Effectiveness of a heat exchanger

If the heat exchanger was of infinite size, the space-temperature curves would eventually meet and no further heat could be transferred. The fluid in Example 1.11 would cool the water down to 3°C. The effectiveness of a heat exchanger can be expressed as the ratio of heat actually transferred to the ideal maximum ... 

Starting with a basic energy balance, derive an expression for the effectiveness of a heat exchanger in which a condensing vapor is used to heat a cooler fluid. Assume that the hot fluid (condensing vapor) remains at a constant temperature throughout the process. 

The effectiveness of a heat exchanger depends on the geometry of the heat exchanger as well as the /low arrangement. Therefore, different types of heat exchangers have different effectiveness relations. Below we illustrate tlie development of the effectiveness e relation for the double-pipe parallel-flow heat exchanger. 

It can be shown that the effectiveness of a heat exchanger is a function of the number of transfer units NTU and the capacity ratio c. That is,... 

The effectiveness of a heat exchanger is independent of the capacity ratio c for NTU values of less than about 0.3. 

With these auxiliary assumptions, the temperature effectiveness of a heat exchanger can be calculated using the following equations after the maldistributed fluid stream is divided into N individual uniform fluid streams ... 

Effect of Uncertainties in Thermal Design Parameters. The parameters that are used ia the basic siting calculations of a heat exchanger iaclude heat-transfer coefficients tube dimensions, eg, tube diameter and wall thickness and physical properties, eg, thermal conductivity, density, viscosity, and specific heat. Nominal or mean values of these parameters are used ia the basic siting calculations. In reaUty, there are uncertainties ia these nominal values. For example, heat-transfer correlations from which one computes convective heat-transfer coefficients have data spreads around the mean values. Because heat-transfer tubes caimot be produced ia precise dimensions, tube wall thickness varies over a range of the mean value. In addition, the thermal conductivity of tube wall material cannot be measured exactiy, a dding to the uncertainty ia the design and performance calculations. 

The values of CJs are experimentally determined for all uncertain parameters. The larger the value of O, the larger the data spread, and the greater the level of uncertainty. This effect of data spread must be incorporated into the design of a heat exchanger. For example, consider the convective heat-transfer coefficient, where the probabiUty of the tme value of h falling below the mean value h is of concern. Or consider the effect of tube wall thickness, /, where a value of /greater than the mean value /is of concern. 

Fypass Flow Effects. There are several bypass flows, particularly on the sheUside of a heat exchanger, and these include a bypass flow between the tube bundle and the shell, bypass flow between the baffle plate and the shell, and bypass flow between the shell and the bundle outer shroud. Some high temperature nuclear heat exchangers have shrouds inside the shell to protect the shell from thermal transient effects. The effect of bypass flow is the degradation of the exchanger thermal performance. Therefore additional heat-transfer surface area must be provided to compensate for this performance degradation. 

Miscellaneous Effects. Depending on individual design characteristics, there are other miscellaneous effects to consider in the determination of the final sizing of a heat exchanger. These include effects of flow maldistribution of both the sheUside and tubeside fluids, stagnant or inactive regions in the tube bundle, and inactive length of the tube in tubesheets. These effects should be individuaUy assessed and appropriate additional areas should be provided. 

System performance in ciyogenic liquefiers and refrigerators is directly related to the effectiveness of the heat exchangers used in the system. For example, the liqiiid yield for a simple J-T cycle as given by Eq. 11-112 needs to be modified to... 

Eluor Daniel has the ability to perform a heat exchanger tube rupture transient analysis consistent with the method referred to in RP-521 ("Model to Predict Transient Consequences of a Heat Exchanger Tube Rupture," by Sumaria et ah). This methodology accounts for effects such as the inertia of the low-pressure liquid, the compressibility of the liquid, the expansion of the exchanger shell or tube chaimels, and the relief valve dynamics. Dynamic simulation can be used to meet the following objectives ... 

The direction of flow is important, as it has a pronounced effect on the efficiency of a heat exchanger. The flows may be in the same direction (parallel flow, cocurrent), in the opposite direction (counterflow), or at right angles to each other (cross-flow). The flow may be either single-pass or multipass the latter method reduces the length of the pass. 

The simulations have been focused on the effect of the heat exchange equipment on reactor stability. To this goal, the minimum value of the group U S that guarantees a thermally stable operation has been determined as a function of the initial reactor temperature Tro (where 7] = Tro has been imposed). The critical US values are reported in Fig. 4.11 and, regardless of the particular criterion adopted, they increase—as expected—when Tl0 increases. 

Dead time is also called transportation lag, because it is the time required for fresh heat transfer fluid to displace the contents of the exchanger and its associated piping. The dead time is the worst enemy of control, because until it has expired, a change in the heat transfer fluid flow (or temperature) will not even begin to have an observable effect. For a heat exchanger, the dead time is usually between 1 and 30 seconds. When the equipment is correctly designed, the dead time is much less than the time constant. 

Hot water enters a counterflow heat exchanger at 99°C. It is used to heat a cool stream of water from 4 to 32°C. The flow rate of the cool stream is 1.3 kg/s, and the flow rate of the hot stream is 2.6 kg/s. The overall heat-transfer coefficient is 830 W/m2 °C. What is the area of the heat exchanger Calculate the effectiveness of the heat exchanger. 

Water at 75°C enters a counterflow heat exchanger. It leaves at 30°C. The water is used to heat an oil from 25 to 48°C. What is the effectiveness of the heat exchanger ... 

B Water at 90°C enters a double-pipe heat exchanger and leaves at 55°C. It is used to heat a certain oil from 25 to 50°C. Calculate the effectiveness of the heat exchanger. 

Hot water at I80°F is used to heat air from 45°F to 115°F in a finned tube cross-flow heat exchanger. The water exit temperature is 125°F. Calculate the effectiveness of this heat exchanger. 

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