Generalized Second-Order Macroscopic Transport Equations

A complete set of macroscopic transport equations suitable for application to experiment is obtained from nonequilibrium thermodynamics. Full account is taken of (i) bulk flow, (ii) conservative external fields (gravitational, centrifugal, and electrostatic), (iii) pressure gradients, and (iv) nonconstancy of thermodynamic and transport coefficients. There result 4(v+1) independent partial differential equations for a v-component system. Four of the equations involve only barycentric velocity, external fields, density, viscosity, and pressure. Independent second-order equations are obtained for the temperature distribution and v−1 mass fraction distributions. The remaining 3v equations can be used to calculate the vectorial heat and diffusion fluxes. In order to take account of nonconstancy of viscosities, diffusivities, etc., a Taylor's series expansion in the spatial coordinates is suggested. A perturbation—iteration scheme can then be used to solve the transport equations for the velocities, the fluxes, and the distributions of temperature, pressure, and v−1 mass fractions. The solutions are polynomials in thermodynamic derivatives of the thermodynamic and transport coefficients.