Heat logarithmic mean temperature difference

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. 

The rate of temperature drop of a fluid as it flows along the length of a heat exchanger is not constant. In order to take account of this nonlinear relationship, the logarithmic mean temperature difference (EMTD) is used. If the inlet and outlet temperatures do not differ widely, an arithmetic mean can be used, because the relationship is considered to be linear. 

The logarithmic mean temperature difference is the same as the temperature difference at the entrance and exit of the heat exchanger, i.e., AT, = AT, = AT ... 

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) ... 

Before equation 12.1 can be used to determine the heat transfer area required for a given duty, an estimate of the mean temperature difference A Tm must be made. This will normally be calculated from the terminal temperature differences the difference in the fluid temperatures at the inlet and outlet of the exchanger. The well-known logarithmic mean temperature difference (see Volume 1, Chapter 9) is only applicable to sensible heat transfer in true co-current or counter-current flow (linear temperature-enthalpy curves). For counter-current flow, Figure 12.18a, the logarithmic mean temperature is given by ... 

When the fluid being vaporised is a single component and the heating medium is steam (or another condensing vapour), both shell and tubes side processes will be isothermal and the mean temperature difference will be simply the difference between the saturation temperatures. If one side is not isothermal the logarithmic mean temperature difference should be used. If the temperature varies on both sides, the logarithmic temperature difference must be corrected for departures from true cross- or counter-current flow (see Section 12.6). 

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... 

As can be seen from the nonlinear temperature profiles, the temperature difference between the fluids varies from one end of the heat exchanger to the other. To find an effective temperature difference between the two fluids, a logarithmic mean temperature difference (LMTD) is defined as... 

It can be shown that the logarithmic mean temperature difference may also be used for the batchwise heating or cooling of fluids. In such cases, the logarithmic... 

This is called the logarithmic mean temperature difference. The temperature profiles are straight when the heat capacities are... 

Because of the strong variations of the heat capacity and therefore of the local heat transfer coefficient at a pseudocritical point, the LMTD (logarithmic mean temperature difference) cannot be used for the evaluation of all of our measurements. 

U - overall heat transfer coefficient, W/m2.°C A - heat transfer area, m2 AT m - logarithmic mean temperature difference (LMTD), °C... 

For a cooler, select from Table 4.4 an approach temperature difference of 5.0 °C, which is an economic rule-of-thumb. This approach is selected rather than the upper limit of 50.0 C to conserve heat, but the surface area will be larger for the 5.0 C approach. From Equation 4.5.8, the exit raw-water temperature, tz, equals 29 °C, Because the raw water has a tendency to scale, it is located on the tube side. At a water temperature of about 50 °C and above, scale formation increases so that the exit water temperature should never exceed 50 °C (122 F). From Equation 4.5.5, the logarithmic-mean temperature difference is... 

But tills, in general, over predicts the heat transfer rate. We show in the next eha)jter that the proper temperature difference for internal flow (flow over lube banks is still internal flow through Ihe shell) is the logarithmic mean temperature difference ATi defined as... 

It Analyze heating and cooling of a fluid flowing in a tube under constant surface temperature and constant surface heat flux conditions, and work with the logarithmic mean temperature difference,... 

W The logarithmic mean temperature difference and the rale of heat loss from the oil are... 

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,... 

The temperature difference between the two fluids decreases from AT, at the inlet to AT-i at the outlet. Thus, it is tempting to use the arithmetic mean temperature AT = (AT, + AT2) as the average icmperalure difference. The logarithmic mean temperature difference ATj is obtained by tracing the actual temperature profile of the fluids along the heat exchanger and is an exact representation of the average temperature difference between the hot and cold fluids. It truly reflects the exponential decay of the local temperature difference. 

Note that ATj is always less than AT. Therefore, using AT in calcula rions instead of AT will overestimate the rate of heat transfer in a heat exchanger between the two fluids. When AT, differs from AT) by no more than 40 percent, the error in using the arithmetic mean temperature difference is less than 1 percent. But the error increases to undesirable levels when AT, differs from A7) by greater amounts. Therefore, we should always use the logarithmic mean temperature difference when determining the rate of heat transfer in a heal exchanger. 

Knowing the inlet and outlet temperatures of both fluids, the logarithmic mean temperature difference for this counter-flov/ heat exchanger becomes... 

SC Can the logarithmic mean temperature difference AFia of a heat exchanger be a negative quantity Explain. 

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