INVERSE PROBLEM OF A ONE-DIMENSIONAL MODEL IN MULTILAYER HEAT CONDUCTION

Abstract

The inverse problem in conducting heat is related to the determination of the boundary condition, rate of heat generation, or thermophysical properties, using temperature measurements at one or more positions of the solid. The inverse problem in conducting heat is mathematically one of the ill-posed problems, because its solution extremely sensitive to measurement errors. For a well-placed problem the following conditions must be satisfied: the solution must exist, it must be unique and must be stable on small changes of the input data. The objective of the work is to estimate the heat flux generated at the tool-chip-chip interface in a manufacturing process. The term "estimation" is used because in the temperature measurements, errors are always present and these affect the accuracy of the calculation of the heat flow.