This study applies a hybrid technique of the Laplace transform and finite-difference methods in conjunction with the least-squares method and experimental temperature data inside the test material to predict the unknown surface temperature, heat flux and absorptivity for various surface conditions in the laser surface heating process. In this study, the functional form of the surface temperature is unknown a priori and is assumed to be a function of time before performing the inverse calculation. In addition, the whole time domain is divided into several analysis sub-time intervals and then these unknown estimates on each analysis interval can be predicted. In order to show the accuracy of the present inverse method, comparisons are made among the present estimates, direct results and previous results, showing that the present estimates agree with the direct results for the simulated problem. However, the present estimates of the surface absorptivity deviate slightly from previous estimated results under the assumption of constant thermal properties. The effect of the surface conditions on the surface absorptivity and temperature is not negligible.
SUMMARYA hybrid scheme of the Laplace transform, finite difference and least-squares methods in conjunction with a sequential-in-time concept, cubic spline and temperature measurements is applied to predict the heat transfer coefficient distribution on a boundary surface in two-dimensional transient inverse heat conduction problems. In this study, the functional form of the heat transfer coefficient is unknown a priori. The whole spatial domain of the unknown heat transfer coefficient is divided into several analysis sub-intervals. Later, a series of connected cubic polynomial function in space and a linear function in time can be applied to estimate the unknown surface conditions. Due to the application of the Laplace transform, the unknown heat transfer coefficient can be estimated from a specific time. In order to evidence the accuracy of the present inverse scheme, comparisons among the present estimates, previous results and exact solution are made. The results show that the present inverse scheme not only can reduce the number of the measurement locations but also can increase the accuracy of the estimated results. Good estimation on the heat transfer coefficient can be obtained from the knowledge of the transient temperature recordings even in the case with measurement errors.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.