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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From Wikipedia, the free encyclopedia. Note that estimating the heat transfer coefficient may be drrivation complicated. Derive the expression for log mean temperature difference LMTD in parallel flow heat exchanger. Variation of the fluid temperatures in a parallel-flow double-pipe heat exchanger.

Download our mobile app and study on-the-go. 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. 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.

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:. Summed together, this becomes.

The temperature change of the hot fluid is a negative quantity, and so a negativesign is added to Eq. Taking values of mCp from above equation and substituting in the integrating solution and solving it. Where Derrivation 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.

The total exchanged energy is found by integrating the local heat transfer q from A to B:. For a given heat exchanger with constant area and heat transfer coefficient, the larger the LMTD, the more heat is transferred.

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

This page was last edited on 23 Decemberat The rate of heat transfer in the differential section of the heat exchanger can also be expressed as. The LMTD is a logarithmic average of the temperature difference between the hot and cold feeds at each end of the double pipe exchanger.

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: 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.

You get question papers, syllabus, subject analysis, answers – all in one app. The use of the LMTD arises straightforwardly from the analysis of a heat exchanger with constant flow rate and fluid thermal properties. Engineering in your pocket Download our mobile app and study on-the-go. 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.

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

## Derivation of Log Mean Temperature Difference (Heat Exchanger

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.

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. Is the log mean temperature difference, which is the suitable form of the average temperature lmmtd for use in the analysis of heat exchangers.

Retrieved from ” https: The heat that leaves the fluids causes a temperature gradient according to Fourier’s law:. A correction factor is also required for other more complex mltd, such as a shell and tube exchanger with baffles. With this definition, the Lmtf can be used to find the exchanged heat in a heat exchanger:. Views Read Edit View history.