| A multi-scale problem of flow and heat transport in porous media is treated in this thesis. First, the problem of flow and heat transfer over a rough surface is treated. Using volume averaging theory, transport models for flow and heat transfer over rough surfaces in porous media are developed in this dissertation. In order to apply the VAT models for flow and heat transfer in porous media, closure schemes for VAT equations are suggested and developed. This part of the hierarchy has separate application to modeling of heat exchange surfaces. Using closed VAT models transport phenomena for flow and heat transfer over rough surfaces is investigated through numerical simulation. Based on the simulation of flow and heat transfer over rough surfaces, heat transfer optimization for enhanced surfaces and three dimensional structures are discussed. An optimization example for pin fin surfaces is studied in this work. This is the smallest scale problem in the porous media network. Based on the study of rough surfaces, the problem of a capillary with a rough inner surface will be solved, as the intermediate scale. Finally, the largest scale problem, a media made up of networks of straight capillaries with inner surface roughness will be treated. |
