Transport phenomena in curvilinear coordinate systems rely on establishing differential conservation laws for mass and momentum where bounding surfaces are defined by constant coordinates rather than planes. The specific mechanism involves transforming Cartesian derivatives into cylindrical equivalents, accounting for geometric scaling factors (such as the $1/r$ term) that arise because surface area varies with radial distance while axial symmetry eliminates angular dependence. This theoretical framework enables the derivation of parabolic velocity profiles and temperature distributions in pipes by applying Newton's law of viscosity within a generalized momentum balance equation containing intrinsic pressure gradient driving forces distinct from heat or mass transfer equations.
Transport phenomena in curvilinear coordinate systems rely on establishing differential conservation laws for mass and momentum where bounding surfaces are defined by constant coordinates rather than…