Thermal wave

Fig. IV-11. A laser beam incident on the liquid surface at angle B is scattered by angle AS by surface thermal waves of wave vector k. (From Ref. 132.)...

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

Thermal reforming Thermal sensitization Thermal stability Thermal transfer Thermal-transfer printing Thermal treatment Thermal wave imaging Thermate Thermate-TH2 Thermate-TH3 Therm-Chek... 

Additionally, a thermal wave is generated in the bed in a similar fashion to that of the thermal wave system. However it is more similar to existing gas... 

A practical means of approaching the performance of multiple bed cycles that only requires two beds is the thermal wave approach patented by Shelton [8] and illustrated in Fig. 14. 

In bed 2 the circulation of hot gas from the bed passes through the inter-loop heat exchanger, through the external cooler (which provides some of the useful output of a heat pump system) and back into bed 2. The gas emerging from the bed remains hot until the thermal wave starts to break through, at which time it undergoes a rapid drop in temperature. 

When the two thermal waves start to break through, the opposite phase of the cycle begins. Valves are switched which effectively swap the two beds over so that bed 1 is cooled and bed 2 is now heated. 

Fig. 16. Convective thermal wave cycle with inert bed regeneration... 

Fig. 17. Schematic layout of a convective thermal wave chiller...

At some time shortly before any of the four thermal waves break through the net effects are ... 

Thermodynamically, the concept is similar to thermal wave systems and predicted COP s are similar. A cooling COP of 0.9 (based on heat input to the cycle), is predicted for one design with modest regeneration efficiency, evaporating at 5°C and condensing at 40°C. 

In situations where absorption of the incident radiation by the transducing gas is troublesome a piezoelectric transducer (made from barium titanate, for example) can be attached to the sample (or sample cuvette in the case of liquids) to detect the thermal wave generated in the sample by the modulated light (8,9). The low frequency, critically damped thermal wave bends the sample and transducer thus producing the piezoelectric response. The piezoelectric transducer will also respond to a sound wave in the solid or liquid but only efficiently at a resonant frequency of the transducer typically of the order of 10 to 100 KHz (see Figure 4). Thus neither in the case of microphonic nor piezoelectric detection is the PA effect strictly an acoustic phenomenon but rather a thermal diffusion phenomenon, and the term "photoacoustic" is a now well established misnomer. 

Equation 17.102 was derived on the assumption that concentration and thermal waves propagated at the same velocity. Amundson et al.<4y> showed that it was possible for the temperatures generated in the bed to propagate as a pure thermal wave leading the concentration wave. A simplified criterion for this to occur can be obtained from equations 17.75 and 17.101. Since there is no adsorption term associated with a pure thermal wave, and if changes within the bed voids are small, then ... 

For a bed initially free of adsorbate, the thermal wave propagates more quickly than the concentration wave if ... 

The velocity with which a pure thermal wave travels through an insulated packed bed may be obtained from equation 17.100 by putting Uq = 0 and (d/dT)(CsAH) = 0 to give ... 

It has been assumed that the gas and solid have the same temperature at any point, and that the fluid concentration is constant throughout a pellet at a value equal to that immediately outside the pellet. Within the limits of these assumptions, the thermal wave velocity up is independent of temperature. As discussed in Section 17.8.4, the velocity of the thermal wave relative to that of the concentration wave can be positive, as it normally is in liquids, negative or zero. 

Figure 17.37 shows a thermal wave plotted as a dotted line of distance against time. The velocity uc of the concentration wave depends on where it is in relation to the thermal wave, as can be seen by comparison with the full line in the Figure 17.37. 

Uj lower/higher temperatures Velocity of a point on a thermal wave m/s LT ... 

Consider the thermal wave given in Fig. 4.4. If a differential control volume is taken within this one-dimensional wave and the variations as given in the figure are in the x direction, then the thermal and mass balances are as shown in Fig. 4.5. In Fig. 4.5, a is the mass of reactant per cubic centimeter, Cj is the rate of reaction, Q is the heat of reaction per unit mass, and p is the total density. Note that alp is the mass fraction of reactant a. Since the problem is a steady one, there is no accumulation of species or heat with respect to time, and the balance of the energy terms and the species terms must each be equal to zero. 

FIGURE 4.5 Balances across a differential element in a thermal wave describing a laminar flame. 

In the first approach it is assumed, as well, that the reaction proceeds by zero-order. Since the rate term d> is not a function of concentration, the continuity equation is not required so we can deal with the more convenient energy equation. Semenov, like Mallard and Le Chatelier, examined the thermal wave as if it were made up of two parts. The unbumed gas part is a zone of no chemical reaction, and the reaction part is the zone in which the reaction and diffusion terms dominate and the convective term can be ignored. Thus, in the first zone (I), the energy equation reduces to... 

---