Inverse Estimation of Surface Heating Condition in a Finite Slab With Temperature-Dependent Thermophysical Properties

Abstract

Temperature and heat flux at the heated surface can be estimated by solving an inverse heat conduction problem (IHCP) based on measured temperature and/or heat flux at the accessible locations (e.g., back surface). Most of the previous studies used temperature measurement data in the objective function, and little work has been done for the inverse numerical algorithm based on heat flux measurement data. In this study, a one-dimensional IHCP in a finite slab is solved by using the conjugate gradient method. The heat flux measurement data are, for the first time, incorporated into the objective function for a nonlinear heat conduction problem with temperature-dependent thermophysical properties. The results clearly show that the inverse approach of using heat flux measurement data in the objective function can provide much better predictions than the traditional approaches in which the temperature measurements are employed in the objective function. Parametric studies are performed to demonstrate the robustness of the formulated IHCP algorithm by testing it for two different materials under different frequencies of the imposed heat flux along with random errors of the measured heat flux at the back surface.

Acknowledgments

The authors thank the Test Resource Management Center (TRMC) Test and Evaluation/Science & Technology (T&E/S&T) Program for their support. This work is funded by the T&E/S&T Program through the U.S. Army Program Executive Office for Simulation, Training, and Instrumentation, contract W900KK-08-C-0002. The authors also express their gratitude to Dr. James L. Griggs for his valuable discussions.

Jianhua Zhou is a research assistant professor in the Department of Mechanical and Aerospace Engineering at University of Missouri, Columbia, Missouri. He received his Ph.D. degree in engineering thermophysics from the Chinese Academy of Sciences, Beijing, China, in 2002. His current research interests include optical and thermal responses in laser-irradiated biological tissues, inverse heat conduction problems, and heat transfer and fluid flow in particulate systems. He is a senior member of AIAA and a member of ASME.

Yuwen Zhang is a professor of mechanical and aerospace engineering at University of Missouri, Columbia, Missouri. His research interests include phase change heat transfer, heat pipes, ultrafast, ultra-intense laser materials processing, and transport phenomena in materials processing and manufacturing. He is the author of more than 130 journal papers and over 90 conference papers, as well as two textbooks. He is a recipient of the 2002 Office of Naval Research (ONR) Young Investigator Award. He is a fellow of the ASME and associate fellow of the AIAA.

J. K. Chen is the William and Nancy Thompson Professor and Director of the Center of Ultrashort, Ultraintense Lasers at the University of Missouri, Columbia, Missouri. He received his Ph.D. in aeronautics and astronautics from Purdue University in 1984. His current research interests include laser effects and ultrafast thermomechanics. He is a fellow of the ASME.

Z. C. Feng is a professor of mechanical and aerospace engineering at University of Missouri, Columbia, Missouri. He has conducted research on design, modeling, and fabrication of MEMS devices and microsensors funded by NSF, NIH, and the U.S. Army PEO. His works include the design and fabrication of microgyroscopes, cell electrochemical sensors, and microfluidic channels for cell sorting. He is a fellow of the ASME.