Fluid Mechanics for Chemical Engineers: with Microfluidics, CFD, and COMSOL Multiphysics 5

Appendix C. Some Vector and Tensor Operations

TABLES 5.2–5.5 gave details of the most frequently used vector operations (gradient and Laplacian of a scalar, divergence and curl of a vector) in rectangular, cylindrical, and spherical coordinates. Here, we give a few more definitions for rectangular Cartesian coordinates, sufficient for the needs of this book.¹

¹ The reader who needs to learn more about vector and tensor operations, including those in cylindrical and spherical coordinate systems, is referred to Appendix A of the excellent text: R.B. Bird, W.E. Stewart, and E.N. Lightfoot, Transport Phenomena, 2nd ed., Wiley & Sons, New York (2002).

Dyadic Product of Two Vectors

The dyadic product uv of two vectors u and v is a tensor, such that ...