Energy transfer equations

Integrated models, in which all mass, momentum, and energy transfer equations, including those in which chemical reactions participate, are solved simultaneously for each time step in the evolution of the system... 

It is possible, however, to simplify the calculation of the energy transfer by assuming that the vapor phase is always a saturated vapor. O Connor (Ol) has shown that the rate of approach of a superheated vapor to saturated conditions is extremely rapid when the superheated vapor is in direct contact with its liquid phase. If the vapor phase is assumed to be saturated, the temperature of the phase can be calculated from an integrated form of the Clausius-Clapeyron equation instead of from the vapor-phase energy-transfer equation. 

Using the Forster energy transfer equations (16), one can calculate that Co2+ and Tb3+ are 13.7 A apart, in excellent agreement with the value of 13.7 A from the protein x-ray structure. This technique should be valuable for future applications to other multimetal ion binding proteins and enzymes. 

In addition to the possibilities of electron transfer (Equation 2) and energy transfer (Equation 4), electron transfer to singlet oxygen (Equation 7) and subsequent deprotonation (Equation 3), or hydrogen transfer to singlet oxygen (Equation 8) (J3) are to be taken into consideration and make an attempt of a differentiation between those postulated mechanisms extremely difficult. 

The observed reversible energy transfer (Equation 21) places the energy of MPT at 255 kJ.mol- (19). 

Unfortunately, preparative experiments of Iwaoka and Kondo (35) are of no direct relation to mechanistic investigations the use of a low pressure mercury lamp provides no selectivity as far as excitation of substrate or products is concerned. However, the fact that photolysis in strong acid solution decreased the bleaching rate would indicate the absence of an anchimeric effect and the results of their investigations by flash photolysis are in agreement with the electron (Equation 2) and energy transfer (Equation 4) reactions upon direct excitation. 

From their earliest formulation, the energy transfer equations have required that the refractive index used must be characteristic of the material between the donor and acceptor. In the simplest situation, where two well-separated and unbound donor and acceptor... 

As in the component balances, a separate energy transfer equation is written for each bulk phase and all energy transfer between the two phases is at the interface. The energy balance for the bulk vapor is... 

Interphase transfer kinetics. At this point, we need to characterize the process that leads to the transfer of the property through the interphase. The transport of the momentum from one phase to another is spectacular when the contacting phases are deformable. Sometimes in these situations we can neglect the friction and the momentum transfer generates the formation of bubbles, drops, jets, etc. The characterization of these flow cases requires some additions to the momentum equations and energy transfer equations. 

The momentum and energy transfer equation for the presented case may be written as ... 

To calculate the transfer processes in the I EG, the boundary-layer approximation is used. According to it, the current density in the bulk IEG is calculated on the basis of the height-average mass-, momentum-, and energy-transfer equations and those in the near-electrode layers. The transfer in the diffusion layers is calculated similarly to the case of quasi-steady-state approximation. 

For nonisothermal reactors, one of the reactor design equations, the energy transfer equation (see above), and an expression for the rate in terms of concentration and temperature must be solved simultaneously to give the conversion as a function of time. Note that the equations may be interdependent each can contain terms that depend on the other equation(s). These equations, except for simple systems, are usually too complex for analytical treatment. 

The spectral overlap integral J can be expressed in terms of either wavenumbers or wavelengths (Equation 2.36). The area covered by the emission spectrum of D is normalized by definition and the quantities / and lx are the normalized spectral radiant intensities of the donor D expressed in wavenumbers and wavelengths, respectively. Note that the spectral overlap integrals J defined here differ from those relevant for radiative energy transfer (Equation 2.33). Only the spectral distributions of the emission by D /,P and, are normalized, whereas the transition moment for excitation of A enters explicitly by way of the molar absorption coefficient sA. The integrals J" and Jx are equal, because the emission spectrum of D is normalized to unit area and the absorption coefficients sA are equal on both scales. 

Our starting point is the balance of radiation energy (transfer equation), obtained from the average of Eq. (10.5) over the wavelength spectrum,... 

Chirikov analysis quantitatively reveals the coupling responsible for the resonant energy transfer. Equation (13) can be transformed to action-angle coordinates via Eqs. (5) and (6), with the result... 

Mass and Energy Transfer Equations in Multi-Component Quasi-Equilibrium Plasma-Chemical Systems... 

In the next two sections the mass and energy transfer equations will be used to obtain realistic solutions for a variety of sinplified adsorption problems. 

Thus, the need for the simultaneous solution of the mass and energy transfer equations is removed. 

The efficiency of energy transfer (equation 16), however, can be high also... 

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