Solution of an inverse transient heat conduction problem in a part of a complex domain

Abstract The purpose of this work is to formulate two simple methods which can be used to solve nonlinear inverse heat conduction problems in a part of a complex-shaped component in the on-line mode. The proposed methods can be useful if temperature measurements are carried out only in a selected part of an outsize element or if the whole element cannot be analysed due to the inverse heat conduction problem being ill-conditioned. It is assumed that the conductive heat transfer occurs through the surfaces separating the domain from the rest of the component. It is shown that the simplifying assumption of thermal insulation on these surfaces, which is often presented in literature, can cause significant errors. Compared to works published previously, if two additional unknown boundary conditions are introduced on the separating surfaces, the inverse problem conditioning deteriorates substantially. Despite this, stable solutions are achieved for “noisy measured data”. The presented methods can be used to optimize the power unit start-up and shutdown operation. They may also enable a reduction in the heat loss arising during the process and extend the power unit life. The methods presented herein can be applied in monitoring systems working both in conventional and nuclear power plants.