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The numerical simulation of fluid flow through a complex geometry with heattransfer is of strong interest for many applications, such as oil-filled powertransformers. A fundamental challenge here is that high resolution is necessaryto resolve the fluid flow phenomena, but this makes simulation of the fullgeometry very expensive in terms of computational power. In this work, wedevelop a simulation methodology that combines a porous-medium approach forsimulating some regions of the domain, coupled with fully resolved simulationsin those regions which are deemed most interesting to study in detail. As onedoes not resolve flow features like thermal boundary layers in the regionsmodeled with the porous approach, the resolution in these parts can be ordersof magnitude coarser. This multiscale approach is validated against the use offully resolved simulations in the whole domain, as well as against analyticalsolutions to the extended Graetz problem. We then apply the approach to thestudy of oil flow and heat transfer in large electric power transformers anddemonstrate a significant reduction in computational cost compared to a fullyresolved approach.

A multiscale porous--resolved methodology for efficient simulation of  heat and fluid transport in complex geometries, with application to electric  power transformers