Coefficients defined

In the thennodynamic fomiiilation of TST the pressure dependence of the reaction rate coefficient defines a volume of activation [24, 25 and 26]... 

Friction Coefficient. In the design of a heat exchanger, the pumping requirement is an important consideration. For a fully developed laminar flow, the pressure drop inside a tube is inversely proportional to the fourth power of the inside tube diameter. For a turbulent flow, the pressure drop is inversely proportional to D where n Hes between 4.8 and 5. In general, the internal tube diameter, plays the most important role in the deterrnination of the pumping requirement. It can be calculated using the Darcy friction coefficient,, defined as... 

Tbe mass-transfer coefficients defined by Eqs. (5-248) and (5-249) are related to each other as follows ... 

With the Laplace operator V. The diffusion coefficient defined in Eq. (62) has the dimension [cm /s]. (For correct derivation of the Fokker-Planck equation see [89].) If atoms are initially placed at one side of the box, they spread as ( x ) t, which follows from (62) or from (63). 

Some authors" express the transfer free energy in the form of an activity coefficient defined by Eq. (8-59). 

Film coefficients defined on an inside tube surface area basis when converted to the larger outside surface area become... 

The long-time behaviour of K (t) is obviously exponential, and the rate is proportional to the diffusion coefficient defined in Eq. (2.42). Therefore the expression... 

In order to show how specific guidelines for the reactor layout can be derived, the maximum allowable micro-channel radius giving a temperature rise of less than 10 K was computed for different values of the adiabatic temperature rise and different reaction times. For this purpose, properties of nitrogen at 300 °C and 1 atm and a Nusselt number of 3.66 were assumed. The Nusselt number is a dimensionless heat transfer coefficient, defined as... 

When the fractions of molecules reflected specularly and diffusively are known, the slip length can be determined, as shovm by Maxwell. Maxwell introduced a tangential momentum accommodation coefficient defined as... 

Here/+ is the mean ionic activity coefficient defined, by analogy with the mean ionic activity, as... 

The intensity of a spectral absorption hand at a given wave length is expressed in terms of absorption or extinction coefficients, defined on the basis of the Beer-Lambert law. The latter states that the fraction of incident h ght absorbed is proportional to the number of molecules in the light path, .e., to the concentration (c) and the path length (1). The law may be expressed mathematically as ... 

When the parameters differ by more than one order of magnitude, matrix A may appear to be ill-conditioned even if the parameter estimation problem is well-posed. The best way to overcome this problem is by introducing the reduced sensitivity coefficients, defined as... 

The coefficients defining the fitted density are obtained via equation (7-27). To avoid the difficulties of dealing with two-electron integrals in a Slater-type basis, is evaluated in this context by a numerical integration on a grid as... 

In conventional analyses of transport based on Fick s laws, the fundamental parameters that define the transport process are the solute diffusion coefficient in the polymer film, DM, and the partition coefficient, KP. Essentially, the diffusion coefficient defines how fast a solute molecule moves, and the partition coefficient... 

Here, ydh is a Debye-Hiickel term, and Z) y and Ejjk are second and third virial coefficients, defined for each pair and triplet of ions in solution. As before, the values of D,j vary with ionic strength, whereas the terms Eijk are constant at a given temperature. 

A discharge coefficient Ch is defined in a similiar fashion to the coefficient defined in section 4-2 ... 

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