An investigation of multi-layer mini-channel heat sinks with channel geometric scale variation suggested by constructal scaling principles

In previous work, we have shown that in single phase flow, stacked multi-layer liquid cooled heat sinks with square or circular channels have advantages over traditional single layer designs with high aspect ratio channels. In particular, it has been found that the thermal performance per unit pressure drop, as characterized by cost effectiveness metric, can be superior when properly optimized. The primary benefits seem to be increased surface area per unit volume available for convective cooling and increased flow area without sacrificing heat conduction paths to the coolant channel surfaces. The principle drawback of stacked multi-layer heat sinks is the difficulty in conducting heat through the metal matrix to the coolant channels farthest from the surface where heat is applied. In previous work we used validated twoequation porous media formulations to model the behavior of these “deterministic” porous heat sinks with good success. Porous media formulations reduce the geometric complexity of the problem to two parameters, namely porosity and pore diameter. With this approach, it was shown that geometric scale variation, in which either the characteristic pore diameter of the channels in each layer or the layer porosity was allowed to vary from layer to layer, could result in lower thermal resistance and lower pressure drop, compared to heat sinks in which the pore diameter and porosity were uniform. Furthermore, the behavior of pore-diameter scaled compared to porosity-scaled heat sinks was quite distinct. In the present study, we examine the behavior of deterministic stacked mini-channel heat sinks with parallel channels of square cross section, where the porosity is varied from layer to layer, but the channel diameter is fixed. The scaling rules, developed in the porous media equivalent models, are based on biologically inspired constructal principles. Such scaling principles have lead to superior optimal designs in a number of engineering applications. Experimentally validated conjugate CFD simulations were used to characterize the heat sinks. It was found that when the porosity is allowed to increase away from the surface onto which heat is applied, the increased mass flow and advection counteracts the cumulative conduction resistance thereby producing a more isothermal heat sink and a lower overall thermal resistance. Increasing the porosity away from the heat source also increased the flow area thereby producing lower overall pressure drop, compared to a non-scaled heat sink, in which the first layer of channels is the same in both cases. The volumetric thermal performance of the porosity scaled heat sinks exceeded the performance of non scaled heat sinks over a wide range of porosity scaling ratios and the pressure drop was consistently lower.