Based on geometric model of metal fiber sintering nodes, with Caputo fractional differential equations, a time fractional surface diffusion model is established. Numerical solution by finite difference method is made. Numerical simulation of metal fiber sintering process is realized. Numerical simulation of sintering process and variation of neck length as fractional order varies from 0 to 1 are obtained. As the order is fixed at 0.9, sintering process at initial included angles of 0°, 30°, 60° and 90° are simulated. It shows that as the order is equal to 1 the result is consistent with integer order diffusion model. Neck radius with integer order and fractional order grows rapidly in initial stage of sintering. With progress of sintering, fractional simulation of sintering neck length appears local fluctuation, and finally grows at an increase rate greater than the integer order. As the order is fixed, the smaller the initial angle, the greater the rate of growth. The fractional order surface diffusion model describes well the complex change of sintering node during fiber sintering process than the integer order surface diffusion model.

Disturbance equations of velocity and temperature fields are built based on Boussinesq approximation,in which second order and higher-order disturbance of Bénard convection are ignored. Transcendental equations controlling Bénard convection are obtained with non-dimensional treatment of variables. Specific parameters of Bénard convection are obtained,which provide reference and guidance for Bénard convection experiments.

Based on a mathematical model of non-Darcy unsteady seepage flows in low-permeability porous media with moving boundary conditions,a differential equation of propagation velocity for moving boundary was deduced.It indicates that propagation velocity of a moving boundary is proportional to the second derivative of formation pressure with respect to radial distance on the moving boundary.And with Lagrange three-point interpolation formula,finite difference scheme of governing equation near a moving boundary was obtained.Exact position of a moving boundary is able to be tracked.Numerical results show that the front tracking method describes propagation behaviors of moving boundary of non.Darcy unsteady seepage flows in low-permeability porous media well.

Magnetic field molding is a key technique in obtaining hish-performance permanent magnetic materials from strontium ferrite,Based on a mathematical model,we focus on effect of domain center and material geometrical center's relative position on magnetic properties of strontium ferrite.It shows that the external magnetic field atcts on magnetic domain center more obviously as the center shifts downward;as the sample is flat and the external magnetic field vertically acts on the sample absolutely.the effect is the greatest,and strontium ferrite in shape anisotropy can be obtained.