ABSTRACT
The knowledge of heat transfer behaviour in composite conductors requires characterization of the heat transfer coefficients at the contact interfaces between constituent materials. This chapter is devoted to such an inverse problem in which a generalized interface condition contains an unknown space- and time-varying interface coefficient that is to be determined from non-invasive temperature measurements on the boundary. The uniqueness of solution holds, but the problem does not depend continuously on the input measured temperature data. A new preconditioned conjugate gradient method (CGM) is utilized to deal with this ill-posedness. In comparison with the standard CGM with no preconditioning, this method has the merit that the gradient of the objective functional does not vanish at the final time, which restores accuracy and stability when the input data is contaminated with noise and when the initial guess is not close to the true solution.
