Heat exchangers temperature driving force

The cost of recovery will be reduced if the streams are located conveniently close. The amount of energy that can be recovered will depend on the temperature, flow, heat capacity, and temperature change possible, in each stream. A reasonable temperature driving force must be maintained to keep the exchanger area to a practical size. The most efficient exchanger will be the one in which the shell and tube flows are truly countercurrent. Multiple tube pass exchangers are usually used for practical reasons. With multiple tube passes the flow will be part counter-current and part co-current and temperature crosses can occur, which will reduce the efficiency of heat recovery (see Chapter 12). 

Heat removed by condensation is easy. The heat-transfer coefficient U for condensation of pure, clean, vapors may be 400 to 1000 Btu per hour per ft2 of heat exchanger surface area, per °F of temperature-driving force. The U value for subcooling stagnant liquid may be only 10 to 30. Condensate backup is the major cause of lost heat transfer for heat exchangers, in condensing service. 

The requirement to leave one end of the tubes free to float creates a rather unpleasant process problem. The most efficient way to transfer heat between two fluids is to have true countercurrent flow. For a shell-and-tube exchanger, this means that the shell-side fluid and the tube-side fluid must flow through the exchanger in opposite directions. When calculating the log-mean temperature driving force (LMTD), an engineer assumes true countercurrent flow between the hot fluid and the cold fluid. 

Local heat flux and driving force x = A(l/T) in a heat exchanger. The temperature increase of the cold stream is AT. 

The rate of heat transfer per unit area of heat exchanger (heat flux), q, will be a function of the temperature driving force AT, tube diameter d, the mean fluid flow velocity u, fluid flow properties density p and viscosity p - and fluid thermal properties - specific heat capacity cp and thermal conductivity k. 

In the Nusselt number, the term (q/AT), the rate of heat transfer per unit area of heat exchanger per unit temperature driving force, is known as the heat transfer coefficient and is given the symbol h. The heat transfer coefficient is used to characterise heat transfer rates. Heat transfer processes are described in more detail in Chapter 4, 11 An Introduction to Heat Transfer . 

The point of this analysis was to characterize the source of inefficiencies in the process as designed. The main heat exchanger was the key item. The authors developed equations which related the area of the heat exchanger and its irreversible entropy change to two controllable design variables namely, the pressure drop, and the hot end temperature driving force between... 

Finally, Table 3.2.1 contains two economic relations or rules-of-thumb. Equation 3.2.20 states that the approach temperature differences for the water, which is the difference between the exit water teir jerature and the wet-bulb temperature of the inlet air, is 5.0 "C (9 °F). The wet-bulb temperature of the surrounding air is the lowest water temperature achievable by evaporation. Usually, the approach temperature difference is between 4.0 and 8.0 C. The smaller the approach temperature difference, the larger the cooling tower, and hence the more it will cost. This increased tower cost must be balanced against the economic benefits of colder water. These are a reduction in the water flow rate for process cooling and in the size of heat exchangers for the plant because of an increase in the log-mean-temperature driving force. The other mle-of-thumb. Equation 3.2.21, states that the optimum mass ratio of the water-to-air flow rates is usually between 0.75 to 1.5 for mechanical-draft towers [14]. 

Figure 3.18b shows the same streams plotted with a lower value of AT in- The amount of heat exchanged is increased and the utility requirements have been reduced. The temperature driving force for heat transfer has also been reduced, so the heat exchanger has both a larger duty and a smaller log-mean temperature difference. This leads to an increase in the heat transfer area required and in the capital cost of the exchanger. The capital cost increase is partially offset by capital cost savings in the heater and cooler, which both become smaller, as well as by savings in the costs of hot and cold utilities. In general, there will be an optimum value of ATmin, as illustrated in Figure 3.19. This optimum is usually rather flat over the range 10°C to 30°C.

When heat is exchanged between a surface and a fluid, or between two fluids flowing through a heat exchanger, the local temperature driving force, AT, varies with the flow path. For this condition, the concept of the log-mean temperature difference (LMTD) may be applied when the overall heat-transfer coefficient, U, is given. In this case. 

Because the temperature driving force across the heat exchanger usually varies along the length of the heat exchanger, it is necessary to employ some mean value of the temperature difference in using Equations 2.8 and 2.11. 

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