**Solving Inverse Heat Transfer Problems When Using CFD Modeling**

Paweł Ludowski, Dawid Taler and Jan Taler

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/63807

### **Abstract**

The chapter presents solving steady-state inverse heat transfer problems using Computational Fluid Dynamics (CFD) software. Two examples illustrate the applica‐ tion of the proposed method. As the first inverse problem determining the absorbed heat flux to water walls in furnaces of steam boilers is presented in detail. Three different measurement devices (flux tubes) were designed to identify steady-state boundary conditions in water wall tubes of combustion chambers. The first meter is made of a short eccentric tube in which four thermocouples on the fire side below the inner and outer tube surfaces are installed. The fifth thermocouple is situated at the rear of the tube on the housing side of the water wall tube. The second meter has two longitudi‐ nal fins that are welded to the bare eccentric tube. In the third option of the instru‐ ment, the fins are attached to the water wall tubes but not to the flux tubes as in the second version of the flux tubes. The first instrument is used to measure the heat flux to water walls made from bare tubes, while another two heat flux tubes are designat‐ ed for measuring the heat flux to membrane walls. Unlike the existing devices, the flux tube is not attached to neighboring water-wall tubes. The absorbed heat flux on the outer surface and the heat transfer coefficient at the inner surface of the flux tube are determined from temperature measurements at internal points. The thermal conduc‐ tivity of the flux-tube material is a function of temperature. The nonlinear inverse problem of heat conduction (IHCP) is solved using the least-squares method. Three unknown parameters are determined using the Levenberg–Marquardt method. In each iteration, the temperature distribution in the cross section of the heat flux instrument is determined using the ANSYS/CFX software.

Another inverse heat transfer problem will be a CFD simulation carried out for the platen superheater placed in the combustion chamber of the circulating fluidized bed (CFB) boiler. Velocity, pressure, and temperature of the steam, as well as the tempera‐ ture of the tube wall with the complex cross section, were computed using the ANSYS/ CFX software. The direct and inverse problems were solved. In the first inverse problem, the heat transfer coefficient on the flue-gas side was determined based on the meas‐

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ured steam temperature at the inlet and outlet of the three pass steam superheater. In the second inverse problem, the inlet steam temperature and the heat transfer coefficient on the flue-gas side were estimated using measured steam temperatures at selected locations of the superheater. The Levenberg–Marquardt method was also used to solve the second inverse problem. 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 algorithm was also included in the Python program.

**Keywords:** CFD modeling, inverse heat transfer problem, heat flux measurement, pulverized coal-fired boiler, furnace, water wall, circulating fluidized bed boiler, plat‐ en superheater
