Curvilinear coordinates and physical components: An application to the problem of viscous flow and heat transfer in smoothly curved ducts

Expressions are derived for the gradient, divergence, Laplacian, curl, and material time derivative in terms of general curvilinear coordinates using physical components of all vector quantities. The results are conveniently expressed in terms of two new coefficients, involving physical and reciprocal base vectors. An application to the problem of viscous flow and heat transfer in arbitrarily smoothly curved ducts is presented. In particular, helical ducts are considered.