Double-diffusion Models from a Highly-heterogeneous Medium

A distributed microstructure model is obtained by homogenization from an exact micro-model with continuous temperature and flux for heat diffusion through a periodically distributed highly-heterogeneous medium. This composite medium consists of two flow regions separated by a third region which forms the doubly-porous matrix structure. The homogenized system recognizes the multiple scale processes and the microscale geometry of the local structure, and it quantifies the distributed heat exchange across the internal boundaries. The classical double-diffusion models of Rubinstein (1948) and Barenblatt (1960) are obtained in non-isotropic form for the special case of quasi-static coupling in this homogenized system.