The present paper describes how to apply the Chebyshev orthogonal collocation technique to solve steady-state and unsteady-steady two-dimensional problems. All problems are solved using one single computer algebra, Mathematica . The problems include: (1) steady-state heat transfer in a rectangular bar, (2) steady-state flow in a rectangular duct, (2) steady-state heat transfer in a cooling cyli...

For a nonlinear functional f , and a function u from the span of a set of tensor product interpolets, it is shown how to compute the interpolant of f(u) from the span of this set of tensor product interpolets in linear complexity, assuming that the index set has a certain multiple tree structure. Applications are found in the field of (adaptive) tensor product solution methods for semilinear op...

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...

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...

In this paper, the orthogonal collocation technique is utilized to solve the Poppe method equations for heat and mass transfer in counter flowing wet-cooling towers. The six differential equations for unsaturated and supersaturated air from the Poppe method are simplified, yielding three differential equations that use the Heaviside function. The humidity ratio is demonstrated to be a finite po...

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...

Rigorous mathematical modeling of adsorption processes in packed beds involves time-consuming computations which are considered as the fundamental weakness of such thorough mathematical models. Thus, reducing the computation time was a key factor in improving adsorption mathematical models. In order to achieve this goal, an attempt was made to know how much using different numerical methods inf...