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Concept# Biot number

Summary

The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations, named for the eighteenth-century French physicist Jean-Baptiste Biot (1774–1862). The Biot number is the ratio of the thermal resistance for conduction inside a body to the resistance for convection at the surface of the body. This ratio indicates whether the temperature inside a body varies significantly in space when the body is heated or cooled over time by a heat flux at its surface.
In general, problems involving small Biot numbers (much smaller than 1) are analytically simple, as a result of nearly uniform temperature fields inside the body. Biot numbers of order one or greater indicate more difficult problems with nonuniform temperature fields inside the body.
The Biot number appears in a number of heat transfer problems, including transient heat conduction and fin heat transfer calculations.
**TOC**
The Biot number is defined as:
where:
is the thermal conductivity of the body [W/(m·K)]
is a convective heat transfer coefficient [W/(m2·K)]
is a characteristic length [m] of the geometry considered.
(The Biot number should not be confused with the Nusselt number, which employs the thermal conductivity of the fluid rather than that of the body.)
The characteristic length in most of relevant problems becomes the heat characteristic length, i.e. the ratio between the body volume and the heated (or cooled) surface of the body:
Here, the subscript Q, for heat, is used to denote that the surface to be considered is only the portion of the total surface through which the heat passes.
The physical significance of Biot number can be understood by imagining the heat flow from a small hot metal sphere suddenly immersed in a pool, to the surrounding fluid. The heat flow experiences two resistances: the first for conduction within the solid metal (which is influenced by both the size and composition of the sphere), and the second for convection at the surface of the sphere.

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