Conceptual

Mass and Energy Conservation in Cartesian Coordinates using Shell Balance Method

The core principle is the derivation and application of general differential conservation equations for mass and energy within Cartesian coordinate systems using a shell balance method. This theory formally defines the accumulation, convective transport, diffusive flux (via Fick's law), and source/sink terms to establish a unified framework describing unidirectional or multi-dimensional transport phenomena in fluid systems belonging to chemical engineering and transport processes. The concept relates its parent discipline by providing closed-form partial differential equations that govern field variables like concentration and temperature, requiring specific initial conditions and boundary conditions for solution due to their first-order time dependence and second-order spatial derivatives.