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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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 derivxtion and LMTD holds, but with a correction factor. For a given heat exchanger with constant area and heat transfer coefficient, the larger the LMTD, the dwrivation heat is transferred. Use the fact that the heat exchanger area Ar is the pipe length B – A multiplied by the interpipe distance D:.
Assume heat transfer  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.
The use of the LMTD arises straightforwardly from the analysis of a heat exchanger with constant flow rate and fluid thermal properties. 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: 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 added to Eq. The LMTD is a logarithmic average of the temperature difference between the hot and cold feeds at each end of the double pipe exchanger.
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.
A correction factor is also required for other more complex geometries, such as a shell and tube exchanger with baffles.
Logarithmic mean temperature difference – Wikipedia
Derive the expression for log mean temperature difference LMTD in parallel flow heat exchanger. 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.
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. 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.
Is the log mean temperature difference, which is the suitable form of the average temperature difference for use in the analysis of heat exchangers.
Logarithmic mean temperature difference
The total exchanged energy is found by integrating the local heat transfer q from A to B:. 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. Views Read Edit View history.
From Wikipedia, the free encyclopedia. Note that estimating the heat transfer coefficient may be quite complicated. The heat that leaves the fluids causes a temperature gradient according to Fourier’s law:. Retrieved from ” https: Derivattion our mobile app and study on-the-go.
LMTD -Counter Flow Heat Exchanger – ME Subjects – Concepts Simplified
Variation of the fluid temperatures in a omtd double-pipe heat exchanger. Taking values of mCp from above equation and substituting in the integrating solution and solving it. 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.
Summed together, this becomes. With this definition, the LMTD can be used derivaton find the exchanged heat in a heat exchanger:.