Non-Fourier Effect Response Analysis Of Thermal Boundary Conditions In Cylindrical Coordinate

Thermal conduction is a common phenomenon in nature,and since Fourier summarized the law of thermal conduction,Fourier’s law of thermal conductivity has become the basis for solving all thermal conduction problems.In recent years,with the development of a series of high-tech such as short-pulse laser heating and rapid solidification of metals,as well as the emergence of ultra-freezing and thawing technology of human organs in medicine,the impact of non-Fourier effect has become increasingly prominent.Many people only consider the relaxation time in the control equation when considering the non-Fourier effect,and do not consider the relaxation time in the boundary condition equation,here,this paper selects the simplest one-dimensional cylindrical coordinate system under the thermal conduction model,makes a study on the temperature change when the boundary condition has a non-Fourier effect,and briefly analyzes the stress change under the boundary condition under the cylindrical coordinate and the non-Fourier thermal conduction in the control equation.Since the non-Fourier differential equation for thermal conductivity was proposed,many mathematical models have been invented to describe this process.Many people have done a lot of calculations on the solution of this equation under different conditions,and developed many mathematical methods to predict the non-Fourier temperature field under different geometries and different boundary conditions.At present,most people have only analyzed the temperature field of non-Fourier thermal conductivity,but there are few studies based on the stress field caused by changes in the non-Fourier thermal conduction temperature field.In order to meet the needs of engineering applications,the application of coating structure has been well developed,for the non-Fourier effect of bilayer materials,this paper also did a study,and also made a theoretical analysis of its temperature change and thermal stress change.The main research content of this project is the temperature field and stress field under non-Fourier thermal conductivity conditions,which have the following three aspects:1.According to Fourier’s law of thermal conductivity,the non-Fourier thermal conductivity partial differential equation is extrapolated,and the non-Fourier thermal conductivity model of cylindrical and double-layer cylinders is established.The numerical solution method of Laplace inverse transform was used to analyze the obtained results,and the results of Fourier heat conduction were compared,and the difference between the two was obtained.2.Based on the obtained temperature results of non-Fourier thermal conduction,obtain the expression of thermal stress,study the radial stress and the change of circumferential stress of the cylinder,and compare the thermal stress under Fourier thermal conductivity conditions.3.Instead of considering only the non-Fourier effect in the control equation,this paper also considers the non-Fourier effect in the boundary conditions,and when the relaxation time changes,study the relationship between the maximum value of temperature and the relaxation time and the relationship between thermal stress and relaxation time.