Mathematical modeling of pulp washing on rotary drums and their numerical solution for various adsorption isotherms
The mechanism of the displacement washing of the bed of pulp fibers is mathematically modeled by the basic material balance equation. Linear as well as non-linear adsorption isotherms are used to describe the relationship between the concentration of the solute in the liquor and concentration of the solute on the fibers. In the present study, the numerical solutions are obtained of pulp washing model with different adsorption isotherms. For the numerical solution “pdepe” solver in MATLAB is applied on the axial domain of the system of partial differential equations. Numerical results thus obtained are compared with earlier workers analytically and numerically. The comparison shows that results are in good agreement with both analytically as well as numerically and also show the suitability of the isotherm coupling with the washing model. The technique used in the present investigation is simple, elegant and convenient for solving two point boundary value problems with varying range of parameters.
Washing theory of the porous structure of aggregated materials
Abstract A mathematical model for washing porous materials is developed. Equations based on the pore diffusion controlling the overall washing rate are presented for the concentration of solute as a function of washing period and position in the bed. System differential equations are solved by use of the Laplace transform. The solutions obtained in terms of the transformed variables contain an infinite number of essential singularities which make the method of residues impractical for obtaining an inversion. Approximate solutions using the numerical inverse Laplace transform technique are presented and discussed.
Evaluation of buckling load and dynamic performance of steel shear wall retrofitted with strips made of shape memory alloy
One of the most imperfections of the steel shear wall is out of plane displacements that cause severe damage in both structural and non-structural elements. In this paper, the effects of shape-memory alloys on steel shear walls are investigated. First, a numerical analysis using the finite element method in ABAQUS software has been carried out according to an experimental test. The results of the numerical analysis have been verified with experimental results. Next, shape-memory alloy fibers have been added vertically and horizontally to various parts of the steel shear wall. The results show that retrofitting with the shape-memory alloy reduces the out-of-plane displacement of the steel shear wall under both cyclic and seismic loadings. Besides, the buckling load in the steel shear wall increases when it is retrofitted with the shape-memory alloy. Also, the total out-of-plane movement (accumulated absolute displacements) of the steel shear wall and non-structural damage are controlled by the characteristic of a shape-memory alloy material called “super-elastic”.