Thermodynamic Analysis of Heat and Mass Transfer Using Entropy Production Formalism

Abstract

The understanding of irreversible phenomena in the world around us is of great importance -- not only for the intrinsic value of such understanding, but also for the industrial applications and technological benefits such an understanding brings with it. The main aim of the current work is to explore such phenomena -- with emphasis on treating simultaneous mass and heat transfer -- by studying the entropy production using mathematical modelling.

A model consisting of two connected subsystems containing a binary ideal gas mixture is developed and studied. In the case of a closed system, a perturbation from the equilibrium state give rise to a manifold of constant entropy given the constraints. In the case of an open system, the steady-state is maintained by external reservoir of thermal and chemical nature. The resulting internal mass and heat transfer between the two subsystems give rise to a manifold of constant entropy production given the constraints. In order to investigate these two situations, a variable step-length predictor-corrector method is developed and employed. Both types of manifolds are successfully traced.

By solving the models, a relationship of seemingly deep nature between the two types of manifolds is observed. It is shown that the projections of both manifolds into suitable coordinates in the Cartesian R^2 plane may be described as generalised ellipses, which opens the possibility of a mapping between the two manifolds. Thus, a possible connection between the deviation from equilibrium entropy on the one hand and the constant entropy production of an open, steady-state system is established.

The results from the current work are not yet conclusive as to whether the correlation between the entropy production manifold and manifold of constant entropy may be employed to predict or describe the general behaviour of irreversible processes occurring. However, the results are seen as a promising, and further investigations are recommended.