Modeling and Inverse Design of Convective Heat Transfer in a Grooved Channel Using Proper Orthogonal Decomposition

Abstract

In this study we show that the POD can be used as a useful tool to solve inverse design problems in thermo-fluids. In this respect, we consider a forced convection problem of air flow in a grooved channel with periodically mounted constant heat-flux heat sources. It represents a cooling problem in electronic equipments where the coolant is air. The cooling of electronic equipments with constant periodic heat sources is an important problem in the industry such that the maximum operating temperature must be kept below a value specified by the manufacturer. Geometric design in conjunction with the improved convective heat transfer characteristics is important to achieve an effective cooling. We obtain a model based on the proper orthogonal decomposition for the convection optimization problem such that for a given channel geometry and heat flux on the chip surface, we search for the minimum Reynolds number (i.e., inlet flow speed) for a specified maximum surface temperature. For a given geometry (l = 3.0 cm and h = 2.3 cm), we obtain a proper orthogonal decomposition (POD) model for the flow and heat transfer for Reynolds number in the range 1 and 230. It is shown that the POD model can accurately predict the flow and temperature field for off-design conditions and can be used effectively for inverse design problems.