Transfer in solids featuring channel flows

We investigate the transfer properties of idealised porous materials comprising a diffusive solid pervaded by an array of channels. Using a tracer method, we study how a liquid flowing through these channels may reduce the cooling time of the solid. Accordingly, we define an effective transfer efficiency, which we systematically measure in systems of differing diffusivities, channel radii, lengths and spacings, average flow velocities and flow fields -namely plugged and Hagen-Poiseuille flows. We show that the transfer efficiency scales with a key dimensionless number involving the Péclet number and the channel to solid volume fraction. This scaling exhibits three regimes. Based on the analysis of the advection and diffusion processes in the systems, we introduce a semi-empirical model that captures the entire range of results.