K coefficient

Nitride Stmcture Lattice para-meter, a nm Density, g/cm Micro-hardness Maximum stabiHty tempera-ture, °C Heat con-ductivity, W/(m-K) Coefficient of thermal expansion, /3 X 10- ... 

Hardness Specific gravity Tensile strength. Modulus of elasticity, GN/m Thermal conductivity, W/(m-K) Coefficient of expansion, 10-6"C... 

If in a polynomial P x) = Cqx + Cix -t- + c iX + c = 0, with Cq > 0, the first negative coefficient is preceded by k coefficients which are positive or zero, and if G denotes the greatest of the numerical values of the negative coefficients, then each real root is less than... 

Heat-transfer coefficients in steam-tube dryers range from 30 to 85 J/(m s K). Coefficients will increasewith increasing steam temperature because of increased heat transfer by radiation. In units carrying saturated steam at 420 to 450 K, the heat flux UAT will range from 6300 J/(m s) for difficult-to-diy and organic solids and to 1890 to 3790 J/(m s) for finely divided inorganic materials. The effect of steam pressure on heat-transfer rates up to 8.6 X 10 Pa is illustrated in Fig. 12-71. 

The centerline temperature differential in Zone 3 of the diffuser jet is proportional to the value of the K, coefficient, which, along with the fC, coefficient, depends upon jet and diffuser types and supply conditions. The theoretical value of the K2 coefficient, according to Shepelev, is 2.49. Experimental data reported by Grimitlyn show Ki to be 2.0. 

The K coefficient values for each of the items of pipe, bends, valves, fittings, contractions, enlargements, entrance/exits into/from vessels are additive as long as they are on the same size basis (see Table 2-2 and Figures 2-12A through 2-16). Thus the resistance equation is applicable to calculate the head or pressure loss through the specific system when the combined Rvalue is used. 

The head losses calculated using K coefficients by these figures can be added directly to the total friction head loss for the straight pipe portions of a system. When equivalent lengths are determined, they must be added to the straight pipe before determining the total head loss, as shown in the example calculations for a water system. 

Gqb overburden gradient in psi/ft Gp = pore pressure gradient in psi/ft K = coefficient related to Poisson ratio... 

Example 1.3 The isothermalcc compressibility k, coefficient of cubic expansion a, and pressure coefficient jd are defined as follows dd... 

In practice the experimental values y (x,) are usually measured at equally spaced abscissa values and the convolution is applied in succession to limited portions of the experimental data. In principle the equal spacing of data points along the x axis is not necessary, although it is essential in most numerical applications. It is useful to define the difference y — Y — e, the vector of errors at each point The chosen function F(jc) will be assumed here to be a polynomial of degree k - 1, although it can be a more general function. Then, is a vector composed of the k coefficients in the polynomial... 

Equation (2.13) can be used for the estimation of the /3 and k coefficients from experimental measurements. The data on the solubility of dioxygen in organic compounds are presented in Table 2.2. 

To motivate this approach, suppose that an experiment with n runs will be conducted and a model with k coefficients is to be fit to the data. This model can be represented in matrix notation as... 

Write a program to simulate the behavior of the system. Overall the objective of the simulation is to assist design and operation of the system in a way that the K coefficients may be determined. 

If there are no other IRs common to Y and X, then eqs. (15) show that there are only four non-zero Krs coefficients in K. Depending on the nature of the property it represents, K may be a symmetric matrix, and if this is true here K 2 = X2U leaving three independent coefficients. Equations (13)—(15) hold also for E or T representations since according to the FT the K coefficients that belong to different degeneracy indices are zero, while the coefficients for the same d are independent of d. 

Exercise 15.3-1 Determine the number of independent K coefficients when Y is a vector and X is a symmetric tensor of rank 2, for crystals that belong to the point groups (a) C3V, and (b) D2d. 

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