The Biot number (Bi) is a dimensionless number used in unsteady-state (or transient) heat transfer calculations. It is named after the French physicist Jean-Baptiste Biot (1774-1862), and relates the heat transfer resistance inside and at the surface of a body.

Definition

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The Biot number is defined as:

$\backslash mathrm\{Bi\}\; =\; \backslash frac\{h\; L\_C\}\{\backslash \; k\_b\}$

where:

• h = overall heat transfer coefficient
• L_C = characteristic length, which is commonly defined as the volume of the body divided by the surface area of the body, such that$$

\mathit{L_C} = \frac{V_{\rm body}}{A_{\rm surface}}.

• k_b = Thermal conductivity of the body

Applications

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Values of the Biot number larger than 0.1 imply that the heat conduction inside the body is slower than at its surface, and temperature gradients are non-negligible inside it.

Heat transfer analog

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An analogous version of the Biot number (usually called the "mass transfer Biot number", or $\backslash mathrm\{Bi\}\_m$) is also used in mass diffusion processes:

$\backslash mathrm\{Bi\}\_m=\backslash frac\{h\_m\; L\}\{D\_\{AB\}\}$

where:

• h - overall mass transfer coefficient
• L_C - characteristic length
• D_AB - mass diffusivity.

Dimensionless numbers | Thermodynamics

Biot-Zahl | Nombre de Biot | ビオ数 | Getal van Biot | Liczba Biota