Solubility based calculations using the present solution model can be used for steady-state design of reactors for synthesis of zeolites A and X when nucleation of desired phases is assured.
In opposition to network compensation, where standard regulators are used, the presented solution integrates network with plant.
Using the present analytical solution, the hydrodynamic effects of the angle of incidence, the draft and the width of the structure on the wave forces and hydrodynamic coefficients are discussed in detail which may provide some useful information for the design of rectangular structures in oblique seas.
The approximate solutions using the present method are in high agreement with the exact solutions for (alpha=1).
Using our method, taking n = 1, N = 11,51, x i = i − 1 N − 1, i = 1, 2, ⋯, N Open image in new window, the absolute errors ∣un,N x) − u(x) ∣ between the approximate solution and exact solution are given in Tables 1 and 2. Numerical results compared with that of Tirmizi et al. [15] show that the accuracy of approximate solutions obtained using the present method is higher.
The solution obtained using the present method shows that this approach can effectively solve the problem.
To allow for a ready use of the present solution an efficient MATLAB implementation is provided as supplementary material to this paper.
Subsequently, the present solutions are used to study two important topics in piezoelectric fiber composites, i.e., (1) stress and electrical field fluctuations in the microstructure, (2) the macroscopic effective electroelastic moduli.
Numerical procedures have been developed and used to validate the present solution by comparison with available literature results.
As seen from Figure 3, the present solution obtained using the limit equilibrium method significantly improves the solution of Chen and Rosenfarb (1973) and Soubra (2000) by 42.79% and 17.01% respectively for ϕ = δ = i = 45°.
