Heat exchangers LMTD method

The above derivation for LMTD involves two important assumptions (1) the fluid specific heats do not vary with temperature, and (2) the convection heat-transfer coefficients are constant throughout the heat exchanger. The second assumption is usually the more serious one because of entrance effects, fluid viscosity, and thermal-conductivity changes, etc. Numerical methods must normally be employed to correct for these effects. Section 10-8 describes one way of performing a variable-properties analysis. 

When is the LMTD method most applicable to heat-exchanger calculations ... 

Hot exhaust gases are used in a finned-tube cross-flow heat exchanger to heat 2.5 kg/s of water from 35 to 85°C. The gases [cp = 1.09 kJ/kg °C] enter at 200 and leave at 93°C. The overall heat-transfer coefficient is 180 W/m2 °C. Calculate the area of the heat exchanger using (a) the LMTD approach and (b) the effectiveness-NTU method. 

Tn upcoming sections, we discuss the two methods used in the analysis of heat exchangers. Of these, the log mean temperature difference (or LMTD) method is best suited for the first task and the ffecliveness-NTlJ method for the second task. But first we present some general considerations. 

Therefore, the LMTD method is very suitable for determining the size of a heat exchanger to realize prescribed outlet temperatures when the mass flow rates and the inlet and outlet temperatures of tiie hot and cold fluids are specified. 

With the LMTD method, the task, is to select a heat exchanger that will meet the prescribed heat transfer requirements. The procedure to be followed by the selection process is ... 

The LMTD method could still be used for this alternative problem, but the procedure would require tedious iterations, and Ihus it is not practical. In an attempt to eliminate the iterations from the solution of such problems, Kays and London came up with a method in 1955 called the cffecUveness-NTU method, which greatly simplified heat exchanger analysis. 

We mentioned earlier that when all the inlet and outlet temperatures are specified, the size of the heat exchanger can easily be determined using the LMTD method. Alternatively, it can also be determined from the effectiveness-NTU method by first evaluating the effectiveness e from its definition (Hq. 11-29) and then the NTU from the appropriate NTU relation in Table 11-5. 

Analysis Ihe schematic of (he heat exchanger is given in Fig. 11-30. The outlet temperatures are not specified, and they cannot be determined from an energy balance. The use of the LMTD method in this case will involve tedious iterations, and thus the c-NTU method is indicated. The first step in the c-NTU method is to determine the heal capacity rates of the hot and cold fluids and identify the smaller one ... 

Of the two methods used in the anal5 sis of heat exchangers, the lag mean temperature difference (or LMTD) method is... 

C When the outlet temperatures of the fluids in a heat exchanger are not known, is it still practical to use the LMTD method Explain. 

II-40C Explain how the LMTD method can be used to determine the heat transfer surface area of a multipass shell-and-tube heat exchanger when all the necessary information, including (he oullet temperatures, is given. 

C Under what conditions is the effecliveness-NTU method definitely preferred over the LMTD method in heat exchanger analysis ... 

Water (c, = 4180 J/kg C) enters the 2.5-cm-intemal-diameier tube of a double-pipe counter-flow heat exchanger at 17°C at a rate of 1.8 kg/s, Water is heated by steam condensing at I20 C (/i/g = 2203 kJ/kg) in the shell. If the overall heat transfer coefficient of the heat exchanger is 700 W/in °C, detecraine the length of the tube required in order to heat the water to 80°C using (o) the LMTD method and (b) the e-NTU method. 

Cold water (Cp = 4180 J/kg C) enters the tubes of a heal exchanger with 2-shell passes and 23-Uibe passes at 14"C at a rate of 3 kg/, while hot oil (Cp 2200 J/kg Q enters the shell at 2(X) C at Ihe same mass flow rate. The overall heat transfer coefficient based on the outer surface of Ihe tube is 300 W/m "C and the heat transfer surface area on that side is 20 m Deieiinine the rate of heat transfer using (a) the LMTD method and (b) the e-NTU method. 

The mass flow rate, specific heat, and inlet temperature of the tube-side stream in a double-pipe, parallel-flow heat exchanger are 2700 kg/h, 2.0 kJ/kg K, and 120°C, respectively. The mass flow rate, specific heat, and inlet temperature of the other stream are 1800 kg/h, 4.2 kJ/kg K, and 20°C, respectively. The heat Iranster area and overall heal transfer coefficient are 0.50 and 2.0 kW/m K, respectively. Find the outlet temperatures of both streams in steady operation using (a) the LMTD method and (6) the effcctivcncss-NTU method. 

There are two basic approaches to heat-exchanger design for low temperatures (1) the effectiveness-NTU approach and (2) the log-mean-temperature-dijference (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 effectiveness-NTU approach is used more often when the inlet temperatures and the flow rates are specified for an exchanger with fixed area and the outlet temperatures are to be determined. Both methods are described earlier in Sec. 11. 

For multipass and cross-flow exchangers, the log-mean temperature difference (LMTD) method is still applicable, i.e., the heat transfer rate is... 

When the temperature of either fluid remains constant during the heat exchange resulting from a change of phase (condensation or evaporation), the LMTD method continues to apply, but it may be given a more convenient form. This is done in the next section. 

It is important to note that the NTU method, although devised for performance under different conditions, equally applies to the design of heat exchangers. Therefore, it is a more general method than the LMTD method. Here we recapitulate both methods for a ready reference in heat-exchanger calculations ... 

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