Coefficient, axial

In addition, two distinct axial coefficients exist those associated with models using mean velocities (plug-flow models) and those associated with models using a radial velocity profile. The reason for this difference... 

Bischoff and Levenspiel (B14) present some calculations using existing experimental data to check the above predictions about the radial coefficients. For turbulent flow in empty tubes, the data of Lynn et al. (L20) were numerically averaged across the tube, and fair agreement found with the data of Fig. 12. The same was done for the packed-bed data of Dorweiler and Fahien (D20) using velocity profile data of Schwartz and Smith (Sll), and then comparing with Fig. 11. Unfortunately, the scatter in the data precluded an accurate check of the predictions. In order to prove the relationships conclusively, more precise experimental work would be needed. Probably the best type of system for this would be one in laminar flow, since the radial and axial coefficients for the general dispersion model are definitely known each is the molecular diffusivity. 

Checks on the relationships between the axial coefficients were provided in empty tubes with laminar flow by Taylor (T2), Blackwell (B15), Bournia et al. (B19), and van Deemter, Breeder and Lauwerier (V3), and for turbulent flow by Taylor (T4) and Tichacek et al. (T8). The agreement of experiment and theory in all of these cases was satisfactory, except for the data of Boumia et al. as discussed previously, their data indicated that the simple axial-dispersed plug-flow treatment may not be valid for laminar flow of gases. Tichacek et al. found that the theoretical calculations were extremely sensitive to the velocity profile. Converse (C20), and Bischoff and Levenspiel (B14) showed that rough agreement was also obtained in packed beds. Here, of course, the theoretical calculation was very approximate because of the scatter in packed-bed velocity-profile data. 

Table 7 compares the nominal physical properties of four different filter compositions, which differ in their mean pore diameter. The strength and modulus of elasticity data are those measured at room temperature. The axial coefficient of thermal expansion is the average value over the 25-800°C temperature range. It is clear from Table 7 that... 

For the following fibre composite systems, find the fibre mass firaction at which the axial coefficient of linear thermal expansion becomes zero (assume fibres to be aligned and continuous) ... 

For turbulent flow, there is a significant variation of the radial and axial coefficients, mainly due to inhomogeneity of velocity profiles. It has both diffusion and convection in the central region and near the wall. The dispersion coefficients (s) depend on the velocity gradient and position, see Figure 24.12. 

Material mp c Density gem" Axial thermal conductivity Wm"V- Axial coefficient of thermal expansion 10-6 oQ-1... 

For holmium, there are discrepancies between the values of the axial coefficients estimated from magnetization data by Rhyne et al. (1%7) and by Feron et al. (1970). Rhyne s analysis yielded zero temperature values of k = 3.2xl0 Jm = 1.65X 10 Jm and <6=-1.6x 10 Jm with considerable... 

In the same way as for thermal conductivity, the coefficient of linear thermal expansion of a composite material is a complex function of the thermal expansion coefficients of the matrix (a ) and that of the reinforcement (aj). In the particular case of orthotropic composite materials, the thermal expansion coefficient of each component (i.e., matrix, reinforcement) is a tensor quantity [a ] with only three components a,j, and along the major axis, that is, one in the axial direction (a ) and two in the transversal directions (oc and a j). In the particular case of transversely isotropic materials such as for instance fiber reinforced composites, the axial coefficient of thermal expansion of the material, expressed in W.m K can be approximated by the rule-of-mixtures by means of the Young s moduli of the matrix and of the fiber ... 

Table 2.3. Comparison of measured axial coefficients of thermal expansion and values calculated from computergenerated model structures for h-quartz-type and keatite-type alumino-silicates...

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