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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.
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, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
L is the vertical length; D is the diameter; ν is the kinematic viscosity. The L and D subscripts indicate the length scale basis for the Grashof number. The transition to turbulent flow occurs in the range 10 8 < Gr L < 10 9 for natural convection from vertical flat plates.
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, = where k is the thermal conductivity, ρ the density, and c p the specific heat capacity.
x is the characteristic length; Ra x is the Rayleigh number for characteristic length x; g is acceleration due to gravity; β is the thermal expansion coefficient (equals to 1/T, for ideal gases, where T is absolute temperature). is the kinematic viscosity; α is the thermal diffusivity; T s is the surface temperature
In thermal engineering, Heisler charts are a graphical analysis tool for the evaluation of heat transfer in transient, one-dimensional conduction. [1] They are a set of two charts per included geometry introduced in 1947 by M. P. Heisler [2] which were supplemented by a third chart per geometry in 1961 by H. Gröber.
L is characteristic length. The Rayleigh number can be understood as the ratio between the rate of heat transfer by convection to the rate of heat transfer by conduction; or, equivalently, the ratio between the corresponding timescales (i.e. conduction timescale divided by convection timescale), up to a numerical factor.
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.
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