Mean Driving Force

The design equation used for sizing heat exchangers generally takes the form of 

In any real heat exchanger, the local driving force AT will vary along the length of the exchanger say it varies between ATi at one end of the exchanger to ATo at the other end. Then the question arises which value of AT do you use in (1) The answer turns out to be use the log mean of ATi and ATz  

This turns out to be correct in nearly every situation. We will prove it now for one particular case and leave some other cases to be proved in the homework (HWK 1, Probl. 1) 

Depending on which x we choose, we get a different driving force. The rate ofheat transfer from the hot fluid to the cold fluid in any slice is given by a local heat transfer coefficient U(x)-. 

Integrating (2) as a function of x is difficult since we d have to predict AZ (x). There is a easier way (but a trick is required). Consider steady-state counter-current flow through a double-pipe heat exchanger (shown at right). A steady-state energy balance on the hot fluid gives 

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Log arithmic-Mean Driving Force. As noted eadier, linear operating lines occur if all concentrations involved stay low. Where it is possible to assume that the equiUbrium line is linear, it can be shown that use of the logarithmic mean of the terminal driving forces is theoretically correct. When the overall gas-film coefficient is used to express the rate of absorption, the calculation reduces to solution of the equation... 

D. Rectification in vertical wetted wall column with turbulent vapor flow, Johnstone and Pigford correlation =0.0.328(Wi) Wi P>vP 3000 < NL < 40,000, 0.5 < Ns. < 3 N=, v,.gi = gas velocity relative to R. liquid film = — in film -1 2 " [E] Use logarithmic mean driving force at two ends of column. Based on four systems with gas-side resistance only, = logarithmic mean partial pressure of nondiffusing species B in binary mixture. p = total pressure Modified form is used for structured packings (See Table 5-28-H). 

An, or Amean = Mean driving force on gas or liquid basis... 

Now let us refer to the right-hand side of the above expression. The mean driving force varies with the specified design temperatures and also the ratio of water/air loading (L/G). If we take a low airflow, the air soon rises in temperature and tends to reach equilibrium conditions with the boundary layer. Thus the driving force is reduced. On the other hand, excess air is unnecessary. Therefore, one must adjust the airflow that supply just meets demand. A plot of L/G versus AT MDF is shown in Figure 34.17. This is known as a demand curve. 

Using the mean driving force, integration of equation 13.53 gives ... 

The log mean driving force in terms of the liquid phase must now be calculated. Values of Xe corresponding to the gas composition Y may be found from the equilibrium data given (but are not plotted here) as ... 

This is integrated in terms of a log mean driving force,... 

Logarithmic-mean driving force, packed column absorbers, 1 53 Logarithmic mean temperature difference (LMTD), 13 251, 252 Logic circuits, CMOS, 22 251-253 Logic gates, molecular-based, 17 61 Log-mean temperature difference (LMTD), 26 64... 

Driving force at bottom of column = Logarithmic mean driving force =... 

Back-mixing in the impingement zone, the major active region for heat and mass transfer, is critical. This may be favorable for some processes while it is harmful for others since back-mixing usually results in a decreased mean driving force for the processes involved ... 

Overall Gas-Side Transfer Units Using the Log-Mean Driving Force... 

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