Logarithmic correction factors

The value of T is calculated from the logarithmic mean temperature difference multiplied by a correction factor. With single-pass operation, this factor is about 1 except for plate packs of less than 20, when the end effect has a... 

F Geometric factor for radiation or correction factor for logarithmic mean temperature difference ... 

The usual practice in the design of shell and tube exchangers is to estimate the true temperature difference from the logarithmic mean temperature by applying a correction factor to allow for the departure from true counter-current flow ... 

A pure, saturated, vapour will condense at a fixed temperature, at constant pressure. For an isothermal process such as this, the simple logarithmic mean temperature difference can be used in the equation 12.1 no correction factor for multiple passes is needed. The logarithmic mean temperature difference will be given by ... 

When the condensation process is not exactly isothermal but the temperature change is small such as where there is a significant change in pressure, or where a narrow boiling range multicomponent mixture is being condensed the logarithmic temperature difference can still be used but the temperature correction factor will be needed for multipass condensers. The appropriate terminal temperatures should be used in the calculation. 

U = overall heat transfer coefficient Aexisting = existing heat transfer area A A = additional area requirement ATim = logarithmic mean temperature difference Fj = logarithmic mean temperature difference correction factor... 

Two approaches attempt to solve this problem. The one is a transformation of the data to logarithms prior to the statistical calculations corresponding to a logarithmic normal distribution. The other is a modification of the z-scores with correction factors. This method was introduced first in a German standard for proficiency testing (DIN 38402 - 45), which in the meantime partially was transferred into ISO/TS 20612. 

It was noted that the velocity in a channel approaching a weir might be so badly distributed as to require a value of 1.3 to 2.2 for the kinetic energy correction factor. In unobstructed uniform channels, however, the velocity distribution not only is more uniform but is readily amenable to theoretical analysis. Vanonil has demonstrated that the Prandtl universal logarithmic velocity distribution law for pipes also applies to a two-dimensional open channel, i.e., one that is infinitely wide. This equation may be written... 

This result must of course be correted for small values of XQpt using the correction factor mentioned above. For feedwater heaters, a similar result is obtained by expanding the logarithm in Eqn. (15) to obtain a value of Oy = (y-l) /2y which needs another correction factor to conform to Eqn. (15) exactly. This merely introduces a factor of two into Eqn. (A2) so that for feed-water heaters, the corresponding basic results is... 

For substrates reacting as conjugate acids it is sufficient to extrapolate the linear arm of the rate profile to H0 = -6.6, and subtract from log the value of 4.42, which is the logarithm of the rate difference between 100 and 25°C for a reaction of AH = 30 kcal mol-1. (An error of 5 kcal mol-1 in this will produce a maximum error of 0.8 in this correction factor.)... 

FT = correction factor on logarithmic-mean At for counterflow to give mean At, dimensionless defined in Fig. 15-2 g = local gravitational acceleration, ft/(sXs)... 

It was seen from the discussion of heat exchangers that the fluid streams are not strictly countercurrent. Baffles on the shell side induce crossflow, and in a two-tube-pass heat exchanger both countercurrent and cocurrent flow occur. To account for deviations from countercurrent flow, the logarithmic-mean teri5)erature difference is multiplied by a correction factor, F. Thus,... 

Calculate the logarithmic-mean correction factor, F, from Equation 4.5.4. 

Next, calculate the logarithmic-mean temperature difference correction factor, F, from Equation 4.5.4. Calculate F either from Equation 4.10 or use plots of Equation 4.10 given in the chemical engineering handbook [1]. In either case, first calculate the parameters R and S. R and S are defined in Figme 4.7. 

For isothermal condensation, the logarithmic-mean tenperature difference correction factor, F, equals one. Therefore, from Equation 4.7.3 for the existing heat exchanger, the available overall heat-transfer coefficient. 

F logarithmic mean tenperature correction factor or degrees of freedom h heat transfer coefficient or enthalpy... 

Obtain a relation for the logarithmic mean temperature difference for use in the LMTD melhfld, and modify it (or different types of heat exchangers using the correction factor,... 

Figure 4.7 Definition of parameters for the logarithmic-mean-temperature correction factor.

Because the cost of a heat exchanger depends on its size, and because its size will depend on the heat-transfer rate, a rate equation must be introduced. The rate equation is given by Equation 4.4.3. The logarithmic-mean temperature difference in Equation 4.4.3 is given by Equation 4.4.4. Because perfect countercurrent flow can never be achieved in an actual heat exchanger, the logarithmic-mean temperature difference correction factor, F, is needed. For simplicity, Equation 4.10, discussed earlier, is expressed as Equation 4.4.5, which states that F depends only on the terminal temperatures, once a particular heat exchanger is selected. 

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