Disturbance temperature

In Fig. 6.11, two sets of eigenfunctions are shown for the case with K = 5 X 10 and Re = 1000. In Fig. 6.11(a) the case corresponds to LVo = 0.1 for which the hydrodynamic mode attains its maximum growth and thus the eigenfunctions once again represent the disturbance velocity components. In Fig. 6.11(b) the case corresponds to loq = 0.7 and the eigenvalue for this case indicates the thermal mode to be at its maximum growth rate. Hence the plotted function corresponds to the disturbance temperature field. 

As already noted we assume that the gas above the fluid layer is held at a constant temperature To. Assuming local thermal equilibrium, we have seen [Eqs. (12-214)] that the thermal boundary condition for the disturbance temperature at the upper surface can be expressed in the nondimensional form... 

We next consider the boundary conditions on the disturbance temperature. At the lower surface, in the case where the conductivity of the rigid plate is large compared to the liquid, it is... 

Here a is the surface tension, Oq is its value in the undisturbed state, and Ts is the disturbance temperature at the surface. The net surface tension force at a given point on the surface (equal to grad [Pg.99]

In a series of experiments with an isolated perfused bovine kidney, Crezee and Lagendijk (1990) inserted a small plastic tube into the tissue of a bovine kidney and measured the disturbance temperature fields in a plane perpendicular to the tube while heated water was circulated through it, and the kidney cortex was perfused at different rates. They also used thermocouples to map the temperature distribution in the tissue of isolated perfused bovine tongues at various perfusion rates (Crezee et al., 1991). By examining the effect of increased perfusion on the amplitude and width of the thermal profile, they demonstrated that the temperature measurements agre better with a perfusion-enhanced as opposed to the perfusion source term in the Pennes equation. 

Laser Raman diagnostic teclmiques offer remote, nonintnisive, nonperturbing measurements with high spatial and temporal resolution [158], This is particularly advantageous in the area of combustion chemistry. Physical probes for temperature and concentration measurements can be debatable in many combustion systems, such as furnaces, internal combustors etc., since they may disturb the medium or, even worse, not withstand the hostile enviromnents [159]. Laser Raman techniques are employed since two of the dominant molecules associated with air-fed combustion are O2 and N2. Flomonuclear diatomic molecules unable to have a nuclear coordinate-dependent dipole moment caimot be diagnosed by infrared spectroscopy. Other combustion species include CFl, CO2, FI2O and FI2 [160]. These molecules are probed by Raman spectroscopy to detenuine the temperature profile and species concentration m various combustion processes. 

As the spins precess in the equatorial plane, they also undergo random relaxation processes that disturb their movement and prevent them from coming together fiilly realigned. The longer the time i between the pulses the more spins lose coherence and consequently the weaker the echo. The decay rate of the two-pulse echo amplitude is described by the phase memory time, which is the time span during which a spin can remember its position in the dephased pattern after the first MW pulse. Tyy is related to the homogeneous linewidth of the individual spin packets and is usually only a few microseconds, even at low temperatures. 

We can sample the energy density of radiation p(v, T) within a chamber at a fixed temperature T (essentially an oven or furnace) by opening a tiny transparent window in the chamber wall so as to let a little radiation out. The amount of radiation sampled must be very small so as not to disturb the equilibrium condition inside the chamber. When this is done at many different frequencies v, the blackbody spectrum is obtained. When the temperature is changed, the area under the spechal curve is greater or smaller and the curve is displaced on the frequency axis but its shape remains essentially the same. The chamber is called a blackbody because, from the point of view of an observer within the chamber, radiation lost through the aperture to the universe is perfectly absorbed the probability of a photon finding its way from the universe back through the aperture into the chamber is zero. 

Power factor losses under certain conditions cause a temperature rise in the insulation that may result in failure or reduced life of the insulation. In communication wiring the power factor of the insulation plays an important role. Here the actual power loss can represent an appreciable portion of the total energy in the circuit. In addition, this loss disturbs the circuit characteristics of the equipment at both ends of the line. 

Earth to space (sateUite) to earth communication links are relatively insensitive to ionospheric disturbances. Communications between earth and manned space vehicles are barely affected by plasmas when the spaceships are well away from the atmosphere, eg, in orbit or in a translunar trajectory. However, during reentry of a spaceship, a low temperature plasma forms around the vehicle and intermpts the communication links to it (183). Plasmas are incidental to the performance of modem rockets used to explore the solar system. 

Schemes to control the outlet temperature of a process furnace by adjusting the fuel gas flow are shown in Figure 13. In the scheme without cascade control (Fig. 13a), if a disturbance has occurred in the fuel gas supply pressure, a disturbance occurs in the fuel gas flow rate, hence, in the energy transferred to the process fluid and eventually to the process fluid furnace outlet temperature. At that point, the outlet temperature controller senses the deviation from setpoint and adjusts the valve in the fuel gas line. In the meantime, other disturbances may have occurred in the fuel gas pressure, etc. In the cascade control strategy (Fig. 13b), when the fuel gas pressure is disturbed, it causes the fuel gas flow rate to be disturbed. The secondary controller, ie, the fuel gas flow controller, immediately senses the deviation and adjusts the valve in the fuel gas line to maintain the set fuel gas rate. If the fuel gas flow controller is well tuned, the furnace outlet temperature experiences only a small disturbance owing to a fuel gas supply pressure disturbance.

Both control schemes react in a similar manner to disturbances in process fluid feed rate, feed temperature, feed composition, fuel gas heating value, etc. In fact, if the secondary controller is not properly tuned, the cascade control strategy can actually worsen control performance. Therefore, the key to an effective cascade control strategy is the proper selection of the secondary controlled variable considering the source and impact of particular disturbances and the associated process dynamics. 

When the spectral characteristics of the source itself are of primary interest, dispersive or ftir spectrometers are readily adapted to emission spectroscopy. Commercial instmments usually have a port that can accept an input beam without disturbing the usual source optics. Infrared emission spectroscopy at ambient or only moderately elevated temperatures has the advantage that no sample preparation is necessary. It is particularly appHcable to opaque and highly scattering samples, anodized and painted surfaces, polymer films, and atmospheric species (135). The interferometric... 

Open-Loop versus Closed-Loop Dynamics It is common in industry to manipulate coolant in a jacketed reacdor in order to control conditions in the reacdor itself. A simplified schematic diagram of such a reactor control system is shown in Fig. 8-2. Assume that the reacdor temperature is adjusted by a controller that increases the coolant flow in proportion to the difference between the desired reactor temperature and the temperature that is measured. The proportionality constant is K. If a small change in the temperature of the inlet stream occurs, then depending on the value or K, one might observe the reactor temperature responses shown in Fig. 8-3. The top plot shows the case for no control (K = 0), which is called the open loop, or the normal dynamic response of the process by itself. As increases, several effects can be noted. First, the reactor temperature responds faster and faster. Second, for the initial increases in K, the maximum deviation in the reactor temperature becomes smaller. Both of these effects are desirable so that disturbances from normal operation have... 

One such approach is called cascade control, which is routinely used in most modern computer control systems. Consider a chemical reactor, where reac tor temperature is to be controlled by coolant flow to the jacket of the reac tor (Fig. 8-34). The reac tor temperature can be influenced by changes in disturbance variables such as feed rate or feed temperature a feedback controller could be employed to compensate for such disturbances by adjusting a valve on me coolant flow to the reac tor jacket. However, suppose an increase occurs in the... 

FIG. 8-36 Block diagram of the cascade co composition disturbance, while L2 would be a change in the cooling water temperature. 

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