Heat exchanger terminal temperatures

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 equations for counterflow ate identical to equations for parallel flow except for the definitions of the terminal temperature differences. Counterflow heat exchangers ate much mote efficient, ie, these requite less area, than the parallel flow heat exchangers. Thus the counterflow heat exchangers ate always preferred ia practice. 

Mean Temperature Differenee The temperature difference between the two fluids in the heat exchanger vm, in general, vaiy from point to point. The mean temperature difference (AT, or MTD) can be calculated from the terminal temperatures of the two streams if the following assumptions are valid ... 

These refer to hot and cold fluid terminal temperatures, inlet of one fluid versus outlet of the other. For a cross exchanger with no phase change, the ATm gives exact results for true countercurrent flow. Most heat exehang-ers, how ever, deviate from true countercurrent so a correction factor, F, is needed. 

Chapter 1 provides a summary of important equations for estimating the terminal temperatures in a heat exchanger. Here we formalize a short estimating procedure for a countercurrent flow situation. Assume that a specifier of a heat exchanger has defined a preliminary sizing of the unit. The system requires heat and material balances. 

Figure 3. Terminal temperatures in a counterflow heat exchanger.

In actual exchanger operational practice, the U values at the hot and cold terminals of the heat exchanger are not the same and can he significandy different if evaluated only at the spot conditions. In order to obtain an overall coefficient U that represents the transfer of heat throughout the exchanger, the U should he evaluated at the caloric temperature for physical properties and individual film coefficients... 

With heat exchangers, cleaning should be considered as an option when the efficiency has fallen off to some specific level e.g. a terminal temperature difference. With boilers, unless there has been some occurrence which may be alleviated by a particular clean, periodic cleaning to pre-empt corrosion by limiting deposit thickness should be considered... 

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 ... 

This is a conventional water loop heat pump system using a boiler and cooling tower to maintain the water loop temperature (see Measures S15-S17 in Section 6.2). Since outside air handling unit and other terminal devices like unit heaters, wall fin convectors, etc which are often used with this water loop heat pump system need a different operating water temperature than that of the water loop, a plate heat exchanger is used between the primary heating circuit... 

Figure 8.2. Terminal temperatures and temperature differences of a heat exchanger, with unidentified internal flow pattern.

Masso and Rudd (1969), Lee, Masso and Rudd (1970) and Pho and Lapidus (1973) start a match with the two stream inlet conditions and exchange all the heat possible, terminating when one stream reaches its target outlet temperature or when a temperature pinch occurs. Ponton and Donaldson (1974), Donaldson, Paterson and Ponton (1976) and Grossmann and Sargent (1978) start a match at the hot end of both streams (or as close to the hot end of the cold stream as possible). The idea is to introduce necessary utilities at their least cost level while exchanging as much heat as possible. Rathore and Powers (1975) do both, getting two alternative matches and obviously many more alternative networks. 

Frequently, an approximate value of the optimum exit-water ten Derature is all that is required, and a rule-of-thumb will be satisfactory. Table 4.4 hsts the approach tenperature difference, which is the difference between the two terminal temperatures of two passing streams, for several heat exchangers. Several approach temperature differences were taken from Uhich [8], For refrigerants, Ulrich s range of 10 to 50°C is on the high side. Frank [7] recommends a range of 3 to 5°C whereas Walas [3] recommends a value of 5.6 C or less. 

Because the cost of a heat exchanger depends on its size, and because its size will depend on the heat-transfer rate, a rate equation must be introduced. The rate equation is given by Equation 4.4.3. The logarithmic-mean temperature difference in Equation 4.4.3 is given by Equation 4.4.4. Because perfect countercurrent flow can never be achieved in an actual heat exchanger, the logarithmic-mean temperature difference correction factor, F, is needed. For simplicity, Equation 4.10, discussed earlier, is expressed as Equation 4.4.5, which states that F depends only on the terminal temperatures, once a particular heat exchanger is selected. 

The experimental evaluation of other effects associated with the operative temperatures and stoichiometric ratio is performed in a range of pressure around 130 kPa, using the side channel air compressor whose characteristics are described in Table 7.1. The effect of the stack temperature on the voltage measured at the stack terminals is shown in Fig. 7.8. In this case, the temperamre is controlled by varying the water flow rate in the heat exchanger shell while the air flow rate and humidification conditions are the same as those of Fig. 7.7. It can be observed that a decrease in temperamre from 346 to 305 K determines a voltage reduction <10% up to 70% of load (200 A), while a satisfactory stack behavior at 313 K is detected in almost all load conditions (see Sect. 3.3). Then, the effect of the stoichiometric ratio is verified for three different loads at the stack and humidification temperature of 313 K. From Fig. 7.9, it can be noted that values of R higher than 2 are... 

---