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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.
The Fourier number can also be used in the study of mass diffusion, in which the thermal diffusivity is replaced by the mass diffusivity. The Fourier number is used in analysis of time-dependent transport phenomena , generally in conjunction with the Biot number if convection is present.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
Plotted along the horizontal axis is the Fourier number, Fo = αt/L 2. The curves within the graph are a selection of values for the inverse of the Biot number, where Bi = hL/k. k is the thermal conductivity of the material and h is the heat transfer coefficient. [1] [5]
For heat transfer, the Péclet number is defined as = =, where L is the characteristic length, u the local flow velocity, D the mass diffusion coefficient, Re the Reynolds number, Sc the Schmidt number, Pr the Prandtl number, and α the thermal diffusivity,
The opposite is also true: A Biot number greater than 0.1 (a "thermally thick" substance) indicates that one cannot make this assumption, and more complicated heat transfer equations for "transient heat conduction" will be required to describe the time-varying and non-spatially-uniform temperature field within the material body.
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If the Biot number is less than 0.1 for a solid object, then the entire material will be nearly the same temperature, with the dominant temperature difference being at the surface. It may be regarded as being "thermally thin". The Biot number must generally be less than 0.1 for usefully accurate approximation and heat transfer analysis.