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# Characteristic Length

## Description

In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system.

Examples:

Reynolds Number Biot number Nusselt number

In computational mechanics, a characteristic length is defined to force localization of a stress softening constitutive equation. The length is associated with an integration point. For 2D analysis, it is calculated by taking square root of the area. For 3D analysis, it is calculated by taking cubic root of the volume associated to the integrati.

The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations. Gives a simple index of the ratio of the heat transfer resistances inside of and at the surface of a body. This ratio determines whether or not the temperatures inside a body will vary significantly in space, while the body heats or cools over time, from a thermal gradient applied to its surface.

In general, problems involving small Biot numbers (much smaller than 1) are thermally simple, due to uniform temperature fields inside the body. Biot numbers much larger than 1 signal more difficult problems due to non-uniformity of temperature fields within the object. It should not be confused with Nusselt number, which employs the thermal conductivity of the fluid and hence is a comparative measure of conduction and convection, both in the fluid.

The Biot number has a variety of applications, including transient heat transfer and use in extended surface heat transfer calculations.

The formula shown calculates the Characteristic Length.

Related formulas

## Variables

 Lc characteristic length (m) Vbody volume of the body (m3) Asurface surface area of the body (m2)