Basic Transport Equations in Ascending Equiangular Spiral Polar Coordinates

Abstract

Basic transport equations have been expressed in a coordinate system suitable for the analytical study of momentum, heat, and mass transport processes in ascending equinagular spiral tube coils. The chosen coordinate system for the representation of these equations is orthogonal curvilinear possessing proper transformation to the rectangular Cartesian coordinate system. Various tensorial quantities appearing in the tensorial form of the general basic transport equations have been obtained in expanded form in the chosen curvilinear coordinate system. Substitution of these quantities, readily expands all the basic transport equations in their various forms. Illustration has been made for the equation of continuity, the general equation of motion, the Navier-Stokes equation, the equation of energy, and the equation of mass transport. The resulting equations are in forms suitable for analytical and numerical solution.