# 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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A correction factor is also required for other more complex geometries, such as a shell and tube exchanger with baffles. Engineering in your pocket Download our mobile app and study on-the-go.

### Derivation of Log Mean Temperature Difference (Heat Exchanger

The LMTD is a logarithmic average of the temperature difference between the hot and cold feeds at each end of the double pipe exchanger. The use of the LMTD arises straightforwardly from the analysis of a heat exchanger with constant flow rate and fluid thermal properties.

Summed together, this becomes.

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This page was last edited on 23 Decemberat With this definition, the LMTD can be used to find the exchanged heat in a heat exchanger:. 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.

## Logarithmic mean temperature difference

Taking values of mCp from above equation and substituting in the integrating solution and solving it. The total exchanged energy is found by integrating the local heat transfer q from A to B:. 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:. 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.

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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. The temperature change of the hot fluid is a negative quantity, and so a negativesign is added to.

Is the log mean temperature difference, which is the suitable form of the average temperature difference for use in the analysis of heat exchangers. The logarithmic mean temperature difference also known as log mean temperature difference 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.

Assuming the outer surface of the heat exchanger to be well insulated so that any heat transfer occurs between the two fluids, and disregarding any changes in kinetic and potential energy, an energy balance on each fluid in a differential section of the heat exchanger can be expressed as Fig: From Wikipedia, the free encyclopedia.

Use the fact that the heat exchanger area Ar is the pipe length B – A multiplied by the interpipe distance D:. 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.

From first law of thermodynamicsrequires that the rate of heat transfer from the hot fluid be equal to the rate of heat transfer to the cold one. That is, the rate of heat loss from the hot fluid at any section of a heat exchanger is equal to the rate of heat gain by the cold fluid in that section.

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Retrieved from ” https: Variation of the fluid temperatures in a parallel-flow double-pipe heat exchanger. The temperature change of the hot fluid is a negative quantity, and so a negativesign is added to Eq. lmtv

### Logarithmic mean temperature difference – Wikipedia

By using this site, derivatiin agree to the Terms of Use and Privacy Policy. The rate of heat transfer in the differential section of the heat exchanger can also be expressed as.

Note that estimating the heat transfer coefficient may be quite complicated. For a given heat exchanger with constant area and heat transfer coefficient, the larger the LMTD, the more heat is transferred. Assuming the outer surface of the heat exchanger to be well insulated so that any heat transfer occurs between the two fluids, and disregarding any changes in kinetic and potential energy, an energy balance on each fluid in a differential section of the heat exchanger can be expressed as.

The heat that leaves the fluids causes a temperature gradient according to Fourier’s law:.

Derive the expression for log mean temperature difference LMTD in parallel flow heat exchanger.