Thermodynamic coupling due to thermal diffusion, diffusion-thermo, and ob aliam diffusion effects in boundary layers is considered. Decoupling of the set of conservation equations is achieved by diagonalisation of the phenomenological coefficients matrix. A new Peclet number for coupled transfer is defined in terms of the eigenvalues of the diagonal matrix. The specific and overall degrees of thermodynamic coupling are shown to depend both on the values of the coupling coefficients and on the magnitude and direction of the gradients across the boundary layers. The application of the theory is illustrated for coupled transfer in two-phase particulate systems.
The practical advantages of the present method lie in the possibilities to: (a) employ available solutions for (uncoupled) thermal or diffusion boundary layers to analogous cases of coupled transfer using specific degrees of coupling and the newly defined Peclet number; and (b) to estimate the overall degree of thermodynamic coupling for a given flow regime from a known overall degree of coupling for another regime.
The present method establishes similarity rules for thermodynamic coupling in flow systems which enable one to evaluate the overall degree of thermodynamic coupling for a given system from available data on a different system (e.g., from liquid to gaseous system, or vice versa).