Destruction term

In displacement ventilation, there are regions with very low turbulence, and the flow can even be laminar. Hence it is important to use a turbulence model which can handle these regions. The k-f model gives rise to large numerical problems in regions of low turbulence. The reason is thar as k goes to zero, the destruction term in the e equation goes to infinity. The c equation is... 

The destruction term (the last term on the right-hand side) includes and this causes problems as —>0 even if e also goes to zero they must both go to zero at the correct rate to avoid problems, and this is often nor the case. 

Particle conservation in a vessel is governed by the particle-number continuity equation, essentially a population balance to identify particle numbers in each and every size range and account for any changes due to particle formation, growth and destruction, termed particle birth and death processes reflecting formation and loss of particulate entities, respectively. 

The destruction term is defined as the sum of all irreducible transitions starting from any initial state pk p 0) with k 0 and ending with the zero wave number state (the vacuum ) ... 

If we take the interactions of the solvent into account, new possibilities are offered in the possible diagrams for the destruction term to the lowest orders in the screened potential (314), we have new diagrams of the type illustrated in Fig. 14. 

Exergy Balances. Writing a steady-state balance for exergy is just like writing a steady-state energy balance except for one major difference. While energy is conserved, exergy can be annihilated (not lost, but actually consumed), and so the balance must contain a destruction term ... 

This conservation is a consequence of assumption (ii), namely, that mutants originate exclusively through erroneous replication and not through external interferences such as radiation or chemical attack. (If this assumption is relaxed, destruction terms must be subtracted in the conservation law to balance the additional first-order off-diagonal mutation terms.) The nondiagonal elements of the value matrix depend strongly on the Hamming distance d(i,k) between template i and erroneous replica k. For the uniform error rate model the expression reads... 

If we ignore the destruction terms D, the different mutants are fully characterized through their rates for exact replication IV,. This assumption simplifies the following discussion by allowing a single distribution of value parameters f(W) to completely characterize the mutant spectrum, but this is not essential to the argument. Accordingly, we write... 

Note that the conservation equations can be distinguished from the transport equations since they do not contain any production or destruction terms. Nevertheless, the conservation equations may contain terms on the RHS expressing a divergence of fluxes related to transport phenomena. The way in which these flux terms are divided into divergence of transport fluxes or source terms is rather involved, but procedures exist based on a number of requirements on the two types of terms which determine this separation uniquely. 

Our example of a balance equation in Sec. 3.1 would be of interest to demographers but not necessarily to engineers. Let us consider the most important engineering balance, the mass balance. Mass obeys the general balance equation the creation and destruction terms are zero. Thus, the mass balance is... 

Chemical analysis of the exhaust gas indicates that it contains considerable carbon dioxide, so the mass flow rate out is not negligible. Thus, for this equation to be satisfied, there must be significant creation minus destruction of carbon dioxide in the stove i.e, carbon dioxide is formed by combustion in the stove. In this case, the destruction term is negligible, ... 

If we made a similar balance for natural gas, the destruction term would... 

We asserted, without proof, that this abstract quantity, energy, obeys the balance equation, with the creation and destruction terms set equal to zero. This assertion is unprovable it rests on its ability to explain all the careful experiments ever run to test it. 

The possible changes of mass of the system are accounted for by the flow-in or flow-out terms, and the creation or destruction terms must apply equally well to constant-mass land variable-mass systems. For a constant-mass system, we can take the m inside the differential sign in the last equation and rearrange, to show that... 

Here we have not included a destruction term, because the S F in the equation is the vector sum of all the forces acting on the system. If this sum is in the opposite direction of the velocities, then the T.Y dt term is a momentum destruction term it will enter with a minus sign. Most often we divide Eq. 7.12 by dt to find the rate form of the momentum balance ... 

An additional advantage of the CPFR in this case comes from the fact that some secondary metabolites (such as, for example, penicillin) are destroyed by an excessive amount of time in the reactor. This was indicated in Equ. 5.128. In a CSTR, all cells with t > and thus competent to produce the secondary metabolite would at the same time be subject to the negative effect of the destructive term, — fep [Pg.346]

Bimolecular reactions have been described in Chaps. 1 and 3 of this book. The efficiency of these processes can depend on the temperature of the gas. All production and destruction terms (in units of cm s ) in equation (4.1) can be written as kijUiUj for bimolecular (second-order) reactions and kiUi for first-order reactions, with kij the rate coefficient of the reaction between species i and j and n the density of the reactant(s). More details on these expressions can be found in Wakelam et al. [22]. 

This general balance equation and its variants form the basis of much of chemical engineering. If the creation and destruction terms are zero, then it is called a conservation equation. If they are not zero then Eq. 2.1 has no common name, but is widely used, for example, with chemical reactions, where it allows us to compute the changes in various chemicals as a chemical reaction destroys one species and creates another. Remember that it applies only to a system with properly defined boundaries. All balances can be changed to rate equations by dividing both sides by some time interval, dt ... 

In the years 1972-1974 Cmtzen proposed that NO and NO2 could catalyse ozone production in the background troposphere by reactions occurring in the CO and CH4 oxidation chains. Additional photochemical reactions leading to ozone loss were likewise identified. These gross ozone production and destruction terms are each substantially larger than the downward flux of ozone from the stratosphere, which until then had been considered the main source of tropospheric ozone. 

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