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Theorem for the local volume average of a gradient revised

✍ Scribed by Vladimír Veverka

Publisher
Elsevier Science
Year
1981
Tongue
English
Weight
568 KB
Volume
36
Category
Article
ISSN
0009-2509

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✦ Synopsis

The theorem for the local volume average of a gmdient formulated by SIattery[l] is analyzed from the mathematical point of view. It is shown that the expression for the average of a gradient as sum of the gradient of an average and of an interior wall term ("tortuosity") for a porous material is mathematically uncertain. An exact integral formula is derived and an idealization of the problem is suggested. In reasonably selected cases, Slattery's formula can still hold as a DlausibIe aaoroximation. Generally, the resulting differential equations in average quantities have to be applied with caution.

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