Sensitivity Analysis and Design Optimization Methods for Problems of Heat Transfer with Phase Change

The design optimization and sensitivity analysis methodsfor the problems of transient heat transfer with phase change have beenresearched in the paper. On the basis of phase-change temperature fieldsolution with the finite element, time difference, and equivalent heatcapacity methods, the numerical method to compute the first-orderderivatives of temperature with respect to design variables is proposed. Twocomputational schemes of the direct method and the adjoint method have beengiven, and their characteristics have been discussed. The optimization modeland algorithm are built for the transient temperature filed with phasechange. These methods have been implemented within the software JIFEX forfinite element analysis and design optimization. The numerical results ofexample problems are given to illustrate the accuracy of sensitivityanalysis and the effectiveness of design optimization.