LMTD correction factor The driving force for heat transfer is LMTD. Thus LMTD can be used for 1-1 heat exchanger for cocurrent and counter current. However for multi pass exchangers like 1-2, 2-4, etc, a combination of countercurrent and co-current flow exists as the fluid flows through alternate passes . The mean temperature is less than the logarithmic mean calculated for counter-current flow and greater than that based on co-current flow. flow . However, it is convenient to retain the LMTD by introducing a correction factor. Therefore in order to use true heat transfer driving force a correction factor is required into the LMTD. The corrected mean temperature difference is calculated as: True LMTD = LMTD x F F is Correction factor to LMTD for countercurrent flow for various mechanical pass configurations are given in TEMA standard in section 7, page no 7-10. 7 -10.
Although not readily apparent, these equations are symmetric with respect to fluid placement, i.e., switching the two fluids between tubes and shell changes the values of R and P, but leaves F unchanged. Configurations for which the calculated value of F is less than about 0.75 should not be used in practice for several reasons. First, the heat transfer in such a case is relatively inefficient, being less than 75% of that for a counter-flow exchanger. More importantly, the restriction on F is intended to avoid the steeply sloping parts of the curves. Therefore, small deviations from simplifying assumptions (such as no heat loss and constant U) upon which the equations for F are based, can result in an actual F-value much lower than the calculated value. Also, in these regions large changes in F can result from small changes in P, making exchanger performance very sensitive to any deviations from design temperatures. The value of F can be increased by increasing the number of shell passes, up to a practical limit of about six. (Note, however, that the curves become steeper with increasing number of shell passes, requiring still higher values of F.) In extreme cases, true counter flow, for which F =1.0, may be the only practical configuration. F = 1.0 for pure counter-current flow. As co-current flow increases in design arrangement (not flow rate), the F is reduced, and the heat exchanger efficiency falls, It should be noted that in case of condensation or evaporation the correction factor becomes unity (FT =1).
Example: A fluid is to be heated from 100 deg F to 160 deg F by heat exchange with a hot fluid that will be cooled from 230 deg F to 150 deg F. The heat-transfer rate will be 540,000 Btu/h and the hot fluid will flow in the tubes. Will a 1-2 exchanger (i.e., an exchanger with one shell pass and a multiple of two tube passes) be suitable for this service? Find the mean temperature difference in the exchanger.
Refer LMTD correction factor chart for 1 shell and 2 tube pass from TEMA standard. Thus F = 0.73 Since F is less than 0.75, a 1-2 exchanger should not be used Value of F can be increased by increasing number of shell side passes. So selecting 2 shell and 4 tube pass heat exchanger. Now F = 0.94 Hence, an exchanger with two shell passes and a multiple of four tube passes will be suitable. Such an exchanger is called a 2–4 exchanger. The mean temperature difference in the exchanger is calculated as follows.
