Hybrid solution for transient internal convection with axial diffusion: Integral transforms and local instantaneous filtering

This paper seeks to analyze transient convection‐diffusion by employing the generalized integral transform technique (GITT) combined with an arbitrary transient filtering solution, aimed at enhancing the convergence behavior of the associated eigenfunction expansions. The idea is to consider analytical approximations of the original problem as filtering solutions, defined within specific ranges of the time variable, which act diminishing the importance of the source terms in the original formulation and yielding a filtered problem for which the integral transformation procedure results in faster converging eigenfunction expansions. An analytical local instantaneous filtering is then more closely considered to offer a hybrid numerical‐analytical solution scheme for linear or nonlinear convection‐diffusion problems.

The approach is illustrated for a test‐case related to transient laminar convection within a parallel‐plates channel with axial diffusion effects.

The developing thermal problem is solved for the fully developed flow situation and a step change in inlet temperature. An analysis is performed on the variation of Peclet number, so as to investigate the importance of the axial heat or mass diffusion on convergence rates.

This paper succeeds in analyzing transient convection‐diffusion via GITT, combined with an arbitrary transient filtering solution, aimed at enhancing the convergence behaviour of the associated eigenfunction expansions.