A synthetic layout optimization of discrete heat sources flush mounted on a laminar flow cooled flat plate based on the constructal law

A synthetic optimization is presented for the Pareto layouts of discrete heat sources (with uniform heat flux) flush mounted on a flat plate over which laminar flow serves for cooling purpose. The peak temperatures and the flow drag loss are minimizing simultaneously provided that the total heat dissipation rate and the plate length are held constant. The impact of the manufacturing limit, i.e. the minimum length of the heated or the adiabatic patch, on the optimum layout is discussed. The results in general comply with analytical deduction based on the constructal theory. However in a finite length scenario, geometric constraints on the adiabatic spacing differ from that fits the situation in which maximum heat transfer performance alone is to be achieved.