Numerical Determination of the Temperature Dependent Thermophysical Properties in Solid Materials: Experimental Instrumentation

An iterative approach is presented to determine the temperature-dependent thermo-physical properties from the temperature measurements taken at various points of the medium. Network Simulation Method (NSM) is used as the numerical tool in the form of an inverse problem to obtain a stable and exact numerical solution for simultaneously estimating thermal conductivity and specific heat. The approach provides estimations of the functions k(T) and c_e(T), regardless of the waveform of those functions even without a priori information on the kind of dependence concerned. The solutions are reached by a piece-wise functions, whose number of stretches may be specified. The input data (temperature measurements) are obtained from an experimental installation has been designed and using various points of measurement in different solid materials. The sensitivity of the functional versus the slope of the line, at each step, is acceptable and the complete piece-wise solution is very close to the exact thermo-physical properties in all the cases studied. The proposed general procedure may be applied regardless of the kind of temperature dependence for k(T) and c_e(T) as long as these are continuous temperature functions given by an explicit mathematical function or by a finite stretches piece-wise function. The estimations of k(T) and c_e(T) are piece-wise functions with a number of stretches that may be specified to approximate the inverse solutions to the exact values as much as required. The typical functional of these problems contains the simulated measured data taken at three points of the solid. These measurements are compared in the functional with the solution of the partial inverse problem by applying NSM as the numerical technique in each iteration, in order to estimate each of the stretches that conform the whole piece-wise estimation. NSM has been successfully applied before to solve both DHCP and IHCP. Among the advantages of this method is the fact that no mathematical manipulations or convergence criteria are needed to solve the finite difference equations resulting from the discretization of the partial difference equations of the mathematical model. Both tasks are carried out by the powerful software used to solve the network model. The close agreement between the exact solutions and the estimated results shows the potential of the proposed method in finding the accurate value of the temperature-dependent thermo-physical properties in inverse heat conduction problem.