Two-dimensional non-linear inverse heat conduction problem based on the singular value decomposition |
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| Authors: | Juan Andrés Martín García José María Gutiérrez Cabeza Alfonso Corz Rodríguez |
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| Affiliation: | 1. Department of Electrical Engineering, University of Cádiz, Escuela Politécnica Superior de Algeciras, Avda. Ramón Puyol, s/n, 11202 Algeciras, Cádiz, Spain;2. Department of Applied Physics, University of Cádiz, Escuela Politécnica Superior de Algeciras, Avda. Ramón Puyol, s/n, 11202 Algeciras, Cádiz, Spain;3. Department of Industrial and Civil Engineering, University of Cádiz, Escuela Politécnica Superior de Algeciras, Avda. Ramón Puyol, s/n, 11202 Algeciras, Cádiz, Spain;1. School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, PR China;2. Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, PR China;1. Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstraße 15, 99423 Weimar, Germany;2. Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand;1. School of Civil Engineering, Hefei University of Technology, Hefei 230009, PR China;2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, PR China |
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| Abstract: | 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. |
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