Application of a Genetic Optimization Method to a 2-D Constructal-Based Cooling Configuration

The thermal performance of a 2-D section of a prismatic body cooled by internal tubes arranged in a bundle according to the prescriptions of Constructal Theory, is analyzed. The flow inside each tube is fully developed. The heat transfer from the slab to the coolant flowing inside the tubes and the average temperature of the slab provide the metric to evaluate the system thermal performance. In this initial study, all quantities are calculated by reducing the original 3d model to a simplified 2d geometry, corresponding to a section obtained by intersecting the slab with a plane normal to the mean flow direction. One of the possible 2D sections, at an arbitrarily chosen distance from the onset of the fully developed flow regime, has been parameterized to create a design template. A “design of experiment” based on the SOBOL algorithm is used to set an initial family of 2D slab configurations (i.e., different cooling tubes arrangements). A multi-objective genetic algorithm (MOGA II) is then used to optimize the slab thermal performance starting from the initial family set. The results confirm that Constructal Theory correctly predicts the “nearly-optimal” tube arrangement that ensures the minimal average temperature in the solid. However, at least one non-Constructal configuration exists that produces a “better optimum” than Constructal geometry. It is also found that, in the 2-D configuration analyzed here, the two objective functions of “minimum material temperature” and of “maximum heat rejection to the coolant” are concurrent, i.e., they share the same solution space.