Log-mean temperature driving force

At,n = log-mean-temperature driving force from heating medium to the sohds, K. 

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. 

We can explain why the gain changes with temperature by looking at the log mean temperature driving force and the heat transferred to the coolant. The following equation is valid only when the reactor inlet and exit temperatures are higher than the coolant temperature and the reactor temperature increases linearly. This is approximately true for the vinyl acetate reactor. 

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]. 

The above optimization problem is applicable to systems involving air and water only. It ignores vapour superheat at the ejector inlet, vapour sub-cooling and liquid sub-cooling in condenser area calculations, and also assumes a simple log-mean temperature driving force (LMTD) without any correction factor. Hence, condenser area calculations are approximate but sufficient for optimization. Actual condenser design is quite complex for systems... 

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