# Biot Number

on . Posted in Dimensionless Numbers

Biot Number, abbreviated as Bi, a dimensionless number, is the ratio of internal thermal resistance of solid to fluid thermal resistance.  This is used for heat transfer between fluids and solids.  The Biot number helps determine the mode of heat transfer and the relative significance of conduction within the solid compared to convection at the surface.

### Depending on the magnitude of the Biot number, different heat transfer mechanisms dominate

• Bi < 1  -  When the Biot number is much smaller than 1, conduction within the solid material dominates over convection at the surface.  In this regime, heat transfer is primarily governed by thermal conduction, and the temperature distribution within the solid is relatively uniform.
• Bi > 1  -  When the Biot number is much larger than 1, convection at the surface dominates over internal conduction.  In this regime, the heat transfer process is primarily influenced by convective heat transfer at the solid's external surface.  The temperature distribution within the solid is more affected by the convective boundary conditions.
• Bi ≈ 1  -  When the Biot number is close to 1, both conduction within the solid and convection at the surface are of comparable importance.  The temperature distribution within the solid is influenced by both mechanisms.

The Biot number is particularly relevant in situations involving heat transfer through solid materials with convective boundary conditions, such as in heat exchangers, cooling of electronic devices, and other thermal management applications.  It helps assess the relative significance of internal and external thermal resistances and guides the design and optimization of heat transfer systems.

### Biot Number formula

$$Bi \;=\; h \; l_c \;/\; k$$     (Biot Number)

$$h \;=\; Bi \; k \;/\; l_c$$

$$l_c \;=\; Bi \; k \;/\; h$$

$$k \;=\; h \; l_c \;/\; Bi$$

Symbol English Metric
$$\large{ Bi }$$ = biot number $$dimensionless$$
$$\large{ h }$$ = heat transfer coefficient of film coefficient or convective heat transfer coefficient $$Btu\;/\;hr-ft^2-F$$  $$W\;/\;m^2-K$$
$$\large{ l_c }$$ = characteristic length $$ft$$ $$m$$
$$\large{ k }$$ = thermal conductivity of the body $$Btu-ft\;/\;hr-ft^2-F$$  $$W\;/\;m-K$$

Tags: Heat Transfer