Yu Ching Yang

A Nonlinear Inverse Problem in Estimating the Heat Generation in Rotary Friction Welding

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat generation at the interface of cylindrical bars during rotary friction welding process from the knowledge of temperature measurements taken within the stationary bar. In the direct problem, the heat capacity and thermal conductivity are functions of temperature; hence, this is a nonlinear inverse problem. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors in these measurements upon the precision of the estimated results is also considered. Results show that an excellent estimation on the time-dependent heat generation can be obtained for the test cases considered in this study. The current methodology can be applied to the prediction of heat generation in rotary friction welding.

Three-Dimensional Pipe Fouling Layer Estimation by Using Conjugate Gradient Inverse Method

In this study, a conjugate gradient method based inverse algorithm is applied to estimate the unknown three-dimensional fouling-layer profiles on the inner wall of a piping system using simulated temperature measurements taken on the pipe wall. The temperature data obtained from the direct problem are used to simulate the exact temperature measurements. Results show that an excellent estimation on the fouling-layer profiles can be obtained for the two cases investigated in this study. The technique presented here can be used as an alternative to ultrasonic waves fouling detection techniques to provide crucial information for the optimization of cleaning schedule for piping systems.

Estimation of surface heat flux and temperature distributions in a multilayer tissue based on the hyperbolic model of heat conduction

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 in estimating the unknown time-dependent surface heat flux in a skin tissue, which is stratified into epidermis, dermis, and subcutaneous layers, from the temperature measurements taken within the medium. Subsequently, the temperature distributions in the tissue can be calculated as well. The concept of finite heat propagation velocity is applied to the modeling of the bioheat transfer 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 on the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent surface heat flux can be obtained for the test cases considered in this study.

Simultaneous Estimation of Boundary Heat Flux and Convective Heat Transfer Coefficient of a Curved Plate Subjected to a Slot Liquid Jet Impingement Cooling

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to simultaneously estimate the unknown boundary heat flux and convective heat transfer coefficient in a curved plate cooled by an impinging slot jet from the knowledge of temperature measurements taken within the plate. Subsequently, the distributions of temperature in the plate can be determined. It is assumed that no prior information is available on the functional forms of the heat flux and convective heat transfer coefficient; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors and locations in these measurements upon the precision of the estimated results is also considered. Results show that an excellent estimation on the heat flux and convective heat transfer coefficient and temperature distributions can be obtained for the two test cases considered in this study.

An inverse problem in estimating the laser irradiance and thermal damage in laser-irradiated biological tissue with a dual-phase-lag model

Abstract The aim of this study is to solve an inverse heat conduction problem to estimate the unknown time-dependent laser irradiance and thermal damage in laser-irradiated biological tissue from the temperature measurements taken within the tissue. The dual-phase-lag model is considered in the formulation of heat conduction equation. The inverse algorithm used in the study is based on the conjugate gradient method and the discrepancy principle. The effect of measurement errors and measurement locations on the estimation accuracy is also investigated. Two different examples of laser irradiance are discussed. Results show that the unknown laser irradiance and thermal damage can be predicted precisely by using the present approach for the test cases considered in this study.