Simulation of Three-Dimensional Laminar Flow and Heat Transfer in an Array of Parallel Microchannels

Abstract

Heat transfer and fluid flow are studied numerically for a repeating microchannel array with water as the circulating fluid. Generalized transport equations are discretized and solved in three dimensions for velocities, pressure, and temperature. The SIMPLE algorithm is used to link pressure and velocity fields, and a thermally repeated boundary condition is applied along the repeating direction to model the repeating nature of the geometry. The computational domain includes solid silicon and fluid regions. The fluid region consists of a microchannel with a hydraulic diameter of 85.58μm. Independent parameters that were varied in this study are channel aspect ratio and Reynolds number. The aspect ratios range from 0.10 to 1.0 and Reynolds number ranges from 50 to 400. A constant heat flux of 90 W/cm2 is applied to the northern face of the computational domain, which simulates thermal energy generation from an integrated circuit. A simplified model is validated against analytical fully developed flow results and a grid independence study is performed for the complete model. The numerical results for apparent friction coefficient and convective thermal resistance at the channel inlet and exit for the 0.317 aspect ratio are compared with the experimental data. The numerical results closely match the experimental data. This close matching lends credibility to this method for predicting flows and temperatures of water and the silicon substrate in microchannels. Apparent friction coefficients linearly increase with Reynolds number, which is explained by increased entry length for higher Reynolds number flows. The mean temperature of water in the microchannels also linearly increases with channel length after a short thermal entry region. Inlet and outlet thermal resistance values monotonically decrease with increasing Reynolds number and increase with increasing aspect ratio. Thermal and friction coefficient results for large aspect ratios (1 and 0.75) do not differ significantly, but results for small aspect ratios (0.1 and 0.25) notably differ from results of other aspect ratios.