Numerical Of Non-fourier Heat Conduction And Thermal Stress

In most cases the classical Fourier heat conduction law is an excellent description of heat conduction physics. In the practical engineering, heat sources such as lasers and microwaves with extremely short durations, very high frequencies or quite high heat-flux densities, are widely used. Therefore, non-Fourier heat conduction phenomenon has been found in many media. Many researchers have attached much importance to the potentially practical values of the non-Fourier heat conduction in many applications, such as surface thermal processing by laser, rapid metal thawing and solidifying process, temperature control of superconductor, laser and freezing surgery, rapid drying, etc. therefore, the non-Fourier heat conduction has become one of hotspots in the field of heat transfer.Since the non-Fourier heat conduction was postulated in 1985, there are many researchers devouring to accurately predict the non-Fourier temperature fields with a wide range of physical geometry and boundary conditions. Although many researchers obtain the non-Fourier temperature fields, few people give the stress fields associated to the temperature fields. With the improvement of coating technology, layered materials have been widely used. Because the thermal physical parameters are different between two layers, it will cause high stress when sticking together, which may cause cracking. Therefore, it is important to study the stress fields.The main contents include:1) First we deduce the non-Fourier heat conduction equation, and establish the mathematical model in the layered plate. Both backward difference and central difference methods are used to solve the equation. The stability of the backward difference method is proved and a contrast between these two methods is given. At last, we analysis the numerical results.2) Similar to obtain the temperature fields in the layered plate, we first e establish the mathematical model in the layered cylinder. Central difference is used to space discretization, and backward difference is used to time discretization, which result in a system of differential equations. Numerical solutions are obtained in the programming environment MATLAB. At last, we analysis the numerical results.3) Mathematical model in the layered plate are established. Thermal stress fields are made from the calculated temperature field. At last, we take metal base/ceramic coating structure cylinder for example to analysis the numerical results.