  An inverse problem for a stationary heat transfer process is studied for a
totally isolated bar on its lateral surface, made up of two consecutive
sections of different, isotropic and homogeneous materials, perfectly assembly,
where one of the materials, that is unreachable and unknown, has to be
identified. The length of the bar is assumed to be much greater that the
diameter so that a 1D heat transfer process is considered. A constant
temperature is assumed at the end of the unknown part of the rod while the
other end is let free for convection. We propose a procedure to identify the
unknown material of the bar based on a noisy flow measurement at the opposite
end. Necessary and sufficient conditions are derived together with a bound for
the estimation error. Moreover, elasticity analysis is performed to study the
influence of the data in the conductivity estimation and numerical examples are
included to illustrate the proposed ideas and show the estimation performance.
