One-dimensional thermal-hydraulic modeling of manifold microchannel heat sinks

Abstract

A one-dimensional model has been proposed and validated to accurately predict the thermal performance and the flow non-uniformity of the manifold microchannel heat sinks. To this end, one-dimensional governing equations are derived from the integral relations of momentum and energy over appropriately-defined two separate control volumes. Specifically, a control volume for the momentum balance is defined in the fluid region, including a dividing flow junction where the main fluid stream branches off from the manifold to the microchannels. A control volume for the energy balance in the solid region is defined so that it incorporates an individual microchannel and its solid substrate. All the friction factors, minor loss coefficients, and heat transfer coefficient in the one-dimensional governing equations are analytically determined without introducing any fitting parameters. By solving the derived one-dimensional governing equations, the flow distribution among the microchannels and the temperature distribution within the solid substrate are estimated. In order to verify the proposed model, a series of 3-D numerical simulation is conducted over a wide range of geometric parameters and operating conditions. This range includes the channel aspect ratio (AR) from 3 to 15, the Reynolds number at the manifold inlet from 560 to 3190, the dimensionless hydraulic flow length from 0.012 to 0.123, and the dimensionless thermal flow length from 0.002 to 0.023. It is shown that the model provides an accurate prediction of the thermal performance and the flow non-uniformity of MMC heat sinks: the total thermal resistance and the coefficient of variation (CV) of the flow distribution among the microchannels are estimated within the root mean square percentage error (RMSPE) of 6% and 23% for 51 data points. A useful design guideline for the uniform flow and temperature distribution within a MMC heat sink is recommended based on a proposed explicit correlation for predicting the flow non-uniformity derived from the developed model: the magnitude of the dynamic pressure at the manifold inlet should be kept smaller than the channel pressure drop. Consequently, this study emphasizes that the non-uniform flow distribution among the microchannels should be taken into account for accurately predicting the thermal performance of MMC heat sinks. By accounting for the non-uniformity in the flow distribution, the significant improvement is made over the earlier model with an error reduction of 81%.