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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.
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 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.
The Sherwood number (Sh) (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation. It represents the ratio of the total mass transfer rate (convection + diffusion) to the rate of diffusive mass transport, [1] and is named in honor of Thomas Kilgore Sherwood. It is defined as follows
A larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100–1000 range. [2] A similar non-dimensional property is the Biot number, which concerns thermal conductivity for a solid body rather than a fluid. The mass transfer analogue of the Nusselt number is the Sherwood number.
It is common in the field of mass transfer system design and modeling to draw analogies between heat transfer and mass transfer. [2] However, a mass transfer-analogous definition of the effectiveness-NTU method requires some additional terms. One common misconception is that gaseous mass transfer is driven by concentration gradients, however ...