One dimensional inverse heat conduction problem with the Walsh method

The Walsh functions are used to obtain the space dependent thermal conductivity in one dimensional time dependent heat conduction medium. Although it is necessary to measure the temperatures in interior points, the Walsh reveals the real values without any numerical constraints. The proposed algorithm is quite different from other algorithms in that it is one-directional, that is, no iteration is necessary, and is numerically stable regardless of the functional characteristics of the thermal conductivity. This permits the estimation of yjermal conductivity when the medium consists of different materials