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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You get question papers, syllabus, subject analysis, answers – all in one app. Retrieved from ” https: 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:.

The temperature change of the hot fluid is a negative quantity, and so a negativesign is lmte to Eq. For a given heat exchanger with constant area and heat transfer coefficient, the larger the LMTD, the more heat is transferred. 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. 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. 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.

Engineering in your pocket Download our mobile app and study on-the-go. Use the fact that the heat exchanger area Ar is the pipe length B – A multiplied by the interpipe distance D:. From Wikipedia, the free encyclopedia. Is the log mean temperature difference, which is the suitable form of the average temperature difference for use in the analysis of heat exchangers. By using this site, you agree to the Terms of Use and Privacy Policy.

## LMTD -Counter Flow Heat Exchanger

Note that estimating the heat transfer coefficient may be quite complicated. 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 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.

Taking values of mCp dedivation above equation and substituting in the integrating solution and solving it.

The LMTD is a logarithmic average of the temperature difference between the hot and cold feeds at each end of the double pipe exchanger. Download our mobile app and study on-the-go. The heat that leaves the fluids causes a temperature gradient according to Fourier’s law:.

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. Views Read Edit View history.

## Derivation of Log Mean Temperature Difference (Heat Exchanger

The rate of heat transfer in the differential section of the heat exchanger can also be expressed as. 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.

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

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

The total exchanged energy is found by integrating the local heat transfer q from A derivatiom B:. With this definition, the Derivatoon can be used to find the exchanged heat in a heat exchanger:.

The temperature change of the hot fluid is a negative quantity, and so a negativesign is added to. Summed together, this becomes. A correction factor is also required for other more complex geometries, such as a shell and tube exchanger with baffles. This page was last edited on 23 Decemberat ltd 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.

The use of the LMTD arises straightforwardly from the analysis of a heat exchanger with constant flow rate and fluid thermal properties.