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A discrete variable topology optimization method of internally finned ducts in heat exchangers for efficient thermal performance is proposed. Fully developed convective heat transfer (FDCHT) model, which has been extensively employed and well checked in practical thermal engineering applications, is considered here. Under the uniform wall temperature boundary condition, the energy equation of the FDCHT model can be mathematically formulated as a generalized eigenvalue equation, and the total thermal resistance reflecting the thermal performance can be related to the eigenvalue. The well-known eigenvalue optimization formulation and sensitivity analysis is applied to this optimization problem. Significantly, the physical reality, such as precise Nusselt number, is maintained by using the discrete variable method, i.e., Sequential Approximate Integer Programming. Here, only the 0–1 densities denoted to solid and fluid are involved so that blurry intermediate zones and interpolation schemes are avoided. The practical engineering conditions of fixed pumping power and fixed fluid volume flow rate are discussed under the unified framework, respectively. Several designs of internally finned ducts without any blurry zone are obtained. The optimized design conforms to the three-dimensional precise Conjugate Heat Transfer calculation. Numerical results show that contrary to the design method by predefined heat transfer coefficient, the proposed method can automatically obtain the optimal shape and spacing of fins since the spatially varying effect of convective heat transfer has been achieved. [ABSTRACT FROM AUTHOR]

Engineering design problems often involve non-linear criterion functions, including inequality and equality constraints, and a mixture of discrete and continuous design variables. Optimization approaches entail substantial challenges when solving such an all-inclusive design problem. In this paper, a modification of the Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints while dealing with mixed-discrete variables. Continuous search (particle motion), as in conventional PSO, is implemented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest-feasible-vertex criterion. This approach is expected to alleviate the undesirable difference in the rates of evolution of discrete and continuous variables. The premature stagnation of candidate solutions (particles) due to loss of diversity is known to be one of the primary drawbacks of the basic PSO dynamics. To address this issue in high dimensional design problems, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each iteration. The estimated diversity measure is then used to apply (i) a dynamic repulsion away from the best global solution in the case of continuous variables, and (ii) a stochastic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is applied to a wide variety of standard test problems: (i) a set of 9 unconstrained problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) problems. We also explore the applicability of this algorithm to a large scale engineering design problem--wind farm layout optimization. [ABSTRACT FROM AUTHOR]