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Constructal Design of Double-T Shaped Cavity with Stochastic Methods Luus-Jaakola and Simulated Annealing

In this paper it is proposed a comparison between two stochastic methods, Simulated Annealing and Luus-Jaakola algorithms, applied in association with Constructal Design to the geometric optimization of a heat transfer problem. The problem consists in a solid body with an internal uniform heat generation, which is cooled by an intruded cavity that is maintained at a minimal temperature. The other surfaces are kept as adiabatic. The objective is to minimize the maximum excess of temperature (θmax) in the solid domain through geometric optimization of the isothermal double-T shaped cavity. The problem geometry has five degrees of freedom, but in this study four degrees of freedom are evaluated, keeping fixed the ratio H/L (ratio between the height and length of the solid domain) as well as the cavity constraints. The search for the optimal geometry is performed by Simulated Annealing and the Luus-Jaakola algorithm with different configurations or set of main parameters. Each algorithm is executed twenty times and the results for θmax, and corresponding geometry ratios, are recorded. Results of two heuristics are compared in order to select the best method for future studies about the complete optimization of the cavity, as well as, the evaluation of constraints over the thermal performance of the problem. The method employed to compare and rank the different versions of the two algorithms is a statistical tool called multi-comparison of Kruskal-Wallis. With this statistical method it is possible to classify the algorithms in three main groups. Results showed that the Simulated Annealing with hybrid parameters of Cooling Schedule (BoltzExp and ConstExp2) and traditional ones (Exponential) led to the highest probability to find the global optimal shape, while the results obtained with the Luus-Jaakola algorithm reached to several local points of minimum far from the best shape for all versions of the algorithm studied here. However, the Luus-Jaakola algorithm led to the lowest magnitude of maximum excess of temperature, showing that the implementation of hybrid methods of optimization can be an interesting strategy for evaluation of this kind of problem.