Thermal Property Parameter Inversion For 2-D Heat Conduction Problems Based On The BEM

Inverse heat conduction problems are of great significance in theory and engineerings. The inversion of thermal property parameters is one of inverse heat conduction problems (IHCP), which is playing an increasingly important role in aerospace, chemical, metallurgy and other engineering fields. The research background of inverse heat conduction problems is introduced. The current research status of inverse heat conduction problems is reviewed. The boundary element method (BEM) is used to build the numerical analysis model for 2-D heat conduction problems. The thermal property parameters are inversely identified by different methods.For the 2-D steady heat conduction problem with temperature-dependent thermal conductivity, the nonlinear governing equation is simplified to Laplace operator form with Kirchhoff transformation, then the boundary integral equation(BIE) is obtained and discretized with constant elements. Measuring points locate on the boundary. The Gauss-Newton method is used to optimize the objective function. For one-parameter and double-parameter identification, effects of element division, measuring point number and convergence factor on the inverse results are analyzed. With the increase of the element number and the decrease of random noises, the results become more accurate. The number of measuring points has no obvious influence on inverse results. With the decrease of convergence factor, the iteration step increases.For steady state heat conduction problems with heat source and temperature-dependent thermal conductivity, the BIE is discretized with linear elements. With the existence of domain integration, the radial integral method (RIM) is used to transform domain integration into boundary integration. Measuring points are located in the domain. The conjugate gradient method is used to optimize the objective function. One-parameter and double-parameter inverse problems are also considered. Effects of element division, measuring point number, interior point number and convergence factor on inverse results are discussed. With the decrease of random noises, the results are more accurate. With the increase of the element number and mersuring points, the results become more accurate. For one-parameter inverse problems, the number of interior points has no obvious influence on results, but inverse results tend to be more accurate with the increase of interior points.For transient state heat conduction problems with temperature-dependent thermal conductivity, the BIE is discretized with linear elements. The inverse thermal property parameters are defined as the optimization variables. The complex variable differentiation method(CVDM) is employed to compute the gradient matrix of the objective function. Effects of time step length, measuring point number and random noise on inverse results are investigated. With the decrease of time step length and the increase of the measuring points number, the convergence rate quickens.The thermal property coefficients are identified for heat conduction problems with orthotropic material. Measuring points are set in the domain. The conjugate gradient method is used to optimize the objective function. The number of measuring point has a little influence on inverse results.Numerical examples show the effectiveness and stability of the different methods.