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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.
The characteristic length in most relevant problems becomes the heat characteristic length, i.e. the ratio between the body volume and the heated (or cooled) surface of the body: = Here, the subscript Q, for heat, is used to denote that the surface to be considered is only the portion of the total surface through which the heat passes.
In thermal fluid dynamics, the Nusselt number (Nu, after Wilhelm Nusselt [1]: 336 ) is the ratio of total heat transfer to conductive heat transfer at a boundary in a fluid. Total heat transfer combines conduction and convection. Convection includes both advection (fluid motion) and diffusion (conduction). The conductive component is measured ...
For heat diffusion with a characteristic length scale ... is the characteristic length through which ... The mass-transfer Fourier number can be applied to the study ...
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
For heat transfer, the Péclet number is defined as: P e L = L u α = R e L P r . {\displaystyle \mathrm {Pe} _{L}={\frac {Lu}{\alpha }}=\mathrm {Re} _{L}\,\mathrm {Pr} .} 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 ...
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