Thermal effectiveness factor

For an endothermic reaction there is a decrease in temperature and rate into the pellet. Hence 17 is always less than unity. Since the rate decreases with drop in temperature, the effect of heat-transfer resistance is diminished. Therefore the curves for various are closer together for the endothermic case. In fact, the decrease in rate going into the pellet for endothermic reactions means that mass transfer is of little importance. It has been shown that in many endothermic cases it is satisfactory to use a thermal effectiveness factor. Such thermal 17 neglects intrapellet mass transport that is, ri is obtained by solution of Eq. (11-72), taking C = Q. 

A limiting case of intrapellet transport resistances is that of the thermal effectiveness factor In this situation of zero mass-transfer resistance, the resistance to intrapellet heat transfer alone establishes the effectiveness of the pellet. Assume that the temperature effect on the rate can be represented by the Arrhenius function, so that the rate at any location is given by r = A... 

The internal effectiveness factor rj thus obtained is named a thermal effectiveness factor [9, 38]. 

The Ft correction factor is usually correlated in terms of two dimensionless ratios, the ratio of the two heat capacity flow rates R and the thermal effectiveness P of the exchanger ... 

Reactions in porous catalyst pellets are Invariably accompanied by thermal effects associated with the heat of reaction. Particularly In the case of exothermic reactions these may have a marked influence on the solutions, and hence on the effectiveness factor, leading to effectiveness factors greater than unity and, In certain circumstances, multiple steady state solutions with given boundary conditions [78]. These phenomena have attracted a great deal of interest and attention in recent years, and an excellent account of our present state of knowledge has been given by Arls [45]. 

Thermal transpiration and thermal diffusion will not be considered here, but it would be incorrect to assume that their influence is negligible, or even small in all circumstances. Recent results of Wong et al. [843 indi cate that they may Influence computed values of the effectiveness factor iby as much as 30. An account of thermal transpiration and thermal diffu-Ision is given in Appendix I. 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

Convective heat transfer is often nsed as an adjnuct to other modes, particnlarly to the coudnctive mode. It is often more convenient to consider the agitative effecl a performance-improvement iuflneuce on the thermal diffnsivity factor Ot, modifying it to Ot, the effective valne. 

Powder Insulation A method of reahzing some of the benefits of multiple floating shields without incurring the difficulties of awkward structural complexities is to use evacuated powder insulation. The penalty incurred in the use of this type of insulation, however, is a tenfold reduction in the overall thermal effectiveness of the insulation system over that obtained for multilayer insulation. In applications where this is not a serious factor, such as LNG storage facihties, and investment cost is of major concern, even unevacuated powder-insulation systems have found useful apphcations. The variation in apparent mean thermal conductivity of several powders as a function of interstitial gas pressure is shown in the familiar S-shaped curves of Fig. 11-121. ... 

Interrupting fault currents that are mostly inductive (Section 13.4.1) and occur at very low power factors. They are excessive in magnitude, and cause high thermal effects and electromagnetic forces on the arc chamber, the contacts and the contact mounting supports. 

By forced convection The factors that can influence the temperature of the enclosure, installed outdoors are wind and snow, other than forced cooling. But their effect on actual cooling may be small. Sometimes this happens and sometimes not. It is better to ignore this effect when estimating various thermal effects. Natural convection and radiation will take account of this. 

Treatment of thermal conductivity inside the catalyst can be done similarly to that for pore diffusion. The major difference is that while diffusion can occur in the pore volume only, heat can be conducted in both the fluid and solid phases. For strongly exothermic reactions and catalysts with poor heat conductivity, the internal overheating of the catalyst is a possibility. This can result in an effectiveness factor larger than unity. 

To determine emission data, as well as the effect that fuel changes would produce, it is necessary to use the appropriate thermal conversion factor from one fuel to another. Table 6-5 lists these factors for fuels in common use. 

Example 2.21 A rod of plastic is subjected to a steady axial pull of 50 N and superimposed on this is an alternating axial load of 100 N. If the fatigue limit for the material is 13 MN/m and the creep rupture strength at the equivalent time is 40 MN/m, estimate a suitable diameter for the rod. Thermal effects may be ignored and a fatigue strength reduction factor of 1.5 with a safety factor of 2.5 should be used. 

The major reasons for the beluu ior of vertical temperature in water bodies are the low thermal condnctii ity and the absorption of heat in the first few meters. As tlie surface waters begin to heat, transfer to low er layers is reduced and a stability condition develops. The prediction of thermal behavior in lakes and reser oirs is an important power plant siting consideration and also is a major factor in preienting e.xcessive thermal effects on sensitive ecosystems. Furthermore, the extent of thermal stratification influences the vertical dissolved ox)gen (DO) profiles where reduced DO often results from minimal exchiuige with aerated water. ... 

For other environments, such as in sea-water or in chemical plants, exposure conditions that most nearly duplicate those of the related service and are at the same time reproducible, are used. Impingement by water or water carrying entrained solids, thermal effects and physical abuse are among the factors to be considered. 

If temperature gradients are small, Cr may be regarded as effectively constant. Furthermore, Kart is a function of composition, being approximately proportional to the product x, Xr. It is therefore useful to work in terms of the thermal diffusion factor a, where ... 

Thermal effects can be the key concern in reactor scaleup. The generation of heat is proportional to the volume of the reactor. Note the factor of V in Equation (5.32). For a scaleup that maintains geometric similarity, the surface area increases only as Sooner or later, temperature can no longer be controlled,... 

The two factors F, and FJ are very complex and not known. It is virtually certain, however, that each contains several terms. For example, where long-lived radiation-produced species influence the yield, Fj must contain terms such as A 1 — (At + l)c (l — e ) which expresses the average age of the atoms produced. The subsequent thermal effects are often describable in terms of first-order reactions so that FJ must contain one or more terms of the form (1 — Up to the present, there has not been enough information available on any system to make careful statement of Eq. (5) worthwhile. 

Establishing the process sensitivity with respect to the above-mentioned factors is crucial for further scale-up considerations. If the sensitivity is low, a direct volume scale-up is allowed and the use of standard batch reactor configurations is permitted. However, many reactions are characterized by a large thermal effect and many molecules are very sensitive to process conditions on molecular scale (pH, temperature, concentrations, etc.). Such processes are much more difficult to scale up. Mixing can then become a very important factor influencing reactor performance for reactions where mixing times and reaction times are comparable, micromixing also becomes important. 

Insulin aggregation and precipitation was an impediment to the development of implantable devices for insulin delivery as noted by several investigators working with conventional insulin infusion devices [51-54]. The potential causes of the observed aggregation and precipitation are thermal effects, mechanical stress, the nature of the materials in contact with the insulin solution, formulation factors, and the purity of the insulin preparation. 

The terms involving the subscript j represents the contribution of atom j to the computed structure factor, where nj is the occupancy, fj is the atomic scattering factor, and Ris the coordinate of atom i. In Eq. (13-4) the thermal effects are treated as anisotropic harmonic vibrational motion and U =< U U. > is the mean-square atomic displacement tensor when the thermal motion is treated as isotropic, Eq. (13-4) reduces to ... 

Sharma et al. [153] have devised a gentle accelerated corrosion test using a kinetic rate equation to establish appropriate acceleration factors due to relative humidity and thermal effects. Using an estimate for the thermal activation energy of 0.6 eV and determining the amount of adsorbed water by a BET analysis on Au, Cu and Ni, they obtain an acceleration factor of 154 at 65°C/80% RH with respect to 25 °C/35-40% RH. 

The development of composite micro/mesoporous materials opens new perspectives for the improvement of zeolytic catalysts. These materials combine the advantages of both zeolites and mesoporous molecular sieves, in particular, strong acidity, high thermal and hydrothermal stability and improved diffusivity of bulky molecules due to reduction of the intracrystalline diffusion path length, resulting from creation of secondary mesoporous structure. It can be expected that the creation of secondary mesoporous structure in zeolitic crystals, on the one hand, will result in the improvement of the effectiveness factor in hydroisomerization process and, on the other hand, will lead to the decrease of the residence time of products and minimization of secondary reactions, such as cracking. This will result in an increase of both the conversion and the selectivity to isomerization products. 

Random error arises as the result of chance variations in factors that influence the value of the quantity being measured but which are themselves outside of the control of the person making the measurement. Such things as electrical noise and thermal effects contribute towards this type of error. Random error causes results to vary in an unpredictable way from one measurement to the next. It is therefore not possible to correct individual results for random error. However, since random error should sum to zero over many measurements, such an error can be reduced by making repeated measurements and calculating the mean of the results. 

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