A two-dimensional inverse problem in imaging the thermal conductivity of a non-homogeneous medium

A two-dimensional inverse heat conduction problem is solved successfully by the conjugate gradient method (CGM) of minimization in imaging the unknown thermal conductivity of a non-homogeneous material. This technique can readily be applied to medical optical tomography problem. It is assumed that no prior information is available on the functional form of the unknown thermal conductivity in the present study, thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements obtained on the medium surface. The advantages of applying the CGM in the present inverse analysis lie in that the initial guesses of the unknown thermal conductivity can be chosen arbitrarily and the rate of convergence is fast. Results show that an excellent estimation on the thermal conductivity can be obtained within a couple of minutes CPU time at Pentium II-350 MHz PC. Finally the exact and estimated images of the thermal conductivity will be presented.