Optimization of functionally graded metallic foam insulation under transient heat transfer conditions

The problem of minimizing the maximum temperature of a structure insulated by a functionally graded metal foam insulation under transient heat conduction is studied. First, the performance of insulation designed for steady-state conditions is compared with uniform solidity insulation. It is found that the optimum steady-state insulation performs poorly under transient conditions. Then, the maximum structural temperature of a two-layer insulation with constant solidity for each layer is minimized by varying the solidity profile for a given total thickness and mass. It is found that the cooler inner layer of the optimal design has high solidity, while the hotter outer layer has low solidity. This is in contrast to the steady-state optimum, where the solidity profile is the reverse.