Geometric inverse estimation for the inner wall of a furnace under transient heat conduction based on dual reciprocity boundary element method

Abstract

A boundary shape estimation problem for the furnace’s inner surface is solved using the dual reciprocity boundary element method (DRBEM) and the conjugate gradient method (CGM) under transient heat conduction. The DRBEM is utilized to eliminate the drawbacks of traditional numerical methods and classical boundary element method of discretizing the entire computational domain, with only boundary discretization. The inversion results are obtained by applying the CGM to minimize the objective function, in which the sensitivity coefficients are calculated with the complex variable derivation method (CVDM), making the calculation precise and independent of step size. To verify the accuracy of the DRBEM in solving the transient heat conduction problem, the influencing factors including radial-basis function, the number of internal collocation points, and time step size are investigated. The influences of measurement time interval, future time step, initial guess, measurement error, and the number and position of measurement points on the inversion results are analyzed. Meanwhile, the effectiveness of the proposed approach is tested by numerical examples, and the inversion results show that it is stable, accurate, and efficient for identifying different and complicated unknown boundary shapes of the furnace.