Heat-Flux Estimation in a Nonlinear Heat Conduction Problem with a Dual-Phase-Lag Model

Abstract

In this study, an inverse algorithm based on the conjugate-gradient method and the discrepancy principle is used to solve the inverse nonlinear dual-phase-lag heat conduction problem in estimating the time-dependent boundary heat flux based on the measured back surface temperature. The accuracy of the presented method for solving the inverse problem is examined by utilizing two examples. The effects of measurement error, initial guess, measurement location, phase lag of heat flux, and nonlinearity on the accuracy of estimation are evaluated. The results demonstrate that the proposed method is an accurate and robust method to determine inversely the boundary heat flux in the hyperbolic heat conduction with the nonlinear behavior, even when the input data contain measurement errors. In addition, when the sensor is placed far from the heated surface, it is more difficult to conduct the reconstruction of the heat flux by using the non-Fourier model than the Fourier model. The comparison results obtained from the linear and nonlinear solutions demonstrate that, when the thermal conductivity is an increasing function of temperature, the accuracy of inverse solution is higher.