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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 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.
LMTD is just the mean temperature difference (ie, just an arithmetic mean), it just turns out the arithmetic mean using infinitesimal steps has a log in it (see the derivation section)! Calling it a logarithmic mean just confuses the issue and makes it appear more abstract than it actually is. 'F' is a 'correction factor'.
The number of transfer units (NTU) method is used to calculate the rate of heat transfer in heat exchangers (especially parallel flow, counter current, and cross-flow exchangers) when there is insufficient information to calculate the log mean temperature difference (LMTD). Alternatively, this method is useful for determining the expected heat ...
with a corresponding factor graph shown on the right. Observe that the factor graph has a cycle. If we merge (,) (,) into a single factor, the resulting factor graph will be a tree. This is an important distinction, as message passing algorithms are usually exact for trees, but only approximate for graphs with cycles.
This graph is called the "Van 't Hoff plot" and is widely used to estimate the enthalpy and entropy of a chemical reaction. From this plot, − Δ r H / R is the slope, and Δ r S / R is the intercept of the linear fit.
Below is a graph fragment of an example LDPC code using Forney's factor graph notation. In this graph, n variable nodes in the top of the graph are connected to (n−k) constraint nodes in the bottom of the graph. This is a popular way of graphically representing an (n, k) LDPC code.
That is, observed temperatures above 60 °F (or the base temperature used) typically correlate with a correction factor below "1", while temperatures below 60 °F correlate with a factor above "1". This concept lies in the basis for the kinetic theory of matter and thermal expansion of matter , which states as the temperature of a substance ...
where J is the emission current density, T is the temperature of the metal, W is the work function of the metal, k is the Boltzmann constant, q e is the Elementary charge, ε 0 is the vacuum permittivity, and A G is the product of a universal constant A 0 multiplied by a material-specific correction factor λ R which is typically of order 0.5.