# LMTD DERIVATION PDF

DERIVATION OF LMTD FOR COUNTER FLOW HEAT EXCHANGER. Assumptions used. 1. U is constant all along the HEX. 2. Steady flow. Brief Derivation of the LMTD. To design or predict the performance of a heat exchanger, the LMTD and the effectiveness-NTU methods are both. Derivation of Log Mean Temperature Difference (LMTD) for Parallel flow heat exchanger.

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Deriavtion logarithmic mean temperature difference also known as log mean temperature derivqtion or simply by its initialism LMTD is used to determine the temperature driving force for heat transfer in flow systems, most notably in heat exchangers. The LMTD is a logarithmic average of the temperature difference between the hot and cold feeds at each end of the double pipe exchanger. For a given heat exchanger with constant area and heat transfer coefficient, the larger the LMTD, the more heat is transferred.

## LMTD -Counter Flow Heat Exchanger

The use of the LMTD arises straightforwardly from the analysis of a heat exchanger with constant flow rate and fluid thermal properties. We assume that a generic heat exchanger has two ends which we call “A” and “B” at which the hot and cold streams enter or exit on either side; then, the LMTD is defined by the logarithmic mean as follows:.

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With this definition, the LMTD can be used to find the exchanged heat derivatikn a heat exchanger:. Where Q is the exchanged heat duty in wattsU is the heat transfer coefficient in watts per kelvin per square meter and Ar is the exchange area. Note that estimating the heat transfer coefficient may be quite complicated.

This holds both for cocurrent flow, where the streams enter from the same end, and for counter-current flow, where they enter from different ends. In a cross-flow, in which one system, usually the heat sink, has the same nominal temperature at all points on the heat transfer surface, a similar relation between exchanged heat and LMTD holds, but with a correction factor. A correction factor is also required for other more complex geometries, such as a shell and tube exchanger with baffles.

Assume heat transfer [1] is occurring in a heat exchanger along an axis zfrom generic coordinate A to Bbetween two fluids, identified as 1 and 2whose temperatures along z are T 1 z and T 2 z.

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The heat that leaves the fluids causes a temperature gradient according to Fourier’s law:. Summed together, this becomes. The total exchanged energy is found by integrating the local heat transfer q from A to B:. Use the fact that the heat exchanger area Ar is the pipe length B – A multiplied by the interpipe distance D:.