Conjugate flows and forces

Equation (3.141) shows that results from a sum of the products of conjugate flows and forces... 

Using a dissipation function or entropy production equation, the conjugate flows and forces are identified and used in the phenomenological equations for simultaneous heat and mass transfer. Consider the heat and diffusion flows in a fluid at mechanical equilibrium not undergoing a chemical reaction. The dissipation function for such a system is... 

For identifying conjugate flows and forces, we may use the dissipation function per unit area of membrane. A representative dissipation function is... 

Therefore, Jv and AP and Jd and All are the pairs of conjugate flows and forces. If the solution is sufficiently dilute, then Jv JWVW. With the identified flows and forces, the linear phenomenological equations are... 

As Eq. (10.84) is an appropriately derived dissipation function consisting of the conjugate flows and forces, the Onsager s reciprocal rules states that /.( = LJt. 

The non-equilibrium thermodynamic approach to models of epithehal transport begins with the identification of a system of relevant fluxes, J, and conjugate driving forces, A i [19]. With this system the energy dissipation of the model, 4>, may be expressed as a sum of the products of conjugate flows and forces... 

The matrix of phenomenological coefficients is symmetric provided that the conjugate flows and forces are identified by the entropy production equation or the dissipation function. 

Using a dissipation function or entropy production equation, the conjugate flows and forces are identified and used in the phenomenological equations for simultaneous heat and mass transfer. 

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