Biot number

Physical key figure
Surname	Biot number
Formula symbol	${\displaystyle {\mathit {Bi}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {Bi}}={\frac {R_{\mathrm {th} }}{R_{\mathrm {s} }}}}$
${\displaystyle R_{\mathrm {th} }}$ Thermal resistance ${\displaystyle R_{\mathrm {s} }}$ Heat transfer resistance
Named after	Jean-Baptiste Biot
scope of application	transient heat conduction

The Biot number ( symbol : Bi , according to Jean-Baptiste Biot ) is a dimensionless number of thermodynamics and fluid mechanics .

Like the Fourier number, it is used to calculate heating and cooling processes and indicates the ratio of the heat (conductivity) resistance of the body to the heat transfer resistance of the surrounding medium when heat is transported through the surface of a body :

${\displaystyle {\mathit {Bi}}={\frac {R_{\mathrm {th} }}{R_{\mathrm {s} }}}.}$

The following applies to plane geometry:

${\displaystyle R_{\mathrm {th} }={\frac {L}{\lambda _{\mathrm {s} }\cdot A}};\qquad R_{\mathrm {s} }={\frac {1}{\alpha \cdot A}}}$

${\displaystyle \Rightarrow {\mathit {Bi}}={\frac {\alpha \cdot L}{\lambda _{\mathrm {s} }}}}$

With

• L = characteristic length of the solid body, e.g. B. the layer thickness that has to be heated,
• A = cross-sectional area of ​​the solid body
• λ _s = specific thermal conductivity of the solid material ( s = solid )
• α = (specific) heat transfer coefficient to the flowing fluid .

In this way, the Biot number is formally equal to the Nusselt number , in which, however, the specific thermal conductivity  λ _{l of} the fluid is used instead of  λ _s and  L has a different meaning.

A large Biot number means that temperature differences within the solid body are greater than in the boundary layer of the fluid, so that an improvement in the external heat transfer, e.g. B. by forced instead of free convection , the process is not significantly accelerated. This connection is important, for example, in the industrial thawing and freezing of food .

The similarity theory states that the temperature fields of two geometrically similar structures are similar if their Biot numbers are the same, regardless of the scale .

Individual evidence

1. ↑ ^{a b c} Wolfgang Polifke, Jan Kopitz: Heat transfer basics, analytical and numerical methods . Pearson Deutschland GmbH, 2009, ISBN 978-3-8273-7349-6 , p. 78 ( limited preview in Google Book search).
2. ↑ Hans Dieter Baehr, Karl Stephan : Heat and mass transfer . Springer-Verlag, 2013, ISBN 978-3-642-36558-4 , pp. 134 ( limited preview in Google Book search).
3. ↑ ^{a b} Kneer, Aron: Numerical investigation of the heat transfer behavior in different porous media . KIT Scientific Publishing, 2014, ISBN 978-3-7315-0252-4 , pp. 122 ( limited preview in Google Book search).
4. ↑ Heike P. Schuchmann, Harald Schuchmann: Food process engineering raw materials, processes, products . John Wiley & Sons, 2012, ISBN 3-527-66054-2 ( limited preview in Google Book Search).