Indicators, energy balance

This derivation indicates a strong coupling between the momentum equation and the energy equation, which implies that the momentum and energy balance equations should be solved as a coupled system. In particular, the dis-... 

Many cliciiiical reactions evolve or absorb heat. When applying energy balances (consenatioit law for energy) in tccluiical calculations the heat (enthalpy) of reaction is often indicated in mole units so that tliey can be directly applied to demonstrate its chemical change. To simplify the presentation that follows, examine the equation ... 

Energy intake is only part of the equation. We can also adjust our energy balance by exercising. Various forms of exercise require different average energy outputs. Exercise involves doing thermodynamic work. The table in the next column Indicates that the amount of work depends on the type of exercise and the amount of mass being displaced. 

The bread and butter tools of the practicing chemical engineer are the material balance and the energy balance. In many respects chemical reactor design can be regarded as a straightforward application of these fundamental principles. This section indicates in general terms how these principles are applied to the various types of idealized reactor models. 

Since indicators for energy balance have been less explored than the others, some consideration will be devoted to them Spedding et al. (1981) stated that the single most important aspect of agricultural efficiency in the future is likely to be that of energy use. 

The material and energy balances of a tubular vessel are based on the conservation law, Eq 2.42, applied to a differential ring between r and r+dr and z and z+dz. A material balance is derived, for example, in problem P5.08.01, and is quoted in Table 2.6 along with the heat balance. The result is a pair of second order partial differential equations, usually nonlinear, that must be solved numerically. Table 2.6 indicates one possible procedure, but computer software is plentiful. 

In Figure 10.4 an attempt has been made to indicate the energy balance i.e. the difference between internally generated energy and that received from adjacent zones) for each zone. 

First, the energy balance line T A represents the situation where insufficient heat is liberated by reaction to raise the temperature to a high enough level for the reaction to be self-sustaining. Hence, conversion is negligible. At the other extreme, if we have more than enough heat liberated, the fluid will be hot and conversion essentially complete. This is shown as line T B. Finally, line T C indicates an intermediate situation which has three solutions to the material and... 

The equation of motion and the equation of energy balance can also be time averaged according to the procedure indicated above (SI, pp. 336 et seq. G7, pp. 191 et seq. pp. 646 et seq.). In this averaging process there arises in the equation of motion an additional component to the stress tensor t(,) which may be written formally in terms of a turbulent (eddy) coefficient of viscosity m(I) and in the equation of energy balance there appears an additional contribution to the energy flux q(1), which may be written formally in terms of the turbulent (eddy) coefficient of thermal conductivity Hence for an incompressible fluid, the x components of the fluxes may be written... 

For the production of fine dispersed PEG by expanding C02-saturated solutions, a first assumption indicates that the starting conditions should be near the liquefaction curve in order to reach the solid-gas region after the expansion. An initial estimation can be performed by calculating an energy balance which takes into account the ... 

The differential energy balances of Eqs. (6.10) and (6.15) with the friction term of Eq. (6.18) can be integrated for compressible fluid flow under certain restrictions. Three cases of particular importance are of isentropic or isothermal or adiabatic flows. Equations will be developed for them for ideal gases, and the procedure for nonidcal gases also will be indicated. 

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