Microstructure-Induced Finite-Speed Heat Propagation in Fluids Through Porous Media: Analytical Results

Abstract

In nonisothermal setting, microstructural interactions may determine finite-speed heat propagation. We consider such an effect in the dynamics of a viscous incompressible complex fluid (i.e., one with “active” microstructure) through a porous medium. Nonlocal actions and nonlinear damping are considered as determined by the solid–fluid and microstructural interactions. After a choice of constitutive structures and the introduction of a specific truncation of some higher-order terms, we prove existence and uniqueness of global strong solutions to the balance equations. We also analyze pertinent weak solutions.