A heatsink is a hierarchical multilevel device with many parameters required for its description. Volume Averaging theory (VAT) is used to used to rigorously cast the point wise conservation of energy, momentum and mass equations into a form that represents the thermal and hydraulic properties of the micro channel (porous media) morphology and to describe the hierarchical nature of the heatsink. Closure for the upper level is obtained using VAT to describe the lower level and a simple plane fin with inner surface augmentation is chosen to demonstrate the process. The lower level augmentation chosen is an in line array of dimples with two parameters, pitch and diameter, needed for their description, along with a scale roughened surface with either forward or downward scales. The mid-level description requires fin pitch, base and tip thickness, shape, and height and the upper-level requires overall heatsink height, width and length, and baseplate thickness. A common size heatsink (4 inch width and length and 1 inch overall height) with a required heat removal of one kilowatt, an inlet temperature of 20°C, and a maximum allowable center temperature of 65°C is used to demonstrate an approach to heatsink optimization. This is an 8 parameter problem. Significant improvement in performance (heat removal/pumping power) and reduction in thermal resistance are shown to be achievable.

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