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This note presents the results of a study of a simple model of an air-cooled electronic device mounted on a circuit board. The model includes a flush-mounted heater to represent the electronic device, a two-layer substrate to represent the circuit board, and a steady shear flow to represent the cooling fluid.
Ortega provides a good review of the literature and a comprehensive introduction to conjugate methods applied to electronic cooling, emphasizing simple shear flows and single-layer substrates to illustrate basic principles. Ortega also describes two-layer effects by including infrared thermographs of a convectively cooled glass/epoxy circuit board with copper traces, which produce significant anisotropy, with larger in-plane relative to out-ofplane conductivity in the circuit board.
There have been few conjugate studies with multiple conduction layers. Zebib and Wo simulated a protruding electronic module on a three-layer circuit board, but the geometry was fixed and only three fluid velocities were used. Gorobets analyzed a fin with a low-conductivity coating to simulate the effects of fin fouling. Chen et al. developed a solution that included solid, liquid, and gas phases to simulate laminar condensation on a fin. In a series of papers Lee and co-workers (Palisoc and Lee, Lee et al.) studied several different substrates with up to five layers, but these studies approximated the convective cooling by a spatially-uniform heat transfer coefficient.
This note builds upon the work of one of us (Cole) for a single-layer substrate, in which results were presented for various values of the dimensionless substrate thickness and the conjugate Peclet number, (kf /ks)Pe1/3. The present study adds a second layer to the substrate described by a single additional parameter that combines the thickness and conductivity of the added layer.