  We analyze an optimization problem of the conductivity in a composite
material arising in a heat conduction energy storage problem. The model is
described by the heat equation that specifies the heat exchange between two
types of materials with different conductive properties with Dirichlet-Neumann
boundary conditions on the external part of the domain, and on the interface
characterized by the resisting coefficient between the highly conductive
material and the less conductive material. The main purpose of the paper is to
compute a shape gradient of an optimization functional in order to accurately
determine the optimal location of the conductive material using a classical
shape optimization strategy. We also present some numerical experiments to
illustrate the efficiency of the proposed method.
