HOT WIRE METHOD FOR THE THERMAL CHARACTERIZATION OF MATERIALS: INVERSE PROBLEM APPLICATION

Abstract

An experimental set-up of the hot wire method is presented. The present design
allows the measurement of the temperatures at two different points on the heating
wire with an acquisition system that performs measurements at a frequency of 1kHz
with a 12 bit numerical converter. An analytical solution for the direct model for the
time dependent problem of heat transfer is employed. It is based on the quadrupole
method which basically consists in a transfer matrix approach which is possible
through the use of Laplace transforms. It extends the electrical analogy of heat
transfer problems using the notion of impedance, and allows to take into account the
thermal behavior of the wire, as well as contact resistance and heat loss effects in a
very simple straightforward way. In the identification process carried on the
temperature experimental data relies on a sampling of the data that is
logarithmically spaced in time. The initial guesses for the thermal conductivity
values are obtained applying the well known and ideal model of the linear
temperature evolution versus the logarithm of the time. These values are used to
start up the algorithms that are applied in the minimization of the cost functional of
the squared residues between measured and calculated temperatures. The precision
of the estimates is assessed with the calculated confidence bounds obtained by the
variance-covariance matrix at the converged solution.