Multi-objective optimization for problems involving convective heat transfer

In this chapter, focused on Computational Fluid Dynamics (CFD)based optimization for problems involving convective heat transfer, we present our approach for the multi-objective shape optimization of periodic wavy channels, representative of the repeating module of many heat exchangers. The first problem is of fundamental nature and considers the geometric parametrization and shape optimization of two- and three-dimensional periodic wavy channels. The geometry of the channel is parametrized either by means of linear-piecewise profiles or by non-uniform rational B-splines. The second case, of industrial interest, illustrates the development and application of an automatic method for the design of gas turbine recuperators. After a literature review of shape optimization in heat transfer, we describe in detail both aforementioned problems in terms of physical assumptions and mathematical formulation. In the numerical methods section we indicate the CFD codes used and describe the implementation of periodic boundary conditions. Thereafter in the geometry parametrization section, we illustrate the different types of numerical geometry representation used in the two problems, and the corresponding definition of the design variables whose variation leads to different shapes of the computational domain. After a comprehensive classification and description of optimization methods and algorithms, we present the results obtained for the two different cases. For both problems the objectives considered are the maximization of heat transfer rate and the minimization of friction factor, with the additional objective of minimization of heat transfer surface for the recuperator module. Since there is no single optimum to be found, we use a multi-objective genetic algorithm and the so-called Pareto dominance concept. The results obtained are very encouraging, and the procedure described can be applied, in principle, to even more complex convective problems.