  The numerical simulation of fluid flow through a complex geometry with heat
transfer is of strong interest for many applications, such as oil-filled power
transformers. A fundamental challenge here is that high resolution is necessary
to resolve the fluid flow phenomena, but this makes simulation of the full
geometry very expensive in terms of computational power. In this work, we
develop a simulation methodology that combines a porous-medium approach for
simulating some regions of the domain, coupled with fully resolved simulations
in those regions which are deemed most interesting to study in detail. As one
does not resolve flow features like thermal boundary layers in the regions
modeled with the porous approach, the resolution in these parts can be orders
of magnitude coarser. This multiscale approach is validated against the use of
fully resolved simulations in the whole domain, as well as against analytical
solutions to the extended Graetz problem. We then apply the approach to the
study of oil flow and heat transfer in large electric power transformers and
demonstrate a significant reduction in computational cost compared to a fully
resolved approach.
