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The LMTD is a steady-state concept, and cannot be used in dynamic analyses. In particular, if the LMTD were to be applied on a transient in which, for a brief time, the temperature difference had different signs on the two sides of the exchanger, the argument to the logarithm function would be negative, which is not allowable.
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 ...
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 ...
Graph of 2 dimensional plot. In addition to the east (E) and west (W) neighbors, a general grid node P, now also has north (N) and south (S) neighbors. The same notation is used here for all faces and cell dimensions as in one dimensional analysis. When the above equation is formally integrated over the Control volume, we obtain
Equation-free coarse time-stepper applied to the illustrative example differential equation system using = and () =. The solution of the differential equation rapidly moves to the slow manifold for any initial data. The coarse time-stepper solution would agree better with the full solution when the 100 factor is increased.
This equation permits the prediction of an unknown transfer coefficient when one of the other coefficients is known. The analogy is valid for fully developed turbulent flow in conduits with Re > 10000, 0.7 < Pr < 160, and tubes where L/d > 60 (the same constraints as the Sieder–Tate correlation). The wider range of data can be correlated by ...
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.
A more accurate correction factor can be obtained using Knudsen correction. When using nitrogen gas for core plug measurements, the Klinkenberg correction is usually necessary due to the so-called Klinkenberg gas slippage effect. This takes place when the pore space approaches the mean free path of the gas