Simultaneous Heat Source and Boundary Condition Estimation in Axisymmetric Transient Inverse Heat Conduction Problems
by
Aziz Azimi
Ph.D. Candidate - School of Mechanical Engineering - Sharif University of Technology - Azadi Ave. - Tehran - Iran
Coauthors: Siamak Kazemzadeh Hannani and Bijan Farhanieh (School of Mechanical Engineering - Sharif University of Technology)

The development of engineering softwares for the study of Inverse Heat Conduction Problems (IHCPs) has widely investigated for applications in industrial and research areas. Time-space IHCPs have been used to estimate time or time-space varying unknown heat generation, surface boundary conditions and thermophysical properties using one or more temperatures measured by sensors inside or on the boundaries of the physical domain. Mathematically, IHCPs, unlike the direct heat conduction problems, belong to a class of “ill-posed” problems which do not satisfy the “well-posed” conditions introduced by Hadamard. In fact, the IHCPs are very sensitive to random errors in the measured temperature data, thus requiring special techniques for their solutions in order to satisfy the stability condition.

In this research, a simultaneous heat source and boundary condition estimation using parameter and function-estimation techniques is presented for the solution of an axisymmetric transient inverse heat conduction problem (IHCP). The IHCP involves simultaneous unknown time varying heat generation and time-space varying boundary conditions estimation. Two techniques are considered, Levenberg-Marquardt scheme for parameter estimation and adjoint conjugate gradient method for function estimation. To have fewer numbers of unknown coefficients for estimation, polynomials are used in the parameter estimation scheme. The measured transient temperature data needed in the inverse solution are made by exact or inexact (noisy) data. The results of the present study are compared to exact heat source and temperature (heat flux) boundary conditions.

Date received: August 28, 2004