Flow and heat transfer performance of asymmetric fractal tree network in fractal porous media

Abstract

This study aims to investigate the fluid transport and heat transfer characteristics in fractal porous media, introduce asymmetric factors to derive a generalized optimization principle for asymmetric branching flow and heat transfer, and obtain the optimal radius ratio for the superior flow resistance/heat resistance model; and the accurate models of permeability and thermal conductivity of asymmetric tree-fractal networks are developed and validated against the traditional Murray's law and symmetric tree-fractal network models. The results show that (a) the symmetric case can be regarded as a special case of the asymmetric fractal network model, and Murray's law is correct only for the symmetric bifurcation (flow percentage Ψi = 0.5), and the errors predicted by Murray's law for the asymmetric case with a flow percentage of 10% (Ψi = 0.1, n = 1) are 23.5% and 33.1% with respect to the optimal radius ratio of flow and heat transfer, respectively. (b) The symmetric case has the largest flow resistance and the smallest thermal resistance. The asymmetric length factor and radius ratio have significant effects on the dimensionless flow resistance/thermal resistance of the asymmetric fractal network, and there is a critical radius ratio (βm = 0.84), where a larger asymmetric length factor is detrimental to the flow of the tree-like branching network when β < βm, while the opposite effect is observed when β > βm. (c) The asymmetric radius factor affects the optimal radius ratio for thermal conductivity, but does not change the maximum value of thermal conductivity. (d) The pressure gradient and heat transfer coefficient in the fractal microchannel are related to the variation of the volume flow rate and the increase in the heat flux will weaken heat transfer.