The identification of the piecewise homogeneous thermal conductivity of conductors subjected to a heat flow test

The identification of the piecewise homogeneous thermal conductivity of con ductors with unknown location of the discontinuities is investigated using additional boundary and/or interior measurements of the temperature in heat -flow experiments. A mathematical analysis is performed for the steady-stat e case, whilst for the unsteady case a numerical method based on the bounda ry element method, as a direct solution procedure, combined with an ordinar y least-squares technique subject to bounds on the variables, is employed f or obtaining an inverse numerical solution. The sensitivity coefficients fo r the unspecified boundary conditions and for interior temperatures are cal culated and show the need for interior measurement information to be impose d. For a heat conductor presenting a single discontinuity, it was found tha t, when the number of time measurements is limited then two interior temper ature measurements are necessary and sufficient in order to render a good e stimate of the exact solution, otherwise one may increase the number of tim e measurements at a single interior sensor location to render the same resu lt. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.