The Log Mean Temperature Difference

Consider the double-pipe heat exchanger shown in Fig. 10-2. The fluids may flow in either parallel flow or counterflow, and the temperature profiles for these two cases are indicated in Fig. 10-7. We propose to calculate the heat transfer in this double-pipe arrangement with 

A - surface area for heat transfer consistent with definition of U AT, = suitable mean temperature difference across heat exchanger 

An inspection of Fig. 10-7 shows that the temperature difference between the hot and cold fluids varies between inlet and outlet, and we must determine the average value for use in Eq. (10-5). For the parallel-flow heat exchanger shown in Fig. 10-7, the heat transferred through an element of area dA may be written 

This differential equation may now be integrated between conditions 1 and 2 as indicated in Fig. 10-7. The result is 

Returning to Eq. (10-6), the products m,( and mhch may be expressed in terms of the total heat transfer q and the overall temperature differences of the hot and cold fluids. Thus 

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It is thus always possible to achieve the interval design with (S -1) matches and each match operating with the log mean temperature difference of the interval. ... 

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-... 

In the field of heat transfer, a good example of this category of shortcut design method is the famous F correction factor to correct the log mean temperature difference of shell and tube heat exchangers for deviations from true countercurrent flow. For multipass heat exchangers, the assumptions are ... 

Parameters Cj and Cj are specific heats of the cold and hot fluids in Btu respectively, and the log-mean temperature difference is defined as follows ... 

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. 

Note that the Log Mean Temperature Difference (LMTD) is somewhat less than the arithmetic mean, represented by the following ... 

For heat exchangers in true counter-current (fluids flowing in opposite directions inside or outside a tube) or true co-current (fluids flowing inside and outside of a tube, parallel to each other in direction), with essentially constant heat capacities of the respective fluids and constant heat transfer coefficients, the log mean temperature difference may be appropriately applied, see Figure 10-33. ... 

A further advantage of the plate heat exchanger is that the effective mean temperature difference is usually higher than with the tubular unit. Since the tubular is always a mixture of cross and contra-flow in multi-pass arrangements, substantial correction factors have to be applied to the log mean temperature difference (LMTD). In the plate... 

The next step is to decide a suitable evaporating temperature. This will be set by the required load condition and the appropriate temperature differential (AT) across the evaporator. In the context of evaporator selection, the AT used is the difference between the evaporating refrigerant and the temperature of the fluid entering the cooler, not the log mean temperature difference (see [1-5]). 

The following assumptions are made in the derivation of the temperature correction factor F in addition to those made for the calculation of the log mean temperature difference ... 

Prior to discussions of the capital and operating costs, we need to define the temperature driving force for heat transfer. Examine the notation in Figure El 1.3c by definition the log mean temperature difference ATlm is... 

In the case where the equilibrium curve is straight, the logarithmic mean driving potential (which is similar to the log-mean temperature difference used in heat... 

In the convection zone of the heater, some heat also is transferred by direct radiation and reflection. The several contributions to overall heat transfer specifically in the convection zone of fired heaters were correlated by Monrad [Ind. Eng. Chem. 24,505 (1932)]. The combined effects are approximated by item 10 of Table 8.16, which is adequate for estimating purposes. The relation depends on the temperature of the gas film which is taken to be the sum of the average process temperature and one-half of the log mean temperature difference between process and flue gas over the entire tube bank. The temperature of the gas entering the convection zone... 

The log mean temperature difference LMTD is simply the average or weighted temperature difference between the hot side and the cold side of the exchanger. Use Eq. (5.10) to determine this mean average temperature. It is simply, as the term indicates, the average temperature difference between the tube and shell sides of the exchanger. 

The temperature driving force for heat transfer between the reaction liquid at temperature Tr and the coil is the log-mean temperature difference given in Eq. (2.19). The heat transfer rate is given by... 

In a liquid-liquid exchanger, the total heat transferred (Q) from the hot process fluid to the cooling water is dependent on the overall heat transfer coefficient (U), the heat transfer area (A), and the log mean temperature difference (ATm). Therefore, any of these can be manipulated to control Q. 

In practice, condenser temperatures are as shown in Figure 6.1(b) (both vapour and coolant temperatures change) and in the equation for (0, the log mean temperature difference should be used for A Tm. 

Calculate the required area for heat exchange The heat exchanged is given by Equation (42), where the log mean temperature difference is given by (see Figure 21) ... 

The process conditions in the FEHE (counter-current flow with no phase change and constant physical properties) lend themselves naturally to calculating the duty on the basis of the log mean temperature difference (LMTD) ... 

This temperature difference is called the log mean temperature difference (LMTD). Stated verbally, it is the temperature difference at one end of the heat exchanger less the temperature difference at the other end of the exchanger... 

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