Constrained optimal duct shapes for conjugate laminar forced convection

The complex variable boundary element method (CVBEM) is used to analyze conjugate heat transfer in solids with cooling passages of general, convex cross section. The method is well-suited to duct cross sections with high curvature and high aspect ratios because the whole-domain boundary integrals are path independent and analytic. The effects of channel boundary curvature on overall heat transfer are quantified for the first time. Shape-constrained optimal solutions involving fixed pressure drop and fixed pump work are presented. Increased channel boundary curvature is shown to decrease the optimal distance between parallel channels by increasing fin efficiency.