Unidirectional transport in cylindrical coordinates requires reformulating conservation laws to account for varying surface areas and non-orthogonal basis vectors distinct from Cartesian systems. The governing equations introduce metric-dependent terms, such as the radial area scaling factor $1/r$, which necessitates using similarity solutions specifically for line sources (infinitesimally thin wires) where boundary conditions are defined by total flux rather than fixed temperature due to zero cross-sectional area at the source centerline. This theoretical framework applies fundamentally to transport phenomena in axisymmetric geometries, distinguishing between conductive/convective fields that admit logarithmic profiles and viscous velocity fields which require additional angular acceleration terms within the vector analysis formalism of curvilinear coordinates.
Unidirectional transport in cylindrical coordinates requires reformulating conservation laws to account for varying surface areas and non-orthogonal basis vectors distinct from Cartesian systems. The…