Temperature, dimensionless INDEX

I = temperature uniformity index (temperatures expressed in C), dimensionless. 

Here, K is sometimes referred to as the consistency index and has units that depend on the value of the power law index, n—for example, N-s"/m. The power law index is itself dimensionless. Typical values of K and n are listed in Table 4.4. In general, the power law index is independent of both temperature and concentration, although fluids tend to become more Newtonian (n approaches 1.0) as temperature increases and concentration decreases. The consistency factor, however, is more sensitive to temperature and concentration. To correct for temperature, the following relationship is often used ... 

We recall that c is the velocity of the molecules. The index on v means that we calculate the number of collisions necessary for reaction in the part of the zone where the reaction rate is highest and conditions are most conducive, so that i/min is the minimum value of v. Finally, tp is a dimensionless quantity of order (but less than) unity, algebraically (but not exponentially) dependent on the reaction mechanism, the activation heat, the temperatures T0 and TB, and the reagent concentrations. From the formula it is obvious first of all that u is always many times smaller than c, and less than the speed of sound. This fact will be important for the theory of detonation (Part II). 

RI Resilience index, kW (16) s Scale factor for family of hyperrectangles used to define the flexibility index, dimensionless (10) t Vector of temperatures T Temperature, K... 

In the petroleum industry a dimensionless number termed the viscosity index has been used to describe the temperature dependence of a fluid s kinematic viscosity. The calculation of viscosity index involves the use of published look-up tables [388], In terms of relative changes, a higher viscosity index represents a smaller decrease in viscosity with increasing temperature. 

The refractive index of a substance is a dimensionless constant that normally decreases with increasing temperature values are taken at 20°C or 25°C using the mean value taken for the two sodium lines of the spectrum. The optical systems that are used to exploit the refractive index for detection purposes are many and varied. One procedure is to construct a cell in the form of a hollow prism through which the mobile phase can flow. A ray of light is passed through the prism, which will be deviated from its original path, and is then focused onto a photocell. As the refractive... 

The estimation of Rav for characteristic parameter values shows that Rav where Aq = d/Re /" is the internal scale of turbulence. In a turbulent flow, both heat and mass exchange of drops with the gas are intensified, as compared to a quiescent medium. The delivery of substance and heat to or from the drop surface occurs via the mechanisms of turbulent diffusion and heat conductivity. The estimation of characteristic times of both processes, with the use of expressions for transport factors in a turbulent flow, has shown that in our case of small liquid phase volume concentrations, the heat equilibrium is established faster then the concentration equilibrium. In this context, it is possible to neglect the difference of gas and liquid temperatures, and to consider the temperatures of the drops and the gas to be equal. Let us keep all previously made assumptions, and in addition to these, assume that initially all drops have the same radius (21.24). Then the mass-exchange process for the considered drop is described by the same equations as before, in which the molar fluxes of components at the drop surface will be given by the appropriate expressions for diffusion fluxes as applied to particles suspended in a turbulent flow (see Section 16.2). In dimensionless variables (the bottom index 0" denotes a paramenter value at the initial conditions). 

Figure 7.113 Dimensionless temperature versus normal distance for power law fluid with power law index n = 0.5 with isothermal conditions (left) and adiabatic conditions (right)...

Refractive index is a dimensionless constant that normally decreases with increasing temperature values given in the literature are usually measured at ambient temperature using the mean value for the two sodium lines. The refractive indices of some common solvents used as a mobile f iase are given in the Table of Physical Properties of Different Solvents given in the Appendix. 

If the adiabatic temperature rise is AT over the helical length Z and the consistency index in the power-law model depends on temperature according to m = njoe then the dimensionless pressure rise parameter is defined as... 

Here, I, is the dimensionless Kovats retention index that is a function of both temperature and the stationary phase employed. The terms represented by X are retention parameters of the sample and standards. Following this convention, is the retention parameter of the sample under consideration. Any retention parameter, such as the adjusted retention time, t, the net retention volume, the adjusted net retention volume, and the relative retentions, can be used. X is the retention parameter of the sample under consideration, X is the retention parameter of a normal alkane (that is, straight chain or unbranched) of carbon number that elutes earlier than the sample, and X is the retention parameter of a normal Jkane having a carbon number greater than +1 that elutes after the sample. The retention index of a sample is, therefore, 100 multiplied by the carbon number of a hy-... 

Table 12.1 Definitions of Dimensionless Groups, Thermal Conductivity, T, the Flow Temperature (7 or TJ, the Melt Density, AH the Enthalpy Change, Cp the Heat Capacity, b Exponent of Viscosity Temperature Change, n the Power Law Index, the Viscosity...

The energy equation, Eq. 9.39, should be incorporated into the model to account for temperature variation along the filament axial length. Pearson and Shah (1974) solved the system of equations subjected to a linearized analysis and found that the critical draw ratio depends, besides on the power-law index, on the dimensionless number, S ... 

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