Shape sensitivity and optimization for transient heat diffusion problems using the bem

A shape design sensitivity analysis (SDSA) of two‐dimensional transient heat diffusion problems is proposed based on the BIE formulation. The adjoint variable method is used by using the Ionescu—Cazimir integral identity. The procedure is checked against the analytical solution in the case of a rod example, and by numerical comparisons with the finite differencing for a rectangular block under thermal shock and a plunger model. An optimal design problem is then formulated for the plunger and solved to obtain a realistic shape.