The Effects of Geometric Uncertainties on Micro-Channel Heat Transfer—A CFD Study on the Tilted-Cover Problem

The present paper attempts to shed light on issues that so far have been unaddressed in research on micro-channel heat transfer. The first part of the paper summarizes the uncertainty sources likely to be present in micro-channel cooling devices incorporated in the electronic package. The effects of uncertainties on the heat transfer performance of the cooling device are difficult to assess due to the coupling of diverse factors in a narrow physical space. The CFD simulation offers a means to sort out the effects from multiple factors by assuming uncertainties from one of the sources or a set of selected sources into an analytical model.

A model channel is defined to illustrate the application of the CFD-based methodology to situations involving geometric uncertainties. The model has a 20 mm × 20 mm heater plate set in a channel having an adiabatic cover and side-walls and cooled by a dielectric coolant. The tilt of the cover plate is chosen as an uncertainty factor from among all possible factors. CFD simulations were performed for the cases where the nominal channel height was changed from 1 mm to 0.1 mm with a proportionate reduction of the cover tilt from 1° to 0.1°. The results indicate a measure of required stringency in assembling the micro-channel cooling device. Also, a hypothetical experiment is considered where the performance of a channel having an optimum height is compared with that of a non-optimum channel under a given pumping power. Examination of the simulation results revealed that the cover tilts in both channels could blur or amplify the optimality of the channel height to an appreciable extent.