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Current desktop computers typically use fan-heat sinks for cooling the CPU, referred to as active heat sinks. This work seeks to determine the heat rejection limits for such fan-heat sinks, within specific fan and heat sink space limits. A fixed volume, 80 × 60 × 50 mm is chosen as the limiting dimensions, which includes the fan volume. The present work addresses plane fin heat sinks, on which a typical 60 mm fan is mounted. Both duct flow and impinging flow are considered. Analytically based models are used to predict the optimum geometry (minimum convection resistance) for plane fins with duct and impinging flow configurations. Also assessed are the effects of increased fan speed (up to 25%) and heat sink base size (33% increase) on air-cooling limits in duct and impinging flow. Tests on fan-heat sinks are done to validate the predictions. Optimization is also done for an enhanced (offset-strip) fin geometry in duct flow. The plane fin is found to outperform the enhanced geometry.