This study deals with the geometric optimization of a silicon based micro-channel heat sink using a
combined numerical optimization and constructal theory. The objective is to minimize the wall peak
temperature subject to various constraints. The numerical simulations are carried out with fixed
volumes ranging from 0.7 mm3 to 0.9 mm3 and pressure drop between 10 kPa to 60 kPa. The effect of pressure drop on the optimized aspect ratio, solid volume fraction, hydraulic diameter and the minimized peak temperature are reported. Results also show that as the dimensionless pressure drop increases the maximized global thermal conductance also increases.