Thermalization times

When the motor overheats, the thermostat opens, interrupting motorline current. Pilot thermostats mounted on the windings of larger motors trip the motor starter rather than interrupt line current. This method gives good protection for sustained overloads, but because of the thermal time lag between the copper winding and the thermostat it may not provide adequate protec tion for stalled conditions or severe overloads. 

The period after which this can be repeated will depend upon the heating curve and the thermal time constant of the motor, i.e. the time the motor will take to reach thermal equilibrium after repeated starts (See Chapter 3). 

I = time of heating or tripping time of the relay (hours) r = heating or thermal time constant (hours). The larger the machine, the higher this will be and it will vary from one design to another. It may fall to a low of 0.7-0.8 hour. 

In all the above conditions, the rotor would heatup much more rapidly than the stator due to its low thermal time constant (t), and its smaller volume compared to that of the stator, on the one hand, and high-frequency eddy current losses at high slips, due to the skin effect, on the other. True motor protection will therefore require separate protection of the rotor. Since it is not possible to monitor the rotor s temperature, its protection is provided through the stator only. Separate protection is therefore recommended through the stator against these conditions for large LT and all HT motors. 

Temperature Measurement shift. Measurement not representative of process. Indicator reading varies second to second. Ambient temperature change. Fast changing process temperature. Electrical power wires near thermocouple extension wires. Increase immersion length. Insulate surface. Use quick response or low thermal time constant device. Use shielded, twisted pair thermocouple extension wire, and/or install in conduit. 

The analog of the residence time for a nonisothermal reaction is the thermal time ... 

Shirtliffe, S.J., Entz, M.H. and Van Acker, R.C. (2000). Avena fatua development and seed shatter as related to thermal time. Weed Sci., 48, 555-560. 

In a nonattaching gas electron, thermalization occurs via vibrational, rotational, and elastic collisions. In attaching media, competitive scavenging occurs, sometimes accompanied by attachment-detachment equilibrium. In the gas phase, thermalization time is more significant than thermalization distance because of relatively large travel distances, thermalized electrons can be assumed to be homogeneously distributed. The experiments we review can be classified into four categories (1) microwave methods, (2) use of probes, (3) transient conductivity, and (4) recombination luminescence. Further microwave methods can be subdivided into four types (1) cross modulation, (2) resonance frequency shift, (3) absorption, and (4) cavity technique for collision frequency. 

Here the left-hand side is the ratio of power loss at time t, when the mean electron energy is (E), to that at thermalization, and C and n are determinable constants. This idealized equation is not expected to be valid in presence of the Ramsauer effect, but Warman and deHaas apply it anyway to N2, Ar, and He at atmospheric pressure. The method relates the gradual decrease of collision frequency to an increase in conductivity, which finally rides to a plateau interpreted to be the thermal conductivity. The time needed to reach 90% of the thermal conductivity is called the thermalization time (see Table 8.1). 

The method is also applicable to liquids and solids (Sowada and Warman, 1982 Sowada et at, 1982) for the condensed rare gases, a correction is needed for recombination. Sowada et at (1982) obtained the following values of thermalization times, within 20% accuracy, given here in parenthesis as (phase, temperature... 

TABLE 8.1 Experimental Electron Thermalization Times in Various Gases at -300K... 

Sowada and Warman (1982) have described a dc conductivity method for Ar gas at 295 K and 45 atm. Following a 20-ns pulse of irradiation, the conductivity rises to a peak at -50 ns, due to the Ramsauer effect, before settling to a plateau, which is ascribed to thermal conductivity since the collecting field is very low. Since there is little electron loss, the conductivity profile is proportional to the mobility profile this in turn can be considered a kind of image of collision frequency as a function of electron energy. The time to reach the conductivity plateau, -150 ns, is the measure of thermalization time in the present case. At a density of -9 X 1021 cm-3, the conductivity maximum vanishes, indicating the disappearance of the Ramsauer minimum according to Sowada and Warman. 

Two other attempts, without the use of a distribution function, are worth mentioning, as these are operationally related to experiments and serve to give a rough estimate of the thermalization time. Christophorou et al. (1975) note that in the presence of a relatively weak external field E, the rate of energy input to an electron by that field is (0 = eEvd, where vd is the drift velocity in the stationary state. Under equilibrium, it must be equal to the difference between the energy loss and gain rates by an electron s interaction with the medium. The mean electron energy is now approximated as (E) = (3eD )/(2p), where fl = vd /E is the drift mobility and D is the perpendicular diffusion coefficient (this approximation is actually valid for a Maxwellian distribution). Thus, from measurements of fl and D the thermalization time is estimated to be... 

The thusly-obtained thermalization time depends weakly on the initial energy, for which a value 1 eV has been used in the irradiation case. Taking n = 1 gives T(h = 3.0, 1.5, and 0.5 ns respectively for LXe, LKr, and LAr and the values 10.0, 0.9, and 0.6 ps respectively for methane, neopentane, and tetram-ethylsilane, all liquids at their triple points. In these estimates, Schmidt s (1977) data were used for ng and E10. However, taking n = 1 can be very crude, as certain theories and experiments give n = -0.5. On the other hand, the use of 10% nonlinearity of mobility may seem arbitrary, but it has partial compensation in the definition of E10. 

The thermalization time for an electron swarm starting with an initial energy Eg is then given by... 

Extrapolation (admittedly very approximate) of the thermalization time in humid air by microwave conductivity method (Warman et al, 1984) giving tth 4.5 x 10-15 s for unit water fraction. 

Extrapolation, to liquid density, of thermalization time in gaseous water (also approximate) by Christophorou et al. (1975), based on drift velocity and transverse diffusion coefficient measurement, which gives tth 2.0 x 10-1+ s... 

Considering an initial electron energy much larger than kBT, Rips and Silbey show that the distribution of thermalization time is given by the first two moments of the energy loss function (e) per unit time,... 

Ignoring the effect of the initial energy, since that is much greater than kBT, the solution of the above equation gives the thermalization time tih as... 

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