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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Logarithmic mean temperature difference ： ウィキペディア英語版 Logarithmic mean temperature difference 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 LMTD is a logarithmic average of the temperature difference between the hot and cold feeds at each end of the double pipe exchanger. The larger the LMTD, the more heat is transferred. The use of the LMTD arises straightforwardly from the analysis of a heat exchanger with constant flow rate and fluid thermal properties. == Definition == 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: :$LMTD$ =\frac \right ) } =\frac where ''ΔTA'' is the temperature difference between the two streams at end ''A'', and ''ΔTB'' is the temperature difference between the two streams at end ''B''. With this definition, the LMTD can be used to find the exchanged heat in a heat exchanger: :$Q\; =\; U\; \backslash times\; Ar\; \backslash times\; LMTD$ Where ''Q'' is the exchanged heat duty (in watts), ''U'' 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. ==Derivation== Assume heat transfer is occurring in a heat exchanger along an axis ''z'', from generic coordinate ''A'' to ''B'', between two fluids, identified as ''1'' and ''2'', whose temperatures along ''z'' are T1(z) and T2(z). The local exchanged heat flux at ''z'' is proportional to the temperature difference: :$q(z)\; =\; U\; (T\_2(z)-T\_1(z))/D\; =\; U\; (\backslash Delta\backslash ;T(z))/D,$ where ''D'' is the distance between the two fluids. The heat that leaves the fluids causes a temperature gradient according to Fourier's law: ::$\backslash frac=k\_a\; (T\_1(z)-T\_2(z))=-k\_a\backslash ,\backslash Delta\; T(z)$ ::$\backslash frac=k\_b\; (T\_2(z)-T\_1(z))=k\_b\backslash ,\backslash Delta\; T(z)$ Summed together, this becomes :$\backslash frac=\backslash frac=\backslash frac-\backslash frac=K\backslash Delta\; T(z)$ where ''K=ka+kb''. The total exchanged energy is found by integrating the local heat transfer ''q'' from ''A'' to ''B'': :$Q\; =\; \backslash int^\_\; q(z)\; dz\; =\; \backslash frac\; \backslash int^\_\; \backslash Delta\; T(z)\; dz\; =\; \backslash frac\; \backslash int^\_\; \backslash Delta\; T\; \backslash ,dz$ Use the fact that the heat exchanger area ''Ar'' is the pipe length ''A''-''B'' multiplied by the interpipe distance ''D'': :$Q\; =\; \backslash frac\; \backslash int^\_\; \backslash Delta\; T\; \backslash ,dz\; =\; \backslash frac\; \backslash Delta\; T\; \backslash ,dz\}\; \backslash ,dz\}$ In both integrals, make a change of variables from ''z'' to ''Δ T'': :$Q\; =\; \backslash frac\; \backslash Delta\; T\; \backslash frac\backslash ,d(\backslash Delta\; T)\}\; \backslash frac\backslash ,d(\backslash Delta\; T)\}$ With the relation for ''Δ T'' found above, this becomes :$Q\; =\; \backslash frac\; \backslash frac\backslash ,d(\backslash Delta\; T)\}\; \backslash frac\backslash ,d(\backslash Delta\; T)\}$ Integration is at this point trivial, and finally gives: :$Q\; =\; U\; \backslash times\; Ar\; \backslash times\; \backslash frac$, from which the definition of LMTD follows. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Logarithmic mean temperature difference」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.