LMTD

The LMTD, ie, logarithmic mean temperature difference, is an effective overall temperature difference between the two fluids for heat transfer and is a function of the terminal temperature differences at both ends of the heat exchanger. 

This implies that the LMTD or M I D as computed in equations 20 through 26 may not be a representative temperature difference between the two heat-transferring fluids for aU tubes. The effective LMTD or M ID would be smaller than the value calculated, and consequentiy would require additional heat-transfer area. The tme value of the effective M I D may be determined by two- or three-dimensional thermal—hydrauUc analysis of the tube bundle. Baffle—Tube Support PlateXirea. The portion of a heat-transfer tube that passes through the flow baffle—tube support plates is usuaUy considered inactive from a heat-transfer standpoint. However, this inactive area must be included in the determination of the total length of the heat-transfer tube. 

Countercurrent or Cocurrent Flow If the flow of the streams is either completely countercurrent or completely cocurrent or if one or both streams are isothermal (condensing or vaporizing a pure component with negligible pressure change), the correct MTD is the logarithmic-mean temperature difference (LMTD), defined as... 

Cross-flow exchangers of various lands are also important and require correc tion to Be applied to the LMTD calculated by assuming countercurrent flow. Sever cases are given in Fig. 11-4/, g, h, i, and/... 

FIG. 11-4 (Continued) LMTD correction factors for heat exchangers. In all charts, fi = (Ti — T<>y(U — t ) and S = (to — ti)/(Ti — ti). ( ) Cross-flow (drip type), two horizontal passes with U-hend connections (trombone type). (/) Cross-flow (drip type), helical coils with two turns. 

If the vapor is superheated at the inlet, the vapor may first be desuperheated by sensible heat transfer from the vapor. This occurs if the surface temperature is above the saturation temperature, and a single-phase heat-transfer correlation is used. If the surface is below the saturation temperature, condensation will occur directly from the superheated vapor, and the effective coefficient is determined from the appropriate condensation correlation, using the saturation temperature in the LMTD. To determine whether or not condensation will occur directly from the superheated vapor, calculate the surface temperature by assuming single-phase heat transfer. 

LMTD is calculated like a 1 pass-1 pass shell and tube with no F correction factor required in most cases. 

LMTD and overall coefficient are calculated like in PHE section above. 

The most common form has both sides in helical flow patterns, pure countercurrent flow is followed and the LMTD correction factor approaches 1.0. Temperature crosses are possible in single units. Like the spiral-plate unit, different configurations are possible for special apphcations. 

There are two basic approaches to heat-exchanger design for low temperatures (1) the effec tiveness-NTU approach and (2) the log-mean-temperature-difference (LMTD) approach. The LMTD approach is used most frequently when all the required mass flows are known and the area of the exchanger is to be determined. The effec-... 

Although two fluids may transfer heat in either counter-current or cocurrent flow, the relative direction of the two fluids influences the value of the LMTD, and thus, the area required to transfer a given amount of... 

In the basic heat transfer equation it is necessary to use the log mean temperature difference. In Equation 2-4 it was assumed that the two fluids are flowing counter-current to each other. Depending upon the configuration of the exchanger, this may not be true. That is, the way in which the fluid flows through the exchanger affects LMTD. The correction factor is a function of the number of tube passes and the number of shell passes. 

Figures 3-10 and 3-11 can be used to calculate a corrected LMTD from the formula.

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