Validação numérica do descritor invariante do resfriamento conjugado por convecção forçada-condução de aquecedores 3D protuberantes em canais

Abstract

The temperatures of 3D protruding heaters mounted on a conductive substrate in a horizontal rectangular channel in laminar airflow were related to independent power dissipation in each heater by means of a matrix G+ with invariant coefficients. These coefficients, validated numerically in this work, are dimensionless and they were called the conjugate influence coefficients (g+) due to the forced convection-conduction nature of the heaters cooling. The temperature increase of each heater in the channel was quantified so that the contributions due to self-heating and to the power dissipation in the other heaters (both upstream and downstream) were clearly identified. For fixed geometry, fluid and flow rate, substrate and heater conductivities, the conjugate coefficients are invariant with the heat generation rate in the heaters’ array. The results were obtained numerically considering three 3D protruding heaters on a two-dimensional array, using the ANSYS/FluentTM 14.5 software. The conservation equations were solved through a coupled procedure within a single calculation domain comprising the solid and fluid regions, considering steady state flow with constant properties in the laminar regime. Some examples were shown, indicating the effects of the substrate thermal conductivity and the Reynolds number on conjugate influence coefficients.