Steady State Temperature Field Analysis Of Two-Dimensional Graded Plate Under Combined Thermal Boundaries

Functionally gradient materials(2D-FGM)is a new composite material which is composed of two or more kinds of different attribute materials.It has good heat insulation,wear resistance,corrosion resistance,high strength,oxidation resistance and thermal stress relaxation and so on.It is widely used in civil engineering,mechanical manufacturing,aerospace,electrical manufacturing,biomedical and other fields.In this paper,based on the analysis of the existing research results,based on the Fourier heat conduction law,the differential equation of solid heat conduction is established by the first law of thermodynamics.In order to simplify the calculation,the convective heat transfer coefficient and thermal conductivity distribution of2D-FGM plate are in the form of exponential function.Boundary-value problems are limited(The upper boundary of the 2D-FGM plate is the convective heat transfer condition,the left and the right boundary are constant temperature conditions,the undersurface,one is isothermal boundary and the other is constant temperature boundary.).To obtain the steady-state temperature field distribution of the 2D-FGM plane,two methods are used to solve the heat conduction partial differential equation under the convective heat transfer boundary condition.One is the application of the separation of variables method,it can be used to obtain the analytical solution of steady-state temperature field.Another method is to use the weighted residual method to derive the finite element form partial differential equation,and the numerical solution of the steady-state temperature field is obtained by using the finite element method to solve the equation.Finally,the two calculation methods are used to calculate the steady-state temperature field of 2D-FGM plate under the same initial and thermal boundary conditions.Compared with each other,the correctness of the calculation method is verified.In this paper,combined with the practical application environment of FGM plate,through numerical examples,the influence of the thermal conductivity gradient change parameters,the fluid medium temperature,the convective heat transfer coefficient and the geometry dimension of the panel on the distribution of the steady-state temperature field of 2D-FGM plate are analyzed and discussed.The influence of above factors on the ones(undersurface is isothermal boundary or constant temperature boundary)areconsistent,and the effect on the distribution of temperature field is very obvious.The theoretical derivation method and the results of this paper can be used to study the heat conduction problem of FGM plate in thermal environment,can also be used to test other methods which can be used to study the 2D-FGM plate temperature field are correct or not.