The solution of boundary value problems in diffusive heat and mass transfer with convection: Functional analytic methods

An entirely analytical solution to the Graetz problem with a variety of wall boundary conditions was formulated based on a self-adjoint formalism resulting from a decomposition of the convective diffusion equation into a pair of first order partial differential equations. Physically, the decomposition views the convective diffusion process as a pair of stipulations on how the temperature (or concentration) and the axial energy (or mass) flow through a partial tube cross section vary with radial and axial distances. The solutions obtained are simple, and readily computed. A variety of computational results are also discussed physically.