Power dissipation density

Fig. 5.4-15. Interfacial area versus power dissipation density for various reactor types P = power Fv.a = gas flow rate (adapted from Carra and Morbidelli, 1987).

Thick-film resistors can be processed with a tolerance of about 25%. Laser trimming increases the resistance value. Therefore, a resistor is designed to a lower value than desired and will be trimmed to its target value later on. Besides the resistance value required, the power dissipation density is required to design a thick-film resistor. The power dissipation density (Pdensiiy in mW/mm ) is a paste property, which is specified in the data sheet. It is typically related to a 50% trim cut (maximum allowable trim length) and application on prefired alumina. For a stable resistor, the minimum area Ag is determined by the maximmn circuit power dissipation requirement, as in Equation 9.3 ... 

The laser cut influences the electrical behavior and the stability of resistors. Owing to the current density at the end of cut (Figure 9.40), the power density is increased (hot spot). Such hot spots can produce microcracks, decrease the long time stability, and may even destroy the resistor. In addition, the power-dissipation density is reduced (design impact), and the noise is increased, especially if the laser power was too high. 

A further result of the increase of power dissipation in the electrons has consequences for the plasma chemistry. Besides the increased ion densities, also the production of radicals will be increased, which may lead to higher deposition rates. 

The power dissipated at two different frequencies has been calculated for all reactions and compared with the energy loss to the walls. It is shown that at 65 MHz the fraction of power lost to the boundary decreases by a large amount compared to the situation at 13.56 MHz [224]. In contrast, the power dissipated by electron impact collision increases from nearly 47% to more than 71%, of which vibrational excitation increases by a factor of 2, dissociation increases by 45%, and ionization stays approximately the same, in agreement with the product of the ionization probability per electron, the electron density, and the ion flux, as shown before. The vibrational excitation energy thresholds (0.11 and 0.27 eV) are much smaller than the dissociation (8.3 eV) and ionization (13 eV) ones, and the vibrational excitation cross sections are large too. The reaction rate of processes with a low energy threshold therefore increases more than those with a high threshold. 

A crystal activated with Ti + ions presents an absorption that peaks at 514 nm and the corresponding emission spectrum peaks at 600 nm. A sample of this crystal, which has an optical density of 0.6 at the absorption peak, is illuminated with an Ar laser emitting at 514 nm with a power of 2 mW. (a) Determine the laser power of the beam after it passes through the crystal, (b) If the quantum efficiency isrj = 0.6, determine the intensity (in photons per second) emitted as luminescence and the power dissipated as heat in the crystal. 

The parameters included in /3 are the particle density, the adhesion, and the power dissipated by the crystal. Thus, the variation of frequency provides some means for discrimination based on the particle size. The sensitivity decreases for particles with diameter greater than 2 pm and no sensitivity is obtained for particles larger than D 20 pm. 

P= mixing power dissipation, kW VL = liquid volume, m3 pL = density of liquid, kg/m3... 

In Section 3.2.4 we considered the effects of an ideal mass layer on SAW response. In the model used to derive the mass-loading response, the layer was assumed to be (1) infinitesimally thick, and (2) subject only to translational motion by the SAW. Translational motion was found to induce a change in SAW velocity proportional to the areal mass density (pfc) contributed by the film — the mass loading response. Since no power dissipation arises in film translation, no attenuation response was predicted. With an actual film having finite thickness and elastic properties, it is important to also consider the effects of SAW-induced film deformation. Energy storage and power dissipation due to film deformation cause additional contributions to SAW velocity and attenuation that were neglected in the earlier treatment. 

E = (power dissipated)/mass a = surface tension pG = gas density... 

In addition to performance and density scaling, power dissipation has become a third concern that the microprocessor industry must face. Figure 20.7 [3] shows the increase in power consumption by the microprocessor also following Moore s Law. Power dissipation can be broken into two... 

In continuous mechanical emulsification systems based on turbulent flow, the power density Py viz. power dissipated per unit volume of the emulsion) and residence time, L, in the dispersing zone have been found to influence the result of emulsification as measured by the mean droplet size 0(3 2 which is called the Sauter diameter . This dependency is in most cases described by the following expression ... 

The rise velocities of bubbles were derived by Peebles and Garber (1953). Using the techniques of dimensional analysis as was used in the derivation of the power dissipation for rotational mixers, they discovered that the functionality of the rise velocities of bubbles can be described in terms of three dimensionless quantities Gi = gn lpiO, G2 = g f) Vi,Yp]la, and Re = IpiVbflp. Re is a Reynolds number g is the acceleration due to gravity p is the absolute viscosity of fluid p is the mass density of fluid a is the surface tension of fluid and f is the average radius of the bubbles. To give G, and G2 some names, call G, the Peebles number and G2 the Garber number. 

The drag stress in a fluid is proportional to the dynamic pressure PiVpH, where Pi is the mass density of water. Thus, the force on a single blade, = CoApPiVpl. Cj) is the coefficient of drag and Ap is the projected area of the blade in the direction of its motion. Power is force times velocity, so the power dissipation per blade is therefore... 

In cases of a relatively high current density, power dissipation in the capillary may result in significant radial temperature profiles. The plate-height contribution is... 

Under turbulent flow conditions, power dissipation is the controlling factor for mass transfer and phase dispersion. The power drawn by a single impeller in a liquid-gas system is typically lower than that drawn by the same impeller in liquid alone. The presence of the gas reduces the average density of the mixture, and the gas flow regime (e.g., flooding) may cause the impeller blades to be locally surrounded by a higher... 

---