**1. Introduction**

The aim of direct conjugate heat transfer problems was determining the distribution of pressure, velocity, and temperature of the fluid and solid in the analyzed area when boundary conditions are known. In inverse problems, based on temperature measurements at chosen points located within the analyzed domain, boundary conditions are determined. Nonlinear inverse problems are solved iteratively. At every iteration, the direct problem is solved. When analyzed domain has a complex shape, then it is necessary to apply CFD software to solve the direct problem. In particular, when conjugate boundary problem is solved, that is, when the temperature fields in the liquid and solid are determined simultaneously, use of CFD software becomes indispensable. Two inverse problems are solved in this chapter. Identification of boundary conditions in the tube of membrane water wall was carried out in the first example. The subject of the second inverse problem is to identify the temperature of the steam entering the superheater and the identification of the heat transfer coefficient on the outer surface of the superheater. The Levenberg–Marquardt method was used to solve both inverse problems. At every iteration step, a direct conjugate heat transfer problem was solved using the ANSYS/ CFX software. The CFX program was called and controlled by an external program written in Python language. The Levenberg–Marquardt method that was used for solving nonlinear least squares problem was also included in the Python program. This chapter is based mainly on two papers published earlier [1, 2].
