Energy balances with heat effects

Maximum disruption is obtained in a zone close to the probe tip and the biological cells must be kept here for sufficient time to allow disruption to take place. A delicate balance must therefore be struck between the power of the probe and the disruption rate since power ultrasound, with its associated cavitational collapse energy and bulk heating effect, can denature the contents of the cell once released. Indeed for this type of usage it is important to keep the cell sample cool during sonication. The method is very effective and continues to be an important tool in microbiology and biochemistry research. 

In Section 8.1, we discussed that in order to solve reaction enginet problems with heat effects, we needed to relate temperature, conversion, rate of reaction. The energy balance as given in Equation (8-9) is the most venient starting point as we proceed to develop this relationship. 

Examples on How to Ese Table 8-1. Wc now couple the energy balance equations in Table 8-1 with the appropriate reactor mole balance, rate law. stoichiometry algorithm to solve reaction engineering problems with heat effects. For example, recall rate law for a first-order reaction. Equation (E8-1.5) in Example 8-1. 

From these three case.s. (I) adiabatic PFR and CSTR, (2) PFR and PBR with heat effects, and (3) CSTR with heat effects, one can see how one couples the energy balances and mole balances. In principle, one could simply use Table 8-1 to apply to different reactors and reaction systems w ithout further discussion, However, understanding the derivation of the.se equations w ill greatly facilitate their proper application and evaluation to various reactors and reaction systems. Ctmsequenily, the following Sections 8.2. 8.3, 8,4. 8.6, and 8,8 will derive the equations given in Table 8-1. 

P8-11. This problem requires the student to apply the energy balance to membrane reactor. The student will have to derive the necess [f relationships from first principles because there are not formulas given W J membrane reactors with heat effects in the book. 

Combine material and energy balances with equilibrium considerations to determine the number of equilibrium stages required by a tray absorber or stripper when heat effects are important. 

The final result for the cooling fluid s thermal energy balance is similar to (4-70), however, with heat effects due to chemical reaction ... 

Isothermal Gas Flow in Pipes and Channels Isothermal compressible flow is often encountered in long transport lines, where there is sufficient heat transfer to maintain constant temperature. Velocities and Mach numbers are usually small, yet compressibihty effects are important when the total pressure drop is a large fraction of the absolute pressure. For an ideal gas with p = pM. JKT, integration of the differential form of the momentum or mechanical energy balance equations, assuming a constant fric tion factor/over a length L of a channel of constant cross section and hydraulic diameter D, yields,... 

For reactions involving heat effects, the total and component mass balance equations must be coupled with a reactor energy balance equation. Neglecting work done by the system on the surroundings, the energy balance is expressed by... 

With high concentrations, heat effects in the chromatographic column may be important. This would require the simultaneous application of an energy balance and the introduction of a term reflecting the influence of temperature on the adsorption equilibrium. 

There are 12 equations in all (overall material and energy balances side A and B energy balances coil 1 to 8 energy balances) and 36 variables. However, the heat transfer coefficients are not known with any great accuracy. Further, both the side and coil heat transfer coefficients depend on the fire-box temperature. It is therefore necessary to calculate values for the heat transfer coefficients from the data. This effectively reduces the number of independent equations to 11. 

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