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This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The tables also include pure numbers , dimensionless ratios, or dimensionless physical constants ; these topics are discussed in the article.
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.
The Stanton number (St), is a dimensionless number that measures the ratio of heat transferred into a fluid to the thermal capacity of fluid. The Stanton number is named after Thomas Stanton (engineer) (1865–1931). [1] [2]: 476 It is used to characterize heat transfer in forced convection flows.
In fluid mechanics (especially fluid thermodynamics), the Grashof number (Gr, after Franz Grashof [a]) is a dimensionless number which approximates the ratio of the buoyancy to viscous forces acting on a fluid. It frequently arises in the study of situations involving natural convection and is analogous to the Reynolds number (Re). [2]
In the study of heat conduction, the Fourier number, is the ratio of time, , to a characteristic time scale for heat diffusion, . This dimensionless group is named in honor of J.B.J. Fourier , who formulated the modern understanding of heat conduction. [ 1 ]
The Eckert number (Ec) is a dimensionless number used in continuum mechanics. It expresses the relationship between a flow's kinetic energy and the boundary layer enthalpy difference, and is used to characterize heat transfer dissipation. [1] It is named after Ernst R. G. Eckert. It is defined as
The Archimedes number is applied often in the engineering of packed beds, which are very common in the chemical processing industry. [3] A packed bed reactor, which is similar to the ideal plug flow reactor model, involves packing a tubular reactor with a solid catalyst, then passing incompressible or compressible fluids through the solid bed. [3]
Ec is the Eckert number [1] It is the ratio between heat produced by viscous dissipation and heat transported by molecular conduction. i.e., the ratio of viscous heat generation to external heating. The higher its value, the slower the conduction of heat produced by viscous dissipation and hence the larger the temperature rise. [2] [3]