Error Propagation Log Mean Temperature
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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 error propagation mean value hot and cold feeds at each end of the double pipe exchanger. error propagation natural log The larger the LMTD, the more heat is transferred. The use of the LMTD arises straightforwardly from the analysis
Error Propagation For Log Function
of a heat exchanger with constant flow rate and fluid thermal properties. Contents 1 Definition 2 Derivation 3 Assumptions and Limitations 4 References 5 External links Definition[edit] We assume that
Error Propagation Logarithm
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: L M T D = Δ T A − Δ T B ln ( Δ T A Δ T B ) = Δ T error propagation average A − Δ T B ln Δ T A − ln Δ T B {\displaystyle LMTD={\frac {\Delta T_{A}-\Delta T_{B}}{\ln \left({\frac {\Delta T_{A}}{\Delta T_{B}}}\right)}}={\frac {\Delta T_{A}-\Delta T_{B}}{\ln \Delta T_{A}-\ln \Delta T_{B}}}} 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 × A r × L M T D {\displaystyle Q=U\times Ar\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 exchang
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