The Discontious Galerkin Mehtod For Non-Fourier Heat Conduction And Analysis Of Entransy Dissipation Field Of Fourier Heat Conduction

Fourier law implies the propagation velocity of thermal disturbance is infinity, but this is impossible physically. In order to eliminate the paradox, Non-Fourier heat conduction models were set up. Non-Fourier heat conduction effect under ultra rapid heat transfer condition is becoming one of research hot spots in the field of heat transfer because of its important academic significance and enormous potential for application. Heat conduction process is a typical irreversible process. The physical quantity "entransy" is a measure of heat capacity of the object. Entransy does not conserved, dissipation is happening in heat conduction process."Entransy dissipation" represents the loss of the ability to conduct heat and the irreversibility of the process. The analysis of entransy dissipation field, on the one hand, is helpful to. get a comprehensive understanding of the dissipation characteristics of heat conduction process, on the other hand, it also has an important role in guiding the practical problems in heat conduction optimization.One-dimensional and two-dimensional Non-Fourier heat conduction problems are solved analytically, the analytical solutions of the temperature field are obtained and a detailed analysis of the characteristics of temperature fluctuations is carried out. The discontinuous Galerkin method of Non-Fourier heat conduction is given. Discontinuous Galerkin method is used for space discretization and the third-order explicit TVD Runge-Kutta scheme is used for time discretization. The relationship between "entransy" and "entransy dissipation" is derived and the entransy dissipation field of one-dimensional objects is analyzed quantitatively. The synergistic effect of linear thermodynamics of irreversible processes is analyzed by introducing the synergistic coefficient and synergistic matrix.