Examples logarithmic mean temperature difference

Example 1.11 A fluid evaporates at 3°C and cools water from 11.5°C to 6.4°C. What is the logarithmic mean temperature difference and what is the heat transfer if it has a surface area of 420 m and the thermal transmittance is 110 W/ (m K) ... 

The logarithmic mean temperature difference usually is applicable. For example, if the gas goes from 1200 to 150°F and the liquid countercurrently from 120 to 400 F, the mean temperature... 

The logarithmic mean temperature difference usually is applicable. For example, if the gas goes from 1200 to 150°F and the liquid countercurrently from 120 to 400°F, the mean temperature difference is 234.5 and Ng = 4.48. The height of a contact zone then is obtained as the product of the number of transfer units and the height Hg of a transfer unit. Several correlations have been made of the latter quantity, for example, by Cornell, Knapp, and Fair (1960), as modified in the Chemical Engineers Handbook (1973, pp. 18-33, 18.37) and in Perry s Chemical Engineers Handbook (1999, Table 5-28, pp. 5-74 to 5-77). These correlations for Hg... 

Logarithmic mean temperature difference (LMTD) is described on pp. 126-128 of reference 57. It corrects for the curvature of the temperature lines from beginning to end of the heat process whether over time as in batch furnaces or over distance in continuous furnaces. A rough method uses a rule that estimates the mean receiver (load surface) temperature will be the initial load temperature plus of the receiver load surface temperature rise, Trf — Tri, or in Example 3.6, LMTD = 100 + ( )(1050 — 100) = 733°F. 

If one of the fluids is at constant temperature, as in a condenser, no difference exists among countercurrent flow, parallel flow, or multipass flow, and Eq. (11.15) applies to all of them. In countercurrent flow, AT2, the warm-end approach, may be less than ATj, the cold-end approach. In this case, for convenience and to eliminate negative numbers and logarithms, the subscripts in Eq. (11.15) may be interchanged. The LMTD is not always the correct mean temperature difference to use. It should not be used when U changes appreciably or when AT is not a linear function of q. As an example, consider an exchanger used to cool and condense a superheated vapor, with the temperature diagram shown in Fig. 11.6. 

H2 addition is different from other methods of chain termination. For example, when the reaction temperature is raised, the termination rate is multiplied by some factor, which is determined by the activation energy. If the responses of all the sites are approximately the same, the MW distribution is shifted intact to lower MW, without distortion. (To understand why, note that the GPC curve is plotted on a logarithmic MW scale, and the multiplication of the various termination rates by a constant factor amounts to an additive shift across the MW distribution.) However, when H2 is added to the reactor, a new termination pathway is opened, adding to the overall termination rate. If each site is affected equally, then a constant increment is added to the termination rate at each site, which means that the MW distribution should be distorted. High-MW sites should respond proportionately more than the others. 

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