Two-dimensional non-linear inverse heat conduction problem based on the singular value decomposition

• Published in: International journal of thermal sciences 2009-06, Vol.48 (6), p.1081-1093
• Main Authors: García, Juan Andrés Martín, Cabeza, José María Gutiérrez, Rodríguez, Alfonso Corz
• Format: Article
• Language: English
• Subjects: Analytical and numerical techniques; Exact sciences and technology; Function specification method; Fundamental areas of phenomenology (including applications); Heat conduction; Heat transfer; Inverse heat conduction; Physics; Singular value decomposition
• ISSN: 1290-0729; 1778-4166
• DOI: 10.1016/j.ijthermalsci.2008.09.002

In this paper an efficient sequential method is developed in order to estimate the unknown boundary condition on the surface of a body from transient temperature measurements inside the solid. This numerical approach for solving an inverse heat conduction problem (IHCP) takes into account two-dimensional problems, planar or axisymmetric cylindrical, composite materials with irregular boundaries and temperature-dependent thermal properties. The unknown surface condition is assumed to have abrupt changes at unknown times. The regularization procedure used for the solution of the IHCP is based on the singular value decomposition technique. An overall estimate of error is defined in order to find the optimal estimation in the 2D IHCP (linear and non-linear). The stability and accuracy of the scheme presented is evaluated by comparison with the Function Specification Method. This comparative study has been carried out using numerically simulated data, and the parameters considered include shape of input, noise level of measurement, size of time step and temperature-dependent thermal properties. A good agreement was found between both methods. Beside this, the slight differences on estimations and number of future temperatures are discussed in this paper.