# Biot Number Calculator

Created by Krishna Nelaturu
Last updated: Nov 21, 2022

Our Biot number calculator will help you determine the Biot number of a body. The Biot number will help you understand the heat distribution in a body when you heat a part of its surface. In this article, we shall briefly discuss the Biot number, including:

• What is Biot number?
• Biot number equation
• Biot number for spheres and cylinders.

Is your goal to heat a body to a specific temperature? Our heat capacity calculator and specific heat calculator will help you with calculations on how much heat is needed to reach the desired temperature!

## What is Biot number?

The Biot number (Bi) is a dimensionless number used to predict how well a solid material conducts heat. It is named after French physicist Jean Baptiste Biot.

The Biot number is a ratio of the rate of heat transfer by conduction to the rate of heat transfer by convection. If you're heating a rod in a furnace, you can use this number to predict the heat distribution within the rod. Further, we can understand whether the rod will achieve thermal equilibrium quickly.

Objects with a large Biot number require more time to reach thermal equilibrium. However, this increased insulation can also lead to increased energy costs, as it takes longer for heat to escape from the system. As such, engineers must often strike a balance between different competing factors when designing systems that involve heat transfer.

## Biot number equation

The formula for the Biot number is:

$\text{Bi} = \frac{h}{k}L_c$

Where:

• $\text{Bi}$ - Biot number;
• $h$ - Heat transfer coefficient at the body surface in $\rm{W/m^2 \cdot K}$;
• $k$ - Thermal conductivity of the body in $\rm{W/m \cdot K}$; and
• $L_c$ - Characteristic length of the body.

We can calculate the body's characteristic length using the equation:

$L_c = \frac{V}{A}$

Where:

• $V$ - Volume of the body; and
• $A$ - Surface area through which the body is heated.

In other words, the characteristic length depends on the body geometry. Let's look at two common geometries - cylinders and spheres.

• Biot number for cylinder - The characteristic length of the cylinder with radius $r$ and height $H$ would be:
$\qquad L_c = \frac{V}{A} = \frac{\pi r^2 H}{2\pi r (r + H)}\\ [1em] \qquad L_c = \frac{ r H}{2 (r + H)}$

Using this characteristic length in the formula for Biot number, we would get the following:

$\qquad \text{Bi} = \frac{h}{k}\left( \frac{ r H}{2 (r + H)} \right)$
• Biot number for sphere - The characteristic length of the sphere with radius $r$ would be:
$\qquad L_c = \frac{V}{A} = \frac{\frac{4}{3}\pi r^3}{4\pi r^2}\\ [1em] \qquad L_c = \frac{ r}{3}$

Using this characteristic length in the formula for the Biot number, we would get the following:

$\qquad \text{Bi} = \frac{rh}{3k}$

## Using this tool to calculate Biot number

Our Biot number calculator is simple to use:

• Enter the body's surface area and volume. The calculator will determine the characteristic length using these values. If you know the characteristic length, you can enter it directly in its corresponding field.
• Provide the heat transfer coefficient value.
• Enter the thermal conductivity of the material. The calculator will use all the given data to calculate the Biot number.
Krishna Nelaturu
Characteristic length
Surface area
Volume
Biot number
Characteristic length
m
Heat transfer coefficient
W/(m² * K)
Thermal conductivity
W/(m⋅K)
Biot number
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