A method for shape design sensitivity analysis of two-dimensional thermal conducting solid is presented using the material
derivative concept and the adjoint variable method. A general thermal boundary condition with heat convection is considered
in addition to prescribed temperature and heat flux. The method for deriving the sensitivity formula is based on standard
direct boundary integral equation formulation. The sensitivity of a general functional depending on temperature and heat flux
is considered. The method is then applied to obtain the sensitivity analysis is demonstrated by a hollow cylinder problem
with exact solution. A weight minimization problem of a thermal diffuser is considered as a practical application. The sensitivity
by the presented method is compared with that by finite differences and an optimal shape is found by use of an optimization
routine.