Two-dimensional non-Fickian diffusion equation is solved analytically under arbitrary initial condition and two kinds of periodic boundary conditions. The concentration field distributions are analytically obtained with a form of double Fourier series, and the damped diffusion wave transport is discussed. At the same time, the numerical simulation is carried out for the problem with homogeneous boundary condition and arbitrary initial condition, which shows that the concentration field gradually changes from the initial distribution to the steady distribution and it changes faster for the smaller Vernotte number. The numerical results agree well with the experimental results.
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