Geometrical Parameterization and MultiObjective Shape Optimization of Convective Periodic Channels

In this article we describe a general procedure for the geometric parameterization and multiobjective shape optimization of periodic wavy channels, representative of the repeating module of an ample variety of heat exchangers. The two objectives considered are the maximization of heat transfer rate and the minimization of friction factor. Since there is no single optimum to be found, we use a multiobjective genetic algorithm and the so-called Pareto dominance concept. The optimization of the two-dimensional periodic channel is obtained, by means of an unstructured finite-element solver, for a fluid of Prandtl number Pr = 0.7, assuming fully developed velocity and temperature fields, and steady laminar conditions. The geometry of the channel is parameterized either by means of simple linear-piecewise profiles, or by nonuniform rational B-splines, and in the latter case their control points represent the design variables. The results obtained are very encouraging, and the procedure described can be applied, in principle, to even more complex problems.