在本文对竖直圆柱表面自然对流换热系数反演这一研究中，通过粒子群算法中的

In this paper, the inversion of the natural convection heat transfer coefficient on the vertical cylindrical surface is used to control and optimize the natural convection heat transfer coefficient that needs to be inverted by the particle position in the particle swarm algorithm. This paper uses undetermined coefficients and function approximation to invert the natural convection heat transfer coefficients that vary with time. According to the temperature change law of the positive problem constructed in Section 2.1, Newton's cooling law is considered on the upper surface of the vertical cylinder. As the heating progresses, the upper surface temperature shows an exponential function change, and the corresponding natural convection conversion obtained by Newton's cooling law The thermal coefficient also presents an exponential function-type change trend. The second-order exponential function model used in this paper is as follows:

In this paper, the inversion of natural convection heat transfer coefficient on the surface of vertical cylinder is studied, and the natural convection heat transfer coefficient to be inverted is controlled and optimized through the particle position in particle swarm optimization algorithm. In this paper, the natural convection heat transfer coefficient varying with time is inversed by using undetermined coefficient and function approximation. According to the temperature change law of the forward problem constructed in Chapter 2.1, Newton's cooling law is considered on the upper surface of the vertical cylinder. With the progress of heating, the upper surface temperature shows an exponential function change, and the corresponding natural convection heat transfer coefficient obtained from Newton's cooling law will also show an exponential function change trend. The second-order exponential function model adopted in this paper is as follows:

In this paper, in the study of inversion of natural convection heat transfer coefficient of vertical cylinder surface, the natural convection heat transfer coefficient which needs to be inverted is controlled and optimized by particle position in particle swarm optimization. In this paper, the undetermined coefficient and function approximation are used to invert the natural convection heat transfer coefficient with time. According to the temperature change law of the positive problem constructed in chapter 2.1, Newton's cooling law is considered on the upper surface of vertical cylinder. With the heating, the temperature of the upper surface changes exponentially, and the corresponding natural convection heat transfer coefficient obtained by Newton's cooling law also shows an exponential trend. The second-order exponential function model adopted in this paper is as follows: