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This algorithm solves transient diffusion problems, such as heat transfer and Fickian moisture absorption.
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Algorithm for Transient Diffusion Analysis
This algorithm solves transient diffusion problems, such as heat transfer and
Fickian moisture absorption.
In developing a method, for example, for analyzing transient heat transfer
problems, it is important to reduce the prediction errors as much as possible and
yet allow arbitrary sized time-steps.
As shown by the graph, rather than directly determine the temperature, e.g.,
temperature T3, at the end of a time step Delta T, e.g., 1ST TIME-STEP, as is
done by known methods, the temperature, e.g., T1, is calculated at a time Alpha
Delta T into the time-step Delta T using the well known Crank-Nicolson method.
Then, using that calculated temperature T1, a second temperature T2 at time (2-
Alpha)Delta T is calculated again using the Crank- Nicolson method. These
times are equal amounts tx to the right and left of the actual time step (Delta T).
By averaging these two temperatures T1 and T2, the predicted temperature T3 at
time Delta T is obtained For Alpha = .459, it can be shown that the maximum
error is reduced to + or - 6.2%.
This algorithm allows stable and rapid solution of transient diffusion equations
having small geometries with no restriction on the size of the time step. It can be
implemented, for example, in APL or other comparative computer logic.
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