Abstracts Engineering

Analytical solution for inverse heat conduction problem

by Kumar Anagurthi

This thesis describes a new technique for solving the inverse heat conduction problem in a one-dimensional bar. It consists of determination of a heat flux, which is a function of time and which causes a given, experimentally determined temperature profile measured at one end of the bar while the other end is kept insulated. Based on the found heat flux, the temperature profile is then found over the entire bar as a function of time. The algorithm combines the separation of the variables method in conjunction with the least-squares method. A brief description of the differences between direct and inverse heat conduction problems are described first, and criteria that must be met by potentially useful IHCP methods are explained. This is followed by the corresponding literature survey. A general problem of experimental verification of the theory is discussed next. For illustration, a problem of determination of thermal conductivity by the finite difference method, based on the measured temperature profile, is explained in detail. Next, an experimental setup developed at Ohio University and used to study a quenching process is described. The time change of temperatures during this process had been recorded earlier and is regarded as a known function. In the analytical treatment, the heat flux at the end of the bar is assumed as the polynomial function of time with the unknown polynomial coefficients. These coefficients were then calculated by employing the least-squares method to fit the analytically-found solution for the temperature, based on such a flux, and minimizing the error of such a distribution by comparing it with the experimental data. Finally, this heat flux is used to find the analytical solution of the temperature profile over the bar as a function of time. The analytically found temperature profile at the end of the bar was agreed very well with the experimental curve.