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

Abstract

The identification of the piecewise homogeneous thermal conductivity of conductors 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-state case, whilst for the unsteady case a numerical method based on the boundary element method, as a direct solution procedure, combined with an ordinary least-squares technique subject to bounds on the variables, is employed for obtaining an inverse numerical solution. The sensitivity coefficients for the unspecified boundary conditions and for interior temperatures are calculated and show the need for interior measurement information to be imposed. For a heat conductor presenting a single discontinuity, it was found that, when the number of time measurements is limited then two interior temperature measurements are necessary and sufficient in order to render a good estimate of the exact solution, otherwise one may increase the number of time measurements at a single interior sensor location to render the same result.