Optimized topology design of finned ducts for internal flow thermal performance by discrete variable eigenvalue-related optimization

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.