Characteristic lengths surface correlation

The second approach assigns thermal resistance to a gaseous boundary layer at the heat transfer surface. The enhancement of heat transfer found in fluidized beds is then attributed to the scouring action of solid particles on the gas film, decreasing the effective film thickness. The early works of Leva et al. (1949), Dow and Jacob (1951), and Levenspiel and Walton (1954) utilized this approach. Models following this approach generally attempt to correlate a heat transfer Nusselt number in terms of the fluid Prandtl number and a modified Reynolds number with either the particle diameter or the tube diameter as the characteristic length scale. Examples are ... 

If the inner tube is longitudinally finned on the outside surface, the equivalent diameter is used as the characteristic length in both the Reynolds-number and the heat-transfer correlations. The fin effi-... 

One common characteristic of these length scales is that the dimensionless spatial coordinate is identically zero at the plane, axis, or point of symmetry, and r] reaches its maximum value of unity on the external surface of the catalyst. In terms of a universal correlation, a typical characteristic length scale for all catalyst shapes is L = V cataiyst/>S extemai, where Vcataiyst is the volume of catalyst and 5extemai IS the total external surface area. This definition of L reduces to ... 

The additional problems appear when partially eorrelated distribution of adsorption energies is eonsidered [13-15,286-288]. According to this concept, for a given surface, there is a certain characteristic length which defines the size of domains characterized by the same value of adsorption energy. The correlation between different energies of adsorption on different sites, , and y, can be described by a pair density distribution function x ( e ) ... 

We are now in a position to understand under what conditions thermal fluctuations should be important. DeGennes and Taupin introduced the notion of a persistence length fp for a membrane defined as the characteristic length scale. of tne surface normal-normal correlation function - e (n(x) is the unit vector normal to the... 

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