Biot number

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 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.

Equivalently, if the sphere is made of a poorly conducting (thermally insulating) material, such as wood or styrofoam, the interior resistance to heat flow will exceed that of convection at the fluid/sphere boundary, even for a much smaller sphere.

The value of the Biot number can indicate the applicability (or inapplicability) of certain methods of solving transient heat transfer problems.

In this situation, the simple lumped-capacitance model may be used to evaluate a body's transient temperature variation.

When the Biot number is greater than 0.1 or so, the heat equation must be solved to determine the time-varying and spatially-nonuniform temperature field within the body.

Analytic methods for handling these problems, which may exist for simple geometric shapes and uniform material thermal conductivity, are described in the article on the heat equation.

As noted, a Biot number smaller than about 0.1 shows that the conduction resistance inside a body is much smaller than heat convection at the surface, so that temperature gradients are negligible inside of the body.

Combining these relationships with the First law of thermodynamics leads to a simple first-order linear differential equation.

The study of heat transfer in micro-encapsulated phase-change slurries is an application where the Biot number is useful.