Logarithmic temperature difference LMTD

Countercurrent or Cocurrent Flow If the flow of the streams is either completely countercurrent or completely cocurrent or if one or both streams are isothermal (condensing or vaporizing a pure component with negligible pressure change), the correct MTD is the logarithmic-mean temperature difference (LMTD), defined as... 

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... 

As can be seen from the nonlinear temperature profiles, the temperature difference between the fluids varies from one end of the heat exchanger to the other. To find an effective temperature difference between the two fluids, a logarithmic mean temperature difference (LMTD) is defined as... 

U - overall heat transfer coefficient, W/m2.°C A - heat transfer area, m2 AT m - logarithmic mean temperature difference (LMTD), °C... 

Equation (11.15) defines the logarithmic mean temperature difference (LMTD). It is of the same form as that of Eq. (10.15) for the logarithmic mean radius of a thick-walled tube. When AT and A7 are nearly equal, their arithmetic average can be used for AT within the same limits of accuracy given for Eq. 

Logarithmic mean temperature difference (LMTD) is described on pp. 126-128 of reference 57. It corrects for the curvature of the temperature lines from beginning to end of the heat process whether over time as in batch furnaces or over distance in continuous furnaces. A rough method uses a rule that estimates the mean receiver (load surface) temperature will be the initial load temperature plus of the receiver load surface temperature rise, Trf — Tri, or in Example 3.6, LMTD = 100 + ( )(1050 — 100) = 733°F. 

Ti, 11 supply ternperamre of hot and cold streams, F 72, 2 target temperature of hot and cold streams, °F AT i hot end temperature approach, °F AT 2 cold end temperature approach, °F AT ijn logarithmic mean temperature difference (LMTD), °F u shell side cross-flow velocity or tube velocity, ft/h U overall heat transfer coefficient, Btu/(ft °F h)... 

The variable U, A, and 0 represent the overall heat transfer coefficient, the area of the heat exchange, and the temperature difference between the polymer and water streams at different points. The logarithmic-mean-temperature difference (LMTD) is defined in the second part of equation (3). The primary modeling effort was to use this equation to calculate the temperature difference at point 1 since all other variables were known. Unfortunately, this equation has a discontinuity when the temperature difference at points 1 and 2 are equal. This discontinuity makes simulation difficult since it separates the feasible space for the temperature difference into two regions. Equation (3) can be written to avoid this discontinuity. 

The LMTD, ie, logarithmic mean temperature difference, is an effective overall temperature difference between the two fluids for heat transfer and is a function of the terminal temperature differences at both ends of the heat exchanger. 

GTD = Greater Terminal Temperature Difference, °F LTD = Lesser Terminal Temperature Difference, °F LMTD = Logarithmic Mean Temperature Difference, °F = Tj = Inlet temperature of hot fluid, °F Tj = Outlet temperature of hot fluid, °F tj = Inlet temperature of cold fluid, °F q = Outlet temperature of cold fluid, °F... 

Because of the strong variations of the heat capacity and therefore of the local heat transfer coefficient at a pseudocritical point, the LMTD (logarithmic mean temperature difference) cannot be used for the evaluation of all of our measurements. 

Obtain a relation for the logarithmic mean temperature difference for use in the LMTD melhfld, and modify it (or different types of heat exchangers using the correction factor,... 

If one of the fluids is at constant temperature, as in a condenser, no difference exists among countercurrent flow, parallel flow, or multipass flow, and Eq. (11.15) applies to all of them. In countercurrent flow, AT2, the warm-end approach, may be less than ATj, the cold-end approach. In this case, for convenience and to eliminate negative numbers and logarithms, the subscripts in Eq. (11.15) may be interchanged. The LMTD is not always the correct mean temperature difference to use. It should not be used when U changes appreciably or when AT is not a linear function of q. As an example, consider an exchanger used to cool and condense a superheated vapor, with the temperature diagram shown in Fig. 11.6. 

LMTD logarithmic time mean temperature difference, °F M, m mass flow rate for hot and cold streams, Ib/h Mb number of baffles p tube pitch, ft AF pressure drop, psia Q heat duty, MMBtu/h... 

---