The object of this work is the thermal investigation of a polymeric microchannel heat sink designed for the active cooling of small flat surfaces. Its performance, pressure drop, temperature distribution, and thermal resistance are evaluated. A three-dimensional procedure is developed and applied to a geometrical configuration consisting of a circular microduct (with a gas running through it), embedded in a solid substrate with rectangular cross-section. The conjugate heat transfer problem is solved assuming fully developed laminar flow in forced convection. The bottom side of the heat sink receives a uniform heat flux, while the top side is adiabatic. Considering a gas flow with low Prandtl and Reynolds numbers, the temperature distribution is given by the sum of a linear function (in the stream direction) and a numerical solution obtained in 2-D coordinates resorting to a finite element software, based on the Rayleigh–Ritz–Galerkin method, with user-defined error tolerance. Rarefaction, compressibility and viscous dissipation are neglected, i.e., the Knudsen, Mach and Brinkman numbers are low. The theoretical results are shown in some graphs and compared with experimental data concerning helium and nitrogen flows in Nylon circular microducts. The agreement is quite satisfactory.
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