Extension of Material Derivative Concept in Fluid Mechanics

Abstract:

The original definition of material derivative is changing rate relative to the time of a physical quantity which belongs to a fluid particle. But when studying fluid mechanics problems, need in certain cases to calculate the material derivative of some quantities which don’t belong to a fluid particle, such as calculating the material derivative of base vectors of orthogonal curvilinear coordinate system. The original definition of material derivative isn’t suitable for these quantities. Calculating material derivative of these quantities is not clear in concept. To solve this problem, thorough analysis about material derivative was made according to the original definition and calculation formula of material derivative. Results found that the concept of material derivative can be extended and so can apply to any quantities which don’t belong to a fluid particle and are defined in flow fields, including vector or scalar, physical quantities or non physical quantities.

• Periodical: Advanced Materials Research (Volumes 594-597)
• Pages: 2731-2735
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.594-597.2731
• Online since: November 2012
• Authors: Fu Xiang Liu
• Keywords: Extension, Material Derivative, Non Physical Quantity, Physical Quantity, Scalar, Vector

References

[1] Fuxiang Liu: Material Derivative Formulae of Base Vectors and Coordinate Variables and Their Application. China Quality Education Report (In Chinese), Jilin: Jilin Electronic Press (2009.8), P. 377-378

[2] Wangyi Wu: Editor. Fluid Mechanics (In Chinese). First edition. Beijing: Peking University Press (1982.8), P.42,185