An inverse hyperbolic heat conduction problem in estimating pulse heat flux with a dual-phase-lag model

Abstract

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse hyperbolic heat conduction problem with the dual-phase-lag heat transfer model in estimating the unknown boundary pulse heat flux in an infinitely long solid cylinder from the temperature measurements taken within the medium. An efficient numerical scheme involving the hybrid application of the Laplace transform and control volume methods in conjunction with hyperbolic shape functions is used to solve the hyperbolic direct problem. The inverse solutions will be justified based on the numerical experiments in which two different heat flux distributions are to be determined. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors upon the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent pulse heat flux can be obtained for the test cases considered in this study.