LMTD

LMTD is acronym of log mean temperature difference that is used to determine the temperature driving force for heat transfer in flow systems, most remarkable in heat exchangers. The LMTD is a logarithmic average of the temperature difference between the hot and cold systems at each end of the exchanger. If the LMTD is larger, then more heat will be transferred.  The use of the LMTD occurs straightforwardly from the analysis of a heat exchanger with regular flow rate and fluid thermal properties.

When a generic heat exchanger has two ends such as hot and cold streams enter or exit on either side, then the LMTD is meant by the logarithmic mean as follows

Where ΔTA is the temperature between the two flows at end A, and ΔTB is the temperature difference between the two flows at end B. this equation is valid for both parallel flow, where the flows enter from the same end, and for counter-current flow, where they enter from different ends. A third type of stream is cross-flow, in which one system, generally the heat sink, has the same nominal temperature at all points on the heat transfer surface. This follows analogous mathematics, in its reliance on the LMTD, excluding from that a correction factor F often requires to be contained in the heat transfer relationship.

And there are times when the four temperatures employed to calculate the LMTD are not on hand, and the NTU method may then be preferable. Once calculated, the LMTD is generally to calculate the heat transfer in an exchanger according to the simple equation:

Q = U*A* LMTD

Here Q is the exchanged heat duty, U is the heat transfer coefficient and A is the exchange area. When estimating the heat transfer coefficient may be difficult process and has to be considered.

Consider heat transfer is taking place in an exchanger along an axis Z, form generic coordinate A to B between fluids identified as 1 and 2, whose temperatures along z are T1(z) and T2(z). The temperature variances are ΔT (A) at point ΔT (B) at point B, having meant ΔT(z)=T2(z)-T1(z).

The direction of fluid does not require to be considered that is also essential which flow is the hot and which is the cold one as a change of role will be represented by negative numbers. And because LMTD is the average temperature variance of the two flows between A and B it is meant by this formula:

Questions:

• Expand LMTD
• What is LMTD?