Design of metamaterial-based heat manipulators by isogeometric shape optimization

There has been a growing interest in controlled heat flux manipulation to increase the efficiency of thermal apparatus. Heat manipulators control and manipulate heat flow. A key to the effective performance of these heat manipulators is their thermal design. Such designs can be achieved by the materials specially engineered to have outstanding properties that can not be achieved with natural materials (known as metamaterials or meta-structure), whose geometry and material properties can be optimized for a specific objective. In this work, we focus on thermal metamaterial-based heat manipulators such as thermal concentrator (which concentrates the heat flux in a specified region of the domain). The main scope of the current work is to optimize the shape of the heat manipulators using Particle Swarm Optimization (PSO) method. The geometry is defined using NURBS basis functions due to the higher smoothness and continuity and the thermal boundary value problem is solved using Isogeometric Analysis (IGA). Often, nodes as design variables (as in Lagrange finite element method) generate the serrate shapes of boundaries which need to be smoothened later. For the NURBS-based boundary with the control points as design variables, the required smoothness can be predefined through knot vectors and smoothening in the post-processing can be avoided. The optimized shape generated by PSO is compared with the other shape exploited in the literature. The effects of the number of design variables, the thermal conductivity of the materials used, as well as some of the geometry parameters on the optimum shapes are also demonstrated.