Critical steady-state temperature

Critical steady-state temperature (CSST) the highest ambient temperature at which self-heating of a material as handled (in a package, container, tank, etc.) does not result in a runaway but remains in a stationary condition (see Self-Accelerating Decomposition Temperature). 

Because mass flow bins have stable flow patterns that mimic the shape of the bin, permeabihty values can be used to calculate critical, steady-state discharge rates from mass flow hoppers. Permeabihty values can also be used to calculate the time required for fine powders to settle in bins and silos. In general, permeabihty is affected by particle size and shape, ie, permeabihty decreases as particle size decreases and the better the fit between individual particles, the lower the permeabihty moisture content, ie, as moisture content increases, many materials tend to agglomerate which increases permeabihty and temperature, ie, because the permeabihty factor, K, is inversely proportional to the viscosity of the air or gas in the void spaces, heating causes the gas to become more viscous, making the sohd less permeable. 

On decreasing critical temperature in B is denoted by Tc. The critical slope 2 is the lowest value that still leads to a bounded steady-state temperature. By further decreasing of

i),... 

Fig. 5.5. Variation of the steady-state temperature excess 6ss with the Semenov parameter iji indicating the turning point at the critical condition.

If some other parameter of the system, such as the adiabatic temperature excess ad is varied, so the shape of the steady-state locus may deform. For low values of B a in this model, corresponding to weakly exothermic processes, then the hysteresis loop is unfolded, as indicated in Fig. 5.6(c, d), and a simple smooth variation of the steady-state temperature excess with the residence time is observed. Thus, systems can lose criticality as other experimental parameters are changed. 

We will henceforth refer to 6 (e) as the critical value for ignition. A similar discussion can be given to the high-tempera-ture branch, curve C, to show that 6 (e) is the critical point for extinction. One also can show that curve B, which lies between 6 (e) and 6q(g), is unstable, so that there are still only two steady-state temperatures for the system. For e > e, rises monotonically with 6 as any steady-state value can be reached. In this case, there is no criticality and one expects no instabilities. 

We have described a molecular dynamics study of thermal ignition and have presented results on the critical behavior of a self-heating slab. Other quantities which have been examined are temperature profiles and the variation of ignition time with 6 [14]. Comparison of a steady-state temperature distribution at subcritical condition with Eq.(7) reveals a sharp temperature change at the wall boundary, implying that that other boundary condition [18] besides 0(x=l) = 0 should be used. Ignition times are expensive to simulate because a number of runs are required to average out the statistical fluctuations they are also difficult to calculate from continuum theory [9,19,20]. Consequently, only a preliminary comparison has been attempted [14]. 

Volumetric heat generation increases with temperature as a single or multiple S-shaped curves, whereas surface heat removal increases linearly. The shapes of these heat-generation curves and the slopes of the heat-removal lines depend on reaction kinetics, activation energies, reactant concentrations, flow rates, and the initial temperatures of reactants and coolants (70). The intersections of the heat-generation curves and heat-removal lines represent possible steady-state operations called stationary states (Fig. 15). Multiple stationary states are possible. Control is introduced to estabHsh the desired steady-state operation, produce products at targeted rates, and provide safe start-up and shutdown. Control methods can affect overall performance by their way of adjusting temperature and concentration variations and upsets, and by the closeness to which critical variables are operated near their limits. 

When pressure-decay rates less than critical are employed, the gas-phase combustion zone is removed from the propellant surface and extinguished, but not the ignition from within the condensed phase. Therefore, the temperature of the surface material will be above the autoignition temperature, and steady-state combustion will eventually be initiated. This mechanism is consistent with the observation that the luminosity of the combustion zone can vanish without combustion having been completely terminated. 

High pressure equipment has been designed to measure foam mobilities in porous rocks. Simultaneous flow of dense C02 and surfactant solution was established in core samples. The experimental condition of dense CO2 was above critical pressure but below critical temperature. Steady-state CC -foam mobility measurements were carried out with three core samples. Rock Creek sandstone was initially used to measure CO2-foam mobility. Thereafter, extensive further studies have been made with Baker dolomite and Berea sandstone to study the effect of rock permeability. 

We follow the analysis of Frank-Kamenetskii [3] of a slab of half-thickness, rG, heated by convection with a constant convective heat transfer coefficient, h, from an ambient of Too. The initial temperature is 7j < 7 ,XJ however, we consider no solution over time. We only examine the steady state solution, and look for conditions where it is not valid. If we return to the analysis for autoignition, under a uniform temperature state (see the Semenov model in Section 4.3) we saw that a critical state exists that was just on the fringe of valid steady solutions. Physically, this means that as the self-heating proceeds, there is a state of relatively low temperature where a steady condition is sustained. This is like the warm bag of mulch where the interior is a slightly higher temperature than the ambient. The exothermiscity is exactly balanced by the heat conducted away from the interior. However, under some critical condition of size (rG) or ambient heating (h and Too), we might leave the content world of steady state and a dynamic condition will... 

For long heating times, eventually at t —> oo, the temperature just reaches Tig. Thus for any heat flux below this critical heat flux for ignition, gig crit, no ignition is possible by the conduction model. The critical flux is given by the steady state condition for Equation... 

This follows by a steady state energy balance of the surface heated by qe, outside the flame-heated region S. It appears that a critical temperature exists for flame spread in both wind-aided and opposed flow modes for thin and thick materials. Tstmn has not been shown to be a unique material property, but it appears to be constant for a given spread mode at least. Transient and chemical effects appear to be the cause of this flame spread limit exhibited by 7 smln. For example, at a slow enough speed, vp, the time for the pyrolysis may be slower than the effective burning time ... 

The self-heating and ignition of baled or loose wool in bulk storage is discussed and analysed, and steady state thermal explosion theory is applied to the prediction of critical masses and induction periods for storage and transportation situations in relation to ambient temperature. Results obtained were consistent with current safety practices. 

In Chapter 3, the conditions for a chain branching explosion were developed on the basis of a steady-state analysis. It was shown that when the chain branching factor a at a given temperature and pressure was greater than some critical value acrit, the reacting system exploded. Obviously, in that development no induction period or critical chain ignition time rc evolved. 

Finally, one should recognize that determinations of the critical concentration depend wholly on the validity of the equilibrium or steady-state assumptions. If a stable end point for prdtomer-polymer coexistence is not attained, then kinetic factors affect the observed behavior. With the well recognized tendency of tubulin to lose its ability to engage in assembly reactions upon storage even at low temperature, and with the presence of various nucleotide hydrolases and transphosphorylases in microtubule protein, such kinetic effects are a serious problem. 

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