Axial Thermal Gradients

Comparison of steady-state profiles shows that neglecting axial mass diffusion has very little effect on the temperature and concentration profiles even though the axial gradients are significant. However, Figure 16 shows that neglecting the axial thermal dispersion in the gas does affect the solution... 

Start-up and load variations in LMR cause sodium level variations in the hot plenum which load shells emerging in the free level area. Shell loadings are mainly due to the axial thermal gradient, since primary stress loading are generally low or insignificant, the same for wall thermal gradient. 

Junction with head or Axial thermal gradient Membrane Q... 

Thermal Stresses. When the wak of a cylindrical pressure vessel is subjected to a temperature gradient, every part expands in accordance with the thermal coefficient of linear expansion of the steel. Those parts of the cylinder at a lower temperature resist the expansion of those parts at a higher temperature, so setting up thermal stresses. To estimate the transient thermal stresses which arise during start-up or shutdown of continuous processes or as a result of process intermptions, it is necessary to know the temperature across the wak thickness as a function of radius and time. Techniques for evaluating transient thermal stresses are available (59) but here only steady-state thermal stresses are considered. The steady-state thermal stresses in the radial, tangential, and axial directions at a point sufficiently far away from the ends of the cylinder for there to be no end effects are as fokows ... 

Skirts are used in vessels and towers. They transmit high axial and bending loads and offer favorable geometry for thermal gradients. In piping, when loads are beyond the capacity of lugs and tmnnions, skirts are often favored. 

It is also well known that there exist different extinction modes in the presence of radiative heat loss (RHL) from the stretched premixed flame (e.g.. Refs. [8-13]). When RHL is included, the radiative flames can behave differently from the adiabatic ones, both qualitatively and quantitatively. Figure 6.3.1 shows the computed maximum flame temperature as a function of the stretch rate xfor lean counterflow methane/air flames of equivalence ratio (j) = 0.455, with and without RHL. The stretch rate in this case is defined as the negative maximum of the local axial-velocity gradient ahead of the thermal mixing layer. For the lean methane/air flames,... 

C) [103]. For this reason, pulses of high 1-butene concentration were inserted in the micro reactor. Remarkably low axial temperature gradients within the explosion regime at high thermal power were found. The zone of the highest reaction rate shifts with respect to the micro channel length. 

The standard deviation of the Gaussian zones expresses the extent of dispersion and corresponds to the width of the peak at 0.607 of the maximum height [24,25]. The total system variance (ofot) is affected by several parameters that lead to dispersion (Eq. 17.22). According to Lauer and McManigill [26] these include injection variance (of), longitudinal (axial) diffusion variance (of), radial thermal (temperature gradient) variance (of,), electroosmotic flow variance (of,), electrical field perturbation (electrodispersion) variance (of) and wall-adsorption variance (of ). Several authors [9,24,27-30] have described and investigated these individual variances further and have even identified additional sources of variance, like detection variance (erf,), and others... 

The model discretization or the number of collocation points necessary for accurate representation of the profiles within the reactor bed has a major effect on the dimensionality and thus the solution time of the resulting model. As previously discussed, radial collocation with one interior collocation point generally adequately accounts for radial thermal gradients without increasing the dimensionality of the system. However, multipoint radial collocation may be necessary to describe radial concentration profiles. The analysis of Section VI,E shows that, even with very high radial mass Peclet numbers, the radial concentration is nearly uniform and that the axial bulk concentration and radial and axial temperatures are nearly unaffected by assuming uniform radial concentration. Thus model dimensionality can be kept to a minimum by also performing the radial concentration collocation with one interior collocation point. 

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