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The macroscopic governing equations of a compressible multicomponents flow with non-uniform viscosity and with mass withdrawal (due to heterogeneous reactions) in a porous medium are developed. The method of volume averaging was used to transform local (or microscopic) governing equations into averaged (or macroscopic) governing equations. The impacts of compressibility, non-uniform viscosity, and mass withdrawal on the form of the averaged equations and on the value of the macroscopic transport coefficients were investigated. The results showed that the averaged mass conservation equation is significantly affected by mass withdrawal when a specific criterion on the size of the domain is respected. The results also showed that the form of the averaged momentum equations is not affected by mass withdrawal, by compressibility effects or by non-uniform viscosity, provided that the Reynolds number at the pore level is small. Nonetheless, the velocity field is affected by the heterogeneous reaction via the averaged mass conservation equation, and also by viscosity variations due to the presence of the volume-averaged viscosity (which value changes with position) in the averaged momentum equations. A new closure variable definition was proposed to formulate the closure problem, which avoided the need to solve an integro-differential equation in the closure problem. This formulation was used to show that the permeability tensor only depends on the geometry of the porous medium. In other words, that tensor is independent on whether the fluid is compressible/incompressible, has uniform/non-uniform viscosities, and whether mass withdrawal due to heterogeneous reactions is present/absent. [ABSTRACT FROM AUTHOR]

A straightforward procedure is developed to determine dissipation fields (e.g., exergy destruction in conduction, pumping power, Joule heating) from the linear boundary conditions applied on their associated linear diffusion problem (e.g., heat conduction, Darcy flow, electrical flow). The mathematical tool proposed in this article takes advantage of the quadratic (nonlinear) behavior that comes with dissipative fields equations. The first objective of this article is to build a mathematical formulation expressing any dissipation field as a combination of fundamental dissipative fields resulting from decomposed boundary conditions, similarly to linear problems where fundamental solutions may be added with the superposition principle. The second objective is to demonstrate the numerical advantage of this formulation when applied to heat transfer and fluid flow optimization problems. Application of the mathematical tool proposed in this article to boundary control problems provided significant computational time reductions. [ABSTRACT FROM AUTHOR]