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Concept# Heat flux

Summary

In physics and engineering, heat flux or thermal flux, sometimes also referred to as heat flux density, heat-flow density or heat flow rate intensity, is a flow of energy per unit area per unit time. Its SI units are watts per square metre (W/m2). It has both a direction and a magnitude, and so it is a vector quantity. To define the heat flux at a certain point in space, one takes the limiting case where the size of the surface becomes infinitesimally small.
Heat flux is often denoted \vec{\phi}_\mathrm{q}, the subscript q specifying heat flux, as opposed to mass or momentum flux. Fourier's law is an important application of these concepts.
Fourier's law
Thermal conduction#Fourier's law
For most solids in usual conditions, heat is transported mainly by conduction and the heat flux is adequately described by Fourier's law.
Fourier's law in one dimension
\phi_\text{q} = -k \frac{\mathrm{d}T(x)}{\mathrm{d}x}
where

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Improving the energy efficiency of cooling systems can contribute to reduce the emission of greenhouse gases. Currently, most microelectronic applications are air-cooled. Switching to two-phase cooling systems would decrease power consumption and allow for the reuse of the extracted heat. For this type of application, multi-microchannel evaporators are thought to be well adapted. However, such devices have not been tested for a wide range of operating conditions, such that their thermal response to the high non-uniform power map typically generated by microelectronics has not been studied. This research project aims at clarifying these gray areas by investigating the behavior of the two-phase flow of different refrigerants in silicon and copper multi-microchannel evaporators under uniform, non-uniform and transient heat fluxes operating conditions. The test elements use as a heat source a pseudo-chip able to mimic the behavior of a CPU. It is formed by 35 independent sub-heaters, each having its own temperature sensor, such that 35 temperature and 35 heat flux measurements can be made simultaneously. Careful measurements of each pressure drop component (inlet, microchannels and outlet) found in the micro-evaporators showed the importance of the inlet and outlet restriction pressure losses. The overall pressure drop levels found in the copper test section were low enough to possibly be driven by a thermosyphon system. The heat transfer coefficients measured for uniform heat flux conditions were very high and typically followed a V-shape curve. The first branch was associated to the slug flow regime and the second to the annular flow regime. By tracking the minimum level of heat transfer, a transition criteria between the regimes was established, which included the effect of heat flux on the transition. Then for each branch, a different prediction method was used to form the first flow pattern-based prediction method for two-phase heat transfer in microchannels. A non-uniform heat flux creates important temperature gradients in the evaporator, such that the data reduction procedure needs to be adapted to include heat spreading within the evaporator. To do so, a robust multi-dimensional thermal conduction scheme was developed. Once these effects were taken into consideration, the local heat transfer coefficients provided by two-phase flow were found to be the same for uniform and non-uniform heat fluxes, allowing the flow pattern-based method to be extended to non-uniform heat flux conditions. Lastly, with proper control of the mass flow, transient heat flux situations were well handled by the micro-evaporators.

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