| Summary: | A 3D numerical study is used to analyze the flow topology and performance, in terms of heat transfer efficiency and required pumping power, of heat sink devices with different channel aspect-ratio in the presence of tip-clearance. Seven different channel aspect ratios <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mspace width="-0.166667em"></mspace><mi>R</mi></mrow></semantics></math></inline-formula>, from 0.25 to 1.75, were analyzed. The flow Reynolds numbers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula>, based on the average velocity evaluated in the device channels region, were in the range of 200 to 1000. Two different behaviors of the global Nusselt were obtained depending on the flow Reynolds number: for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mo><</mo><mn>600</mn></mrow></semantics></math></inline-formula>, the heat transfer increased with the channels aspect ratio, e.g., for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mo>=</mo><mn>400</mn></mrow></semantics></math></inline-formula>, the global Nusselt number increased by 14% for configuration <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mspace width="-0.166667em"></mspace><mi>R</mi><mo>=</mo><mn>1.75</mn></mrow></semantics></math></inline-formula> when compared to configuration <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mspace width="-0.166667em"></mspace><mi>R</mi><mo>=</mo><mn>0.25</mn></mrow></semantics></math></inline-formula>. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mo>></mo><mn>600</mn></mrow></semantics></math></inline-formula>, the maximum Nusselt is obtained for the squared-channel configuration, and, for some configurations, flow destabilization to a unsteady regime appeared. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mo>=</mo><mn>700</mn></mrow></semantics></math></inline-formula>, Nusselt number reduced when compared with the squared-channel device, 11% and 2% for configurations with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mspace width="-0.166667em"></mspace><mi>R</mi><mo>=</mo><mn>0.25</mn></mrow></semantics></math></inline-formula> and 1.75, respectively. Dimensionless pressure drop decreased with the aspect ratio for all cases. In the context of micro-devices, where the Reynolds number is small, these results indicate that the use of channels with high aspect-ratios is more beneficial, both in terms of thermal and dynamic efficiency.
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