2023 Dr. M. Necati Ozisik Distinguished Lecture Series: “Solution of Inverse Problems in Thermal Systems: A Tribute to Professor Necati Ozisik”

In most analytical and numerical solutions, the basic equations that describe the process, as well as the relevant and appropriate boundary conditions, are known. Interest lies in obtaining a unique solution that satisfies the equations and boundary conditions. This may be termed as the direct or forward solution. However, there are many problems, particularly in practical systems, where the desired result is known, but the conditions needed for achieving this are unknown. These are generally known as inverse problems and are of particular interest in thermal processes and systems. For instance, the temperature, shear, or pressure variation to which a component must be subjected to obtain desired characteristics in a manufacturing system is known or prescribed. However, the boundary and initial conditions, in terms of heat input, pressure, flow rate and temperature, are not known and must be determined by solving the inverse problem. Professor Ozisik carried out extensive fundamental studies on inverse heat transfer problems and developed important strategies for their solution. He authored many papers and books on this topic, leading to considerable interest and research in inverse problems.

This lecture focuses on inverse problems in thermal convection and considers a few fundamental and practical circumstances. The inverse convection problems of a thermal plume or jet in cross flow and of a heat source on a vertical flat plate are of particular interest in environmental problems and in fire safety. The inverse problem involves determination of the strength and location of the heat source or the jet by employing a few selected data points downstream. A major concern is the non-uniqueness of the solution and optimization techniques are used to reduce the uncertainty. A predictor-corrector strategy is outlined, along with optimization to minimize the data points needed and to ensure uniqueness of the solution. Another approach based on search and optimization is developed to solve the inverse natural convection flow due to a finite heat source, such as an electronic component or a fire, on a wall. Similarly, another problem considered here is a furnace whose wall temperature distribution is not known, but a few selected data points on a rod at the center of the furnace are used to solve the inverse problem to determine the wall temperature to a fair level of accuracy and uniqueness. Again, optimization of the process is used to develop an efficient approach and obtain an essentially unique solution. These basic approaches can be extended to other inverse convection transport problems and a few additional examples are given.