internal temperature gradients are important and spatial transient conduction methods are more appropriate.

2) When is lumped capacitance acceptable?

A common engineering rule is Bi ≤ 0.1. In that range, internal resistance is usually small enough that one uniform solid temperature can approximate transient heating or cooling well.

3) Why is characteristic length important?

Characteristic length sets the conduction path scale inside the body. A larger Lc usually increases Bi, making internal gradients more significant for the same material conductivity and convection coefficient.

4) Why can two materials with the same size have different Bi values?

Thermal conductivity changes the denominator of Bi. High-conductivity materials conduct heat internally more easily, so they often show smaller Bi values than low-conductivity materials under the same external conditions.

5) Does a higher convection coefficient always increase Bi?

Yes, if geometry and conductivity stay fixed. Stronger convection lowers external resistance, so internal conduction becomes relatively more important, raising the Biot number.

6) Why is the rectangular prism option useful?

Many real products are block-shaped. Using Lc = V/As lets you represent three-dimensional parts more realistically than forcing them into a slab or cylinder approximation.

7) What is the optional time constant output?

It estimates τ = ρcpLc/h. This helps judge transient response speed under lumped conditions. It is most meaningful when Bi is small enough for a uniform temperature assumption.

8) Should I trust lumped results when Bi is around 0.3?

Use caution. It may still help for a quick estimate, but internal gradients can noticeably affect accuracy. A Heisler chart or transient conduction model is safer for design decisions.