Terminal 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 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. 

AT ] = larger terminal temperature difference, F ATt = smaller terminal temperature difference, °F... 

GTD = Greater Terminal Temperature Difference, °F LTD = Lesser Terminal Temperature Difference, °F LMTD = Logarithmic Mean Temperature Difference, °F = Tj = Inlet temperature of hot fluid, °F Tj = Outlet temperature of hot fluid, °F tj = Inlet temperature of cold fluid, °F q = Outlet temperature of cold fluid, °F... 

In = Natural logarithm to base e MTD = Mean Temperature Difference, °F, see Figure 10-33 = Log mean temperature difference LTD = Atj = Least terminal temperature difference GTD = Atj = Greater terminal temperature difference... 

The C ratio (disregard sign if negative) is evaluated from the estimated overall coefflcients based on the temperatures at the cold and hot ends, respectively. For Figure 10-38, the hot terminal difference is G = Gi — ts the cold terminal temperature difference is h = G2 — hi. 

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 ... 

The equation is the same for co-current flow, but the terminal temperature differences will be (T — fi) and (T 2 — t2). Strictly, equation 12.4 will only apply when there is no change in the specific heats, the overall heat-transfer coefficient is constant, and there are no heat losses. In design, these conditions can be assumed to be satisfied providing the temperature change in each fluid stream is not large. 

The value of F, will be close to one when the terminal temperature differences are large, but will appreciably reduce the logarithmic mean temperature difference when the temperatures of shell and tube fluids approach each other it will fall drastically when there is a temperature cross. A temperature cross will occur if the outlet temperature of the cold stream is greater than the inlet temperature of the hot stream, Figure 12.18c. 

ATin/ATout in Figure 12.49 is the ratio of the terminal temperature differences. 

The design variables considered in the optimization of a large-capacity plant are shown in Figure 3. The relationship between the stage terminal temperature difference (TTD), number of stages, and performance ratio (pounds of water produced per pound of steam condensed) is readily apparent upon examination of Figure 3. Unlike a... 

The most important design variable is the terminal temperature difference. This variable has the strongest influence on the condenser surface required in the evaporators and on the heat economy of the plant. The number of stages also has an effect, but it is considerably less than the effect of the terminal temperature difference. Also, the relationships shown in Figure 3 are for a blowdown concentration of twice that of incoming sea water. However, variation in blowdown concentration has only a minor effect on the economics. 

The optimization of the large-capacity multistage flash evaporator was based on the consumption of the 370 thermal megawatts of energy available from the nuclear steam generator. It was necessary to determine the capital cost for various assumed terminal temperature differences and numbers of stages. Added to the amortized capital cost were all other costs necessary for operation of a complete plant, such as steam, labor, utilities, materials, and overhead. 

Results are shown graphically in Figure 4 for a brine temperature of 220°F., condenser tube velocity of 5 feet per second, blowdown temperature of 90°F., and brine concentration of twice sea water. As can be seen, a minimum water cost for these conditions is obtained with a 50-stage plant operating with a terminal temperature difference of about 4°F. Similar calculations were made for a blowdown concentration of 1.5 times sea water and for a once-through system. By cross plotting, it was then possible to determine the optimum blowdown salt concentration for the plant. It was about 1.7 times sea water. However, the curve is almost flat in the range of 1.5 to 2.0 times sea water. 

Figure 4. Relative water cost as a function of terminal temperature difference for several numbers of stages...

Figure 5. Relation of water cost components to terminal temperature difference for 50-stage sea water conversion plants...

Case B is intended to represent the situation when, after years of service, the heater supplied by B5 has had, say, twenty percent of its tubes plugged. The terminal temperature difference (TTD—the difference between saturated steam temperature and feedwater outlet temperature) can be expected to increase by approximately five degress (°F). If heater number 6, supplied by B6 is in good condition it would nearly pick up the load which heater 5 failed to carry (but less efficiently). These are the circumstances assumed for Case B. 

Hagevap LP (a mixture of sodium tripolyphosphate and lignin sulfonic acid derivatives). The concentration ratio of the sea water was not allowed to exceed 2 and therefore only the alkaline scales could form. As long as the maximum brine temperature did not exceed about 200° F., no evidence of scale deposition was obtained. At 210° to 215° F. there was definite indication of scale from the increase in terminal temperature difference (TTD). At the conclusion of a series of tests the inside surface of the tubes was examined and found to have a very thin layer of loose, powdery deposit (after drying) which rubbed off easily and would not be classed as scale. 

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