We present in this pedagogical paper an alternative numerical method for the resolution of transport phenomena problems encountered in the teaching of the required course on transport phenomena in the graduate chemical engineering curricula. Based on the Chebyshev orthogonal collocation technique implemented in Matlab and Mathematica , we show how different rather complicated transport phenomen...

the kinetic of fischer-tropsch synthesis over a co-precipitated fe-ce catalyst was investigated in a fixed bed micro reactor. experimental conditions were varied as follow: reaction pressure 1-15bar, h¬¬¬2/co feed ratio of 1-3 and space velocity of 3600-5400 h-1 at the temperature range of 270-310°c. 4 models according to the langmuir-hinshelwood-hougen-watson (lhhw) type rate equation were der...

3.1 PRODUCTION OF CLEAN SYNTHESIS GAS......................................................................... 9 3.1.1 Biomass Gasification .............................................................................................. 9 3.1.2 Gas Cleanup.......................................................................................................... 10 3.2 CONVERSION OF SYNTHESIS GAS T...

This paper is intended as a contribution to enhance orthogonal collocation methods. In this, a novel collocation method—TH-collocation—is applied to the biharmonic equation and themerits of such procedure are exhibited. TH-collocation relaxes the continuity requirements and, for the 2D problems here treated, leads to the development of algorithms for which the matrices are sparse (nine-diagonal...

A lumped heat transfer model and parameter estimation technique are proposed for determining key parameters associated with a heat flux Differential Scanning Calorimeter (DSC). The development of a mathematical algorithm utilizing this model and technique is illustrated in Part I of this two-part paper. In Part II, a computational algorithm which has been constructed for the proposed method is ...

Reversible photochromic reactions can be combined with carrier-mediated transport in partially illuminated membranes to achieve very high degrees of flux enhancement. Transport across these membranes can be achieved even against a concentration gradient. Coupled systems of non-linear diffusion-reaction equations for these membranes were solved using the technique of orthogonal collocation on fi...

The utility of orthogonal collocation methods in the solution of optimal control problems relating to Formula One racing is demonstrated. These methods can be used to optimise driver controls such as the steering, braking and throttle usage, and the optimisation of vehicle parameters such as aerodynamic down force distributions. Of particular interest is the optimal usage of energy recovery sys...

Abstract. Stochastic Collocation (SC) has been studied and used in different disciplines for Uncertainty Quantification (UQ). The method consists of computing a set of appropriate points, called collocation points, and then using Lagrange interpolation to construct the probability density function (pdf) of the quantity of interest (QoI). The collocation points are usually chosen as Gauss quadra...