Unified Parametric Optimization Framework for Microchannel Fin Geometries in High-Power Processor Cooling

This study presents a unified parametric optimization framework for the thermal design of microchannel spreaders used in high-power processor cooling. The fin geometry is expressed in a shape-agnostic parametric form defined by fin thickness, top and bottom gap widths, and channel height, without prescribing a fixed cross-section. This approach accommodates practical fin profiles ranging from rectangular to tapered and V-shaped, allowing continuous geometric optimization within manufacturability and hydraulic limits. A coupled analytical-numerical model integrates conduction through the spreader base, interfacial resistance across the thermal interface material (TIM), and convection within the coolant channels while enforcing a pressure-drop constraint. The optimization uses a deterministic continuation method with smooth sigmoid mappings and penalty functions to maintain constraint satisfaction and stable convergence across the design space. The total thermal resistance (Rtot) is minimized over spreader conductivities ks=400-2200 W m^-1 K^-1 (copper to CVD diamond), inlet fluid velocities Uin=0.5-5.5 m s^-1, maximum pressure drops of 10-50 kPa, and fluid pass counts Np∈{1,2,3}. The resulting maps of optimized fin dimensions as functions of ks provide continuous design charts that clarify how material conductivity, flow rate, and pass configuration collectively determine the geometry, minimizing total thermal resistance, thereby reducing chip temperature rise for a given heat load.