Research And Application Of Hyperbolic Lattice Boltzmann Method

With the development of ultra-short pulse laser processing technology and ultra-low temperature technology,scholars have gradually noticed that the traditional Fourier’s law cannot accurately describe the heat transfer behavior in those processes,and named the non-diffusive behavior existing in the heat transfer process as non-Fourier effect.To this end,scholars have proposed a number of theories to correct the deviation between the experiment and Fourier’s law.The most widely used is the heat transfer relaxation time theory(or single-phase relaxation time theory,SPL),which makes the original thermal differential equations from elliptic partial differential equations to hyperbolic partial differential equations.SPL theory can explain some of the non-Fourier effects,but it makes the governing equation describing the law of heat transfer into a complex non-linear wave equation.Although analysis solutions can be obtained for some simple cases,in most cases,the numerical method must be used.Lattice Boltzmann method(LBM)is a new numerical method which developed rapidly in the past thirty years.It has been widely used in the fields of computational fluid mechanics and applied mathematics.However,there is not much discussion about LBM in non-Fourier heat transfer problems.In view of the above reasons,in order to clarify the mechanism of non-Fourier heat transfer problems,this paper investigate non-Fourier heat conduction problems through LBM by a combination method of theoretical analysis and numerical calculations.The specific research content and main results of this article include the following:(1)In view of the actual engineering needs of installing fins on the surface of microelectronic components to achieve rapid heat dissipation,LBM was used to analyze the periodic non-Fourier heat conduction problems in rectangular and triangular fins.Through the simulation analysis of the efficiency of fins,it is known that under the combined effect of periodic boundary conditions and non-Fourier effects,rectangular fins are more efficient,and materials with a large relaxation time when selecting fins are more worthy of consideration.(2)Combining the classic LBM and SPL theory,a new LBM form that can directly solve the non-Fourier heat conduction problem is deduced.This form can be directly degraded to the classic LBM form.Due to the differential equation is a hyperbolic equation which can be used to describe the non-Fourier heat conduction,this form of LBM is called a hyperbolic lattice Boltzmann equation(HLBM).HLBM was combined with two temperature model(TTM)to simulate the heat transfer process of gold film irradiated by femtosecond laser,and compared with the traditional two temperature model.The simulation results show that the result obtained by HLBM-TTM is closer to experimental values.(3)Aiming at the problems of rapid melting and low-temperature freezing,HLBM was combined with the enthalpy method to simulate the non-Fourier heat conduction problem with the solid-liquid phase change.The effects of the non-Fourier effect and solid-liquid thermal diffusivity ratio on the temperature field,interface position,and melting rate were discussed.The simulation results show that the non-Fourier effect causes the phase change to proceed slowly.Increasing the thermal diffusivity of the liquid phase helps to strengthen the phase change process.(4)Aiming at the non-Fourier heat conduction problem in a moving medium,the HLBM is generalized by reconstructing the equilibrium distribution function to enable it to solve the non-Fourier convection-diffusion equation.The comparison between the numerical solution and the exact solution shows that they are basically the same,thus HLBM is reliable.