Yogesh Jaluria
Board of Governors Professor
Mechanical and Aerospace Engineering Department
Rutgers University, Piscataway, NJ, USA
Email: jaluria@soe.rutgers.edu


Inverse Problems in Thermal Energy Processes and Systems


In most engineering problems of fundamental and applied interest, the basic equations that describe the process and the appropriate boundary conditions are known. Then the analytical or numerical solution is directed at obtaining a unique solution that satisfies the equations and the boundary conditions. Such a solution may be described as the direct or forward solution. Different techniques have been developed to solve a wide range of complicated problems involving different modes of transport, complex domains and boundary conditions, combined transport mechanisms and different length and time scales. These analytical and computational methods are well documented and readily available for application to different processes and systems.

However, there are many problems, particularly in practical processes and systems, where the desired result is known or prescribed, but the conditions needed for achieving this result are unknown. The boundary conditions may also be undefined or unknown. Such problems are known as inverse problems since we seek to determine the conditions that would lead to the known desired outcome. The solution of inverse problems is of interest in many different areas such as biology, medicine, and economics. But this is of particular interest in thermal processes and systems. For instance, in manufacturing and advanced materials processing, the time-dependent temperature, shear, or pressure variation which a component must undergo to obtain desired characteristics is often prescribed from material property considerations. An example of this circumstance is the heat treatment of materials. 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. Similarly, in environmental problems, we may be interested in determining the location and energy discharged by a source such as a fire. But, because of hazardous conditions, we are only able to measure temperature, flow, and concentration far downstream from the source. We can then use an inverse solution to locate the source and obtain its input.

This paper focuses on inverse problems in thermal convection and considers a few fundamental and practical circumstances. The inverse problems resulting from a thermal plume or jet in cross flow and from a heat source on a vertical flat surface are of particular interest in environmental problems and in fire safety. The inverse problem involves determining the strength and location of the heat source or the jet by employing a few selected data points downstream, since an extensive collection of data is often expensive and time consuming. A major concern in inverse solutions is the non-uniqueness of the results obtained. Therefore, optimization techniques are needed to reduce the uncertainty in the results. 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 also 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 an optical fiber drawing 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 high level of accuracy and uniqueness. Again, optimization of the process is used to enhance the efficiency of the solution strategy and obtain an essentially unique solution. These basic approaches can be extended to other inverse convection transport problems. A few examples are given to demonstrate the importance of inverse solutions and the versatility of the presented solution strategies.


Dr. Yogesh Jaluria is Board of Governors Professor and Distinguished Professor at Rutgers, the State University of New Jersey. His research work is in the field of thermal science and engineering, covering areas like convection, fires, materials processing, thermal management of electronics, energy, and environment. He is the author/co-author of 10 books, including 4 extensively expanded revised versions. He is also the editor/coeditor of 15 conference proceedings, 16 books, and 20 special issues of archival journals. He has contributed over 600 technical articles, including over 230 in archival journals and 22 book chapters. He has 3 patents and 7 copyrighted software. He has received several awards and honors for his work, such as the prestigious 2020 Holley Medal from ASME for pioneering achievements in optical fiber drawing, 2010 A.V. Luikov Award from the International Center for Heat and Mass Transfer (ICHMT) in recognition of outstanding work done over his career, the 2007 Kern Award from AIChE, the 2003 Robert Henry Thurston Lecture Award from ASME, and the 2002 Max Jakob Memorial Award, the highest international recognition in heat transfer, from ASME and the AIChE. He received the 2000 Freeman Scholar Award and the 1995 Heat Transfer Memorial Award from ASME. He has served as Department Chairman and as Dean of Engineering. He served as Editor-in-Chief of the Journal of Heat Transfer, as Editor of Computational Mechanics and as Editor of Annual Review of Heat Transfer. He served as the Chair of the Executive Committee of the ASME Heat Transfer Division and that of ICHMT. He has served as conference Chair/co-Chair for several international conferences. He is an Honorary Member of ASME, and a Fellow of AAAS, ASTFE and APS. He served as the founding President of the American Society of Thermal and Fluids Engineers (ASTFE) from 2014 to 2019.