Design of metamaterial-based heat manipulators by isogeometric shape optimization

•A shape optimization framework for the design of metamaterial-based heat manipulators is developed.•Smooth, CAD-compatible and easily controllable geometries are achieved by using NURBS basis functions.•An optimized thermal concentrator can accumulate heat ux up to 7 times as large as for standard designs.•An optimized heat cloak-concentrator can collect up to 8 times more flux than conventional designs in addition to cloaking the inner core.•Effect of geometric parameters, conductivities and boundary conditions on optimized shapes is discussed.