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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.
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.
The Fourier number can be derived by nondimensionalizing the time-dependent diffusion equation. As an example, consider a rod of length L {\displaystyle L} that is being heated from an initial temperature T 0 {\displaystyle T_{0}} by imposing a heat source of temperature T L > T 0 {\displaystyle T_{L}>T_{0}} at time t = 0 {\displaystyle t=0 ...
These first Heisler–Gröber charts were based upon the first term of the exact Fourier series solution for an infinite plane wall: (,) = = [ + ], [1]where T i is the initial uniform temperature of the slab, T ∞ is the constant environmental temperature imposed at the boundary, x is the location in the plane wall, λ is the root of λ * tan λ = Bi, and α is thermal diffusivity.
If the system has a Biot number of less than 0.1, the material behaves according to Newtonian cooling, i.e. with negligible temperature gradient within the body. [6] If the Biot number is greater than 0.1, the system behaves as a series solution. however, there is a noticeable temperature gradient within the material, and a series solution is ...
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The Nusselt number is most useful in determining the convective heat transfer coefficient, whereas the Biot number is used in unsteady problems. This is a typical exam question. The " k {\displaystyle k} " in the Biot numer is of a solid, that in the Nusselt number of a fluid.