Time constant thermal

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. 

Figure 2.7 shows the specific heat of He and Cu for T< 1K. Down to 0.1K, the specific heat of both isotopes is larger than that of Cu. For example at 1.5 K (Tables 2.3 and 2.4), the specific heat of both isotopes is about 1.5 J/gK, whereas that of Cu is about 10 5 J/gK. This observation is very important in practical cryogenics for example, it means that the thermal time constant of an apparatus depends on the quantity of helium contained in it. 

Fig. 4.6. Scheme for the calculation of the thermal time constant of a sample connected to a thermal bath by a thermal resistance of negligible value (see text). 

Sometimes, to get data from 4 K up to room temperature, the simplest and more economical way is to let the cryostat warm if the thermal insulation is good and the vacuum chamber is kept under pumping, the warm-up time can be several days. If the experiment thermal time constant is much shorter, data at practically constant temperature can be recorded. 

It can be observed that these thermal conductances G(7) are typical of phonon conduction between two solids at very low temperature, as already reported [45], The value of the heat capacity was calculated from equation C = r G, where the thermal time constant r is obtained from the fit to the exponential relaxation of the wafer temperature. 

The electrothermal feedback also influences the time response of the bolometer. The thermal time constant is re = C/Ge. Using these definitions, the responsivity can be written ... 

The third block in Fig. 2.1 shows the various possible sensing modes. The basic operation mode of a micromachined metal-oxide sensor is the measurement of the resistance or impedance [69] of the sensitive layer at constant temperature. A well-known problem of metal-oxide-based sensors is their lack of selectivity. Additional information on the interaction of analyte and sensitive layer may lead to better gas discrimination. Micromachined sensors exhibit a low thermal time constant, which can be used to advantage by applying temperature-modulation techniques. The gas/oxide interaction characteristics and dynamics are observable in the measured sensor resistance. Various temperature modulation methods have been explored. The first method relies on a train of rectangular temperature pulses at variable temperature step heights [70-72]. This method was further developed to find optimized modulation curves [73]. Sinusoidal temperature modulation also has been applied, and the data were evaluated by Fourier transformation [75]. Another idea included the simultaneous measurement of the resistive and calorimetric microhotplate response by additionally monitoring the change in the heater resistance upon gas exposure [74-76]. 

In the previous paragraph, the basic considerations of FEM modelling have been laid out. The outcome of a static thermal simulation based on this model is a 3-d temperature field T x,y,z). In this section it is discussed, how the characteristic figures, such as thermal resistance and thermal time constant of the membrane, can be deduced. 

The considerations so far rely on constant heating power, and the way how this power is applied to the microhotplate does not play a role. In fact, a monolithically integrated control circuitry does not apply constant power but acts as an adjustable current source. Moreover, for measuring the thermal time constant experimentally, either a rectangular voltage or rectangular current pulse is applied. Analyzing the dynamic temperature response of the system leads to a measured time constant, which... 

Inclusion of the self-heating effect yields an additional temperature dependence of the thermal time constant. Differences in the time constants for heating and cooling are evident, and the real thermal time constant can be observed only in the cooling cycle with 4eat = 0. 

In the simulation, these equations describing the hotplate are coupled to the circuitry. The voltage, Vjit), determines the output current, 4eat(0> of the circuitry, but the circuitry response time is much smaller than the thermal time constant of the microhotplate. A coupled set of equations, those of the system including the microhotplate and the circuitry, is solved during the overall simulation procedure. 

For thermal characterization and temperature sensor calibration a microhotplate was fabricated, which is identical to that on the monoHthic sensor chips, but does not include any electronics. The functional elements of this microhotplate are connected to bonding pads and not wired up to any circuitry, so that the direct access to the hotplate components without electronics interference is ensured. The assessment of characteristic microhotplate properties, such as the thermal resistance of the microhotplate and its thermal time constant, were carried out with these discrete microhotplates. 

In order to determine the thermal time constant of the microhotplate in dynamic measurements, a square-shape voltage pulse was applied to the heater. The pulse frequency was 5 Hz for uncoated and 2.5 Hz for coated membranes. The amplitude of the pulse was adjusted to produce a temperature rise of 50 °C. The temperature sensor was fed from a constant-current source, and the voltage drop across the temperature sensor was amplified with an operational amplifier. The dynamic response of the temperature sensor was recorded by an oscilloscope. The thermal time constant was calculated from these data with a curve fit using Eq. (3.29). As already mentioned in the context of Eq. (3.37), self-heating occurs with a resistive heater, so that the thermal time constant has to be determined during the cooHng cycle. 

Table4.6. Experimentally determined values of the thermal resistance, the thermal time constant, and the temperatm-e homogeneity for uncoated and coated, transistor-heated microhotplates...

The dominant pole of this temperature control system is also determined by the thermal time constant of the microhotplate, which is approximately 20 ms. The open-loop gain of the differential analog architecture (Aql daa) is given by Eq. (5.8) ... 

Because the response time of the detector depends on the thermal time constant of the detector element / electrode assembly, coupled with the electrical time constant of the device capacitance and load resistor - the response versus modulation frequency (f shows a typical l//m form. 

Thermal time constants are about two orders of magnitude greater than the concentration time constants. 

Here the transfer time of the hot carriers is balanced against their thermalization time constant. 

The results for a 55 amp load change are shown in Figures 9.10 and 9.11. Figure 9.10 shows the temperature histories for the cell, interconnect, anode exit gas and cathode exit gas. As can be seen the thermal conditions reach their new equilibrium by approximately / = 800 s, resulting in an exponential time constant of r = 266 s. The temperature change for the gas stream is about 150°C. A calculation of the thermal time constant based on the fully lumped model (Equation (9.28) shows... 

The other side of the heat balance, the cooling rate, can be characterized by the thermal time constant of the reactor ... 

By dividing the reaction time by the thermal time constant, one obtains a dimensionless number, the modified Stanton criterion ... 

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