Thermal dead-zones and convective bottlenecks in complex microchannels: Slip-flow analysis by the method of fundamental solutions

Highly non-convex cross-sections in micro-heat exchangers significantly alter local momentum and energy transport. This study presents a completely meshless numerical framework utilizing the Method of Fundamental Solutions (MFS) coupled with exact analytical particular solutions to evaluate thermohydraulic performance in fully developed laminar microchannel flows under velocity slip and temperature jump conditions. By utilizing analytical polynomial particular solutions, the MFS evaluates governing Poisson equations strictly at the boundary, eliminating internal domain discretization and grid-based numerical artifacts. Following rigorous validation against exact analytical solutions ( > 99.9 % accuracy), the framework demonstrates immense computational superiority. For severe non-convex geometries, the MFS achieves near-spectralaccuracy ( < 0.03 % relative error) against an ultra-refined FEM benchmark using only 500 boundary nodes. This effectively bypasses the > 4 million internal degrees of freedom demanded by standard volumetric solvers, yielding a 35-fold CPU acceleration. A comprehensive parametric investigation reveals that while elongated stadium profiles maximize absolute thermohydraulic efficiency, dense micro-fin arrays and aerodynamic trailing edges paradoxically act as thermal dead-zones. Furthermore, 1D perimetral analysis demonstrates that inward-facing indentations create hydrodynamic bottlenecks, inducing pronounced localized peaks in wall slip velocity and advective cooling, dictating the ultimate limits of microfluidic heat dissipation.