Generation term

In the Couette flow inside a cone-and-plate viscometer the circumferential velocity at any given radial position is approximately a linear function of the vertical coordinate. Therefore the shear rate corresponding to this component is almost constant. The heat generation term in Equation (5.25) is hence nearly constant. Furthermore, in uniform Couette regime the convection term is also zero and all of the heat transfer is due to conduction. For very large conductivity coefficients the heat conduction will be very fast and the temperature profile will... 

When expansion terms are used hut not expanded about the mean, the corresponding t values for the generating terms should not he used. For example, ifi3 =iii2 is used rather than the correct expansion (i — a. )(i2 —12), then the corresponding t values for i and I2 should not he used. 

Thus, an analysis of the lost work, made by calculation of the fraction that each individual lost-work term represents of the total lost work, is the same as an analysis of the rate of entropy generation, made by expressing each individual entropy-generation term as a fraclion of the sum of all entropy-generation terms. 

Inspection of Eqs. (5-5 ), (5-5Z ), and (5-5c) indicates the form of temperatrrre profile for variorrs conditions and geometries and also reveals the effect of the heat-generation term q rrpon the temperatrrre distribrrtions. 

The simplest and most widely used model to explain the response of organic photovoltaic devices under illumination is a metal-insulaior-metal (MIM) tunnel diode [55] with asymmetrical work-function metal electrodes (see Fig. 15-10). In forward bias, holes from the high work-function metal and electrons from the low work-function metal are injected into the organic semiconductor thin film. Because of the asymmetry of the work-functions for the two different metals, forward bias currents are orders of magnitude larger than reverse bias currents at low voltages. The expansion of the current transport model described above to a carrier generation term was not taken into account until now. 

It is interesting to note that independent, direct calculations of the PMC transients by Ramakrishna and Rangarajan (the time-dependent generation term considered in the transport equation and solved by Laplace transformation) have yielded an analogous inverse root dependence of the PMC transient lifetime on the electrode potential.37 This shows that our simple derivation from stationary equations is sufficiently reliable. It is interesting that these authors do not discuss a lifetime maximum for their formula, such as that observed near the onset of photocurrents (Fig. 22). Their complicated formula may still contain this information for certain parameter constellations, but it is applicable only for moderate flash intensities. 

By thermodynamic convention, l Hp < 0 for exothermic reactions, so that a negative sign is attached to the heat-generation term. When there are multiple reactions, the heat-generation term refers to the net effect of all reactions. Thus, the term is an implicit summation over all M reactions that... 

Note that the coefficients on temperatures sum to 1.0 in each equation. This is necessary because the asymptotic solution, > 1, must give 0 = for all i. Had there been a heat of reaction, the coefficients would be unchanged but a generation term would be added to each equation. 

Q and R are generation terms for heat and chemical species respectively, while the pressure gradient Vp plays an analogous role for momentum generation. The heat generation arises from viscous dissipation and from reaction heating ... 

The numerical method of solving the model using computer tools does not require the explicit form of the differential equation to be used except to understand the terms which need to be entered into the program. The heater and the barrel were modeled as layers of materials with varying thermal characteristics. The energy supplied was represented as a heat generation term qg) in a resistance wire material. Equation 1... 

Separating the energy balance into heat loss and heat generation terms Rate of heat loss (Hl) = Rate of heat generation (Hq)... 

FIG. 18 Simplified equivalent circuit for externally biased ITIES under illumination. The perturbations introduced by the photoreactions in Fig. 11 are contained within the generator term g. Cji and are associated with the interfacial capacitance and the uncompensated resistance. (From Ref. 83. Reproduced by permission of the Royal Society of Chemistry.)... 

It is obvious that reducing cr (i.e., increasing the dilution), results in a reduction in the adiabatic temperature rise and, thus, can help to keep the reaction temperature within acceptable constraints. The global heat balance over the system, with all heat generation terms included, is required to obtain the actual adiabatic temperature rise. From the safety perspective, the adiabatic temperature rise is a useful design parameter, although it must be emphasized that it shows only a maximum effect and not a rate. 

The power generation term on the right-hand side of Eq. (3.6) becomes ... 

We have used an ordinary derivative since t is the only independent variable in this lumped system. The units of this component continuity equation are moles of A per unit time. The left-hand side of the equation is the dynamic term. The first two terms on the right-hand side are the convective terms. The last term is the generation term. 

Note the plus sign before the generation term since B is being produced by the reaction. Alternatively we could use the total continuity equation [Eq. (2.3)] since A j j and p are uniquely related by... 

Let us define the time variable r] f) = (3. R xi t),X2 t)) toward obtain-ment of estimated value of heat generation term. Such a variable describes the generation heat due to reaction along the solution of the dynamical model (3). 

The energy equation entails a detailed account of heat generation due to irreversible heat of the electrochemical reaction, reversible (or entropic) heat, and Joule heating. The heat generation term in a CFCD model must be unambiguous and location specific. More discussion is deferred to section 3.3. In addition, the heat accumulation in a porous material consisting of the matrix and fluid is given... 

The energy equation in Table 1 contains location-specific heat generation terms, including Irreversible heat of the electrochemical reaction, reversible en-... 

Among the three heat-generation terms, the irreversible and reversible heat sources of ORR are dominant. For a straight-channel cell shown in Figure 12, the total amount of heat release is 2.57 W, of which the irreversible heat is 55.3%, the reversible heat 35.4%, and the Joule heat only 9.3% The total heat released from the fuel cell can also be estimated from the overall energy balance, i.e. 

By decomposing the vorticity into a mean Zj and a fluctuation u, the mean baroclinic generation terms are... 

It is interesting to note that the streamwise enstrophy is almost as large as the other two components, although the generation term for mean streamwise... 

We search for the solution(s) to this equation. Note that heat removal term R(T) is linear in T, while the heat generation term G(T) contains k(T) and is highly nonlinear. The method we will use to solve this equation is to construct a graph of the left- and right-hand sides and look for intersections that must be the roots of the equation or T solutions to the CSTR. We do this in a plot of R(T) and G(T) versus T. 

These configurations are essentially two reactors connected by the heat exchange area A, and we will consider this in more detail in a later chapter in connection with multiphase reactors. We do not need to write a species balance on the coolant, but the energy balance in the jacket or cooling coil is exactly the same as for the reactor except that we omit the reaction generation term. 

A number of authors [46 to 48] employ the single sphere model in which the packed bed is considered as a set of equal spheres that are under the same state of extraction, and the fluid flowing around them is solute-free. That is, equation (3.4-90) would be valid, but without the generation term [46], The transport at the solid-fluid interface obeys the boundary condition (Eqn. 3.4-94) with C = 0 (fluid-flows at a large velocity). Under these assumptions, there is an analytical solution to the above problem (without axial dispersion) in terms of the Biot number (Bi = k, R/De), included in the following equation ... 

The generating term J fj(r)p(r) is diagrammatically represented by a wiggly arrow (cf. Fig. 5.18) inserted into polymer lines. We then without any change can take ewer the discussion given above for Z[p7 to find that In Z[p.p, a] is given by the set of all connected diagrams with any number of (a - p) -insertions. Functional differentiation reduces a (u p) - insertion to a density insertion. The result, for I tC then is found from Eq. (A 5.8). 

Defining an appropriate generating functional we can modify the argument to deal with any correlation function. For density autocorrelation, for instance, we may introduce a generating term f ddrddr a(r, r ) Vm pm(r)p t(r )... 

G 2) means that the polarization expression (eq 8b) generates terms of order 2 as well. These contribute to / , along with terms that are generated from matrix elements arising from second order wave function corrections absent from eq 8 a. 

The element force vector (fe) is formed by the internal heat generation term and the temperatures in the previous time steps as... 

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