AbstractThe objective of this study is to examine two analytical methods for the design sensitivity analysis of optimal control problems and to develop the analyses necessary for the application of the methods to thermal systems. The two methods are the direct differentiation method and the adjoint variable method. Results for these methods are compared with those obtained using central finite difference approximations for design sensitivity analysis. The adjoint variable method has the potential to reduce significantly computational times for design sensitivity analysis while sacrificing only a small amount of accuracy. As the number of functional requiring design sensitivity analysis increases, however, the adjoint variable method becomes less attractive and the direct differentiation method becomes more attractive.