Inverse Radiative Heat Transfer

Abstract

This focus of this chapter is on inverse problems in radiative heat transfer. Following a brief discussion of the type of inverse problems encountered in this field, a general inverse problem is posed and a formulation to solve it is developed. It is shown that in many cases, the resulting equation is ill-conditioned and requires a special technique called regularization to make it amenable to stable numerical solution. Well-known techniques, such as Tikhonov regularization, and truncated singular value decomposition (TSVD) are discussed and demonstrated through examples. Commonly used gradient-based methods, such as the Newton's method, the conjugate gradient (CG) method, and the Levenberg-Marquardt algorithm are also discussed and demonstrated. Finally, the chapter delves into methods based on metaheuristics, namely simulated annealing and machine learning techniques based on neural networks and other approaches. Practical applications, such as optical tomography, are discussed to close the chapter.