On the numerical solutions of grain hydration models as moving boundary problems

In this thesis, numerical solutions of one dimensional soybean hydration models with constant and variable diffusion coeffcient under different boundary conditions were investigated. The solutions of soybean hydration models, which can be considered as a diffusion model, have been investigated under constant volume and variable volume. The model which is assumed to have no change in volume during hydration known as Hsu model in the literature was solved by using classical finite difference methods. Stability analysis is made and compared with the result in the literature. Then, the numerical solution of the model was solved considering the volume variation by means of a function expressing the movement of the radius of the soybean and the water intake rates were compared with the situation in the constant volume. In the following section, numerical solutions of soybean hydration models which are considered as moving boundary value problem have been mentioned. The models discussed were solved by the fourth and sixth order compact finite difference methods with variable space grid and boundary immobilization methods under both constant diffusion coefficients and variable diffusion coefficients with different boundary conditions. Stability and sensitivity analyzes of the methods were performed. Finally, soybean hydration model with constant diffusion coeffcient and boundary condition reached to equilibrium moisture at the beginning of hydration at surface were investigated. A differential equation expressing the motion of radius is obtained by using the constrained integral method and numerical solution was made. The results obtained were compared with other methods in the literature.