Two dimensional steady-state inverse heat conduction problems

In this work we estimate the surface temperature in two dimensional steady-state in a rectangular region by two different methods, the singular value decomposition (SVD) with boundary element method (BEM) and the least-squares approach with integral transform method (ITM). The BEM method is efficient for solving inverse heat conduction problems (IHCP) because only the boundary of the region needs to be discretized. Furthermore, both temperature and heat flux at the unknown boundary are estimated at the same time. The least-squares technique involves solving the equations constructed from the measured temperature and the exact solution. The measured data are simulated by adding random errors to the exact solution of the direct problem. The effects of random errors on the accuracy of the predictions are examined. The sensitivity coefficients are also presented to illustrate the effect of sensor location on the estimated surface conditions. Numerical experiments are given to demonstrate the accuracy of the present approaches.