## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Research on geometric inverse problem based on the firefly conjugate gradient method

**ABSTRACT**

In this paper the two-dimensional steady-state heat transfer geometric inverse problem is solved using the Finite Element Method (FEM), Conjugate Gradient Method (CGM), and Firefly Algorithm (FA). Based on the finite element method for solving the forward heat transfer model, and based on continuous iterative optimisation of the conjugate gradient method, the accuracy of the error function of the measured and estimated values is kept within a certain range, so that the geometry of the object under test can be calculated in an inverse way. In the study of the forward problem, the temperature field distribution is solved using circular pipes as the research objects, and the feasibility of applying the finite element method to heat transfer problems is verified. The inverse problem takes the circular tube as the object and considers two different corrosion defects on the inner wall of the circular tube. Simultaneously, the firefly algorithm is introduced based on the conjugate gradient method to stochastically optimize the temperature data and suppress the fluctuation of the inversion result. Numerical experiment results indicate that the method in this paper can perform more accurate geometric shape recognition when there is a certain temperature measurement error or the temperature measurement information is relatively complete.

**KEYWORDS**

PAPER SUBMITTED: 2022-12-30

PAPER REVISED: 2023-01-30

PAPER ACCEPTED: 2023-02-08

PUBLISHED ONLINE: 2023-03-11

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