What Is The Biot Number?
The Biot number (Bi) is a dimensionless value in thermodynamics, specifically in heat transfer. The number is named after French physicist Jean-Baptiste Biot. It compares the ease of heat flowing through an object’s surface to how easily it moves within its interior. This is incredibly useful in helping to predict temperature distribution within the body under certain thermal conditions.
- If the Biot number is less than 1, this means heat moves freely inside, so the surface and core temperatures stay nearly the same.
- If the Biot number is less greater than 1, this means the surface heats or cools much faster than the interior, creating a steep temperature gradient.
To learn more about the Biot number and other dimensionless numbers as well as units involved in all thermodynamics studies and beyond, check out the following book:
Biot Number Formula
Where:
- Bi – Biot Number (dimensionless)
- h – Heat Transfer Coefficient at Surface (W/m2 K)
- Lc – Characteristic Length of Material (m)
- k – Thermal Conductivity of Material (W/m K)
We can compute the Lc if we have the Volume (m3) and Area (m2) of a surface through which the material is cooled down or heated up.
Biot Number Calculator
When using the calculator below, If the Characteristic Length is known, input the value into the Characteristic Length cell. If this is unknown, make sure the Characteristic Length cell is empty and then input values into both the Volume and Surface Area in order for the calculation to compute the Characteristic Length for you.
Biot Number Uses In Industry
The Biot number plays a role in multiple industrial applications, especially where heat transfer is a critical factor. Below is an overview of some of the key uses of the Biot number in industry. Remember, the Biot number tells you whether an object’s surface heats or cools much faster than its interior. When Bi ≪ 1, the temperature is uniform inside; when Bi ≫ 1, there’s a steep gradient. Here are some key industries the Biot number is used in:
- Food & Beverage
In pasteurisation and chilling, processors use the Biot number to size tanks and cooling coils so that milk, juice or beer reaches the right temperature evenly; avoiding cold spots that can spoil flavour or safety. - Metal Casting & Heat Treatment
Foundries rely on the Biot number to predict how quickly molten metal solidifies. A low Biot number regime means uniform cooling (fewer internal stresses), while a high Biot number indicates the surface freezes first. This means the Biot number can be used to tailor the process to avoid cracks and other defects. - Pharmaceutical Freeze‐Drying
In lyophilisation of vaccines and delicate biologics, the Biot number guides how fast heat penetrates the frozen slab. If the Biot number is too high, the surface thaws and dries before the core, risking case-hardening (a shell that traps moisture). A moderate Biot number ensures uniform sublimation and prevents under-dried zones that could compromise potency. - Electronics Cooling
From data-centre servers to smartphone chips, designers calculate the Biot number to choose the right thickness for heat sinks or thermal interface materials, ensuring hotspots don’t cook the circuitry before the core can catch up. - Chemical Reactors & Heat Exchangers
In petrochemical plants, the Biot number lets designer know the design of jackets and coils that maintain uniform reactor temperatures; maximising yield and preventing runaway reactions at hot or cold zones.
Hassan graduated with a Master’s degree in Chemical Engineering from the University of Chester (UK). He currently works as a design engineering consultant for one of the largest engineering firms in the world along with being an associate member of the Institute of Chemical Engineers (IChemE).
