Near-critical heat conductivities

Figure 2.16 Comparison of near-critical heat conductivities for CO2 and HjO.

In the case K > fi, the usual diffusion determines the kinetics for any gel shapes. Here the deviation of the stress tensor is nearly equal to — K(V u)8ij since the shear stress is small, so that V u should be held at a constant at the boundary from the zero osmotic pressure condition. Because -u obeys the diffusion equation (4.18), the problem is trivially reduced to that of heat conduction under a constant boundary temperature. The slowest relaxation rate fi0 is hence n2D/R2 for spheres with radius R, 6D/R2 for cylinders with radius R (see the sentences below Eq. (6.49)), and n2D/L2 for disks with thickness L. However, in the case K < [i, the process is more intriguing, where the macroscopic critical mode slows down as exp(- Q0t) with Q0 oc K. 

Stability limits are provided in Fig. 6.6 for two inlet velocities, p = 5 bar and Tjj,j = 700 K, in terms of the critical heat transfer coefficient for extinction. For low thermal conductivities k < 2 W/mK), the reduced upstream heat transfer hinders catalytic ignition (light-off) and causes blowout. The stability limits at low fcs are narrower at higher inlet velocities (Fig. 6.6). In comparison to pure gas-phase combustion studies [18], there is a marked difference at the low behavior, which is discussed qualitatively (since the aforementioned work refers to different geometry and operating conditions). In gas-phase combustion, the blowout limits extend over a narrower range of ( 0.4-0.8 W/mK) and are nearly independent of h (the blowout limit line is almost parallel to the /i-axis). This is because low... 

Furthermore, the 2d RPM also yields a tricritical point, which, however, has a different physical basis [100], Here, tricriticality is founded on the insulator-conductor transition, which changes from second to first order. Notably, in real ionic solutions the conductivity shows two points of inflection one at low densities, which corresponds to the conductor insulator transition in 2d, and one near the criticality [38], Although accompanied by a maximum of the specific heat [68, 69], those changes of the conductivity are soft transitions determined by the mass action law and not cooperative A-transitions, required to allow for a tricritical point. 

At pressures up to 30 MPa and temperatures up to 523 K, the estimated uncertainty ranges from 0.03% to 0.05% in density, 0.03% (in the vapor) to 1% in the speed of sound (0.5% in the liquid), and 0.15% (in the vapor) to 1.5% (in the liquid) in heat capacity. Special interest has been focused on the description of the critical region and the extrapolation behavior of the formulation (to the limits of chemical stability). The uncertainty in viscosity ranges from 0.3% in the dilute gas near room temperature to 5% at the highest pressures. The uncertainty in thermal conductivity is less than 5%. 

The uncertainties of the equation of state are approximately 0.2% (to 0.5% at high pressures) in density, 1% (in the vapor phase) to 2% in heat capacity, 1% (in the vapor phase) to 2% in the speed of sound, and 0.2% in vapor pressure, except in the critical region. For viscosity, estimated uncertainty is 2%. For thermal conductivity, estimated uncertainty, except near the critical region, is 4-6%. 

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