The mathematical modeling of a Pressure Swing Adsorption (PSA) system is discussed in detail for the Skarstrom cycle of two-bed process. The system is used to get pure oxygen product from the air with the use of zeolite 13X as an adsorbent. There are complex partial differential equations (pdes) which may not solve by analytical methods. There is no provision for solving it in any other softwar...

A pertraction membrane plant is designed for the treatment of wastewater containing hexavalent chromium and its recovery for industrial reuse. Pertraction is a new technology that combines the efficiency of emulsion liquid membranes with the advantages of using hollow fibber membrane modules. It can selectively remove low concentrated metals from process streams and reach high concentrations of...

In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and depends on a finite number of random variables. The numerical scheme consists of a finite difference or finite element method in the physica...

The main aim of this paper is to study the material removal phenomenon using the finite element method (FEM) analysis for orthogonal cutting, and the impact of cutting speed variation on the chip formation, stress and plastic deformation. We have explored different constitutive models describing the tool-workpiece interaction. The Johnson-Cook constitutive model with damage initiation and damag...

The non-local hyperbolic partial differential equations have many applications in sciences and engineering. A collocation finite element approach based on exponential cubic B-spline and quintic B-spline are presented for the numerical solution of the wave equation subject to nonlocal boundary condition. Von Neumann stability analysis is used to analyze the proposed methods. The efficiency, accu...

The Cahn–Hilliard equation plays an important role in the phase separation in a binary mixture. This is a fourth order nonlinear partial differential equation. In this paper, we study the behaviour of the solution by using orthogonal cubic spline collocation method and derive optimal order error estimates. We discuss some computational experiments by using monomial basis functions in the spatia...

Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, tota...

In this paper, we provide an analysis on the collocation methods(CM), which uses a large scale of admissible functions such as orthogonal polynomials, trigonometric functions, radial basis functions and particular solutions, etc. The admissible functions can be chosen to be piecewise, i.e., different functions are used in different subdomains. The key idea is that the collocation method can be ...

In this work, we consider an elliptic partial differential equation with a random coefficient solved with the stochastic collocation finite element method. The random diffusion coefficient is assumed to depend in an affine way on independent random variables. We derive a residual-based a posteriori error estimate that is constituted of two parts controlling the stochastic collocation (SC) and t...

This paper is concerned with the numerical analysis of the behavior of a homogeneous tubular reactor in which a cubic autocatalytic reaction is coupled to diffusion and convection transport. The set of one-dimensional partial differential equations describing the reaction-diffusion-convection system is analyzed using different standard reduction techniques (finite difference, orthogonal colloca...