Simple methods for convection in porous media: scale analysis and the intersection of asymptotes

摘要

This article outlines the basic rules and promise of two of the simplest methods for solving problems of convection in porous media. First, scale analysis is the method that produces order-of-magnitude results and trends (scaling laws) for concrete and applicable results such as heat transfer rates, flow rates, and time intervals. Scale analysis also reveals the correct dimensionless form in which to present more exact results produced by more complicated methods. Second, the intersection of asymptotes method identifies the correct flow configuration (e.g. Benard convection in a porous medium) by intersecting the two extremes in which the flow may exist: the many cells limit, and the few plumes limit. Every important feature of the flow and its transport characteristics is found at the intersection, i.e. at the point where the two extremes compete and find themselves in balance. The intersection is also the flow configuration that minimizes the global resistance to heat transfer through the system. This is an example of the constructal principle of deducing flow patterns by optimizing the flow geometry for minimal global resistance. The article stresses the importance of trying the simplest method first, and the researcher's freedom to choose the appropriate problem solving method.