Thermal dispersion effect on microstructural topology optimization

This study investigates the influence of thermal dispersion on homogenization-based topology optimization. Thermal dispersion is an important phenomenon that affects heat transport in porous media due to local variations in the microscopic temperature distribution and non-uniformity of microscopic flow velocity, representing the additional macroscopic thermal diffusion effect induced by fluid flow. Thermal dispersion inevitably occurs inside the porous media, therefore convection effect as well as thermal diffusion effect should be taken into account into the cell problem in the evaluation of the heat transfer coefficient of porous materials. However, most of the previous studies on the design optimization of porous structures ignore the convection, and the effects of thermal dispersion on microstructural topology optimization remain unexplored. The fundamental question driving this study concerns the identification of optimal microstructural topologies that maximize or minimize thermal dispersion. To investigate this issue, we formulate and solve an optimization problem to maximize and minimize the thermal dispersion coefficient to clarify the effect of thermal dispersion on microstructural topology optimization. The objective function is a component of the thermal dispersion tensor derived by homogenization method known as the two-scale asymptotic expansion with drift approach. The sensitivity of the objective function and the adjoint problem are derived based on the continuous adjoint variable method. The influence of thermal dispersion on the optimization is discussed through several numerical examples.