Zygmunt Kolenda

An application of unified least squares method to the mathematical modelling of autocatalytic reactions

Abstract A new approach to the mathematical modelling of mass transfer processes based on the advanced unified least squares method is presented. Contrary to the classical approach, all experimental results are proposed to be included into a mathematical model to enable direct and objective model verification. Special attention is paid to the mass transfer processes during autocatalytic reactions and as an example a numerical mathematical mass transfer model of the autocatalytic dissolution of metallic copper in oxygen-containing ammonia solutions using the rotating disc technique has been worked out.

Entropy-Generation Minimization in Steady-State Heat Conduction

Boundary-value problems of diffusional heat-transfer processes are usually formulated on the basis of the first law of thermodynamics. To obtain the same result when the method of irreversible thermodynamics is applied an additional assumption that the temperature gradient values over the whole domain are reasonably small must be introduced. Such an assumption also means that | T ( x i )− T avg |/ T avg ≪ 1 for all x i ( i = 1, 2, 3), where T ( x i ) is temperature at x i and T avg is the average temperature of the solid. On the basis of the minimum entropy-generation principle, a new formulation of the boundary-value problems is proposed. Applying Euler–Lagrange variational formalism, a new mathematical form of heat-conduction equation with additional heat-source terms has been derived. As a result, the entropy-generation rate of the process can significantly be reduced, which leads to the decrease of the irreversibility ratio according to the Gouy–Stodola theorem. It will be shown that minimization of entropy generation in heat-conduction process is always possible by introducing additional heat sources. The most important conclusion derived from the presented theoretical considerations is directly connected with the solution of the boundary-value problems for solids with temperature-dependent heat-conduction coefficients. In such cases, additional internal heat sources can be arbitrarily chosen as positive or negative. It makes it possible to extend practical applications presented in the literature by Bejan. The problem of heat conduction in anisotropic solids will also be discussed .

Numerical and experimental mathematical modelling of heat and mass transfer processes using unified least squares method

In the case where the mathematical model of heat and mass transfer problems contains measurement results, it becomes possible to determine their influence on the solution and its accuracy using the adjustment procedure based on the least squares principle. In this paper, numerical solutions of the mathematical models of heat conduction and mass transfer processes are presented as examples. Especially unified total least squares method is discussed in detail.

An analysis of heat transfer processes in an internal indirect reforming type solid oxide fuel cell

This paper presents experimental and numerical studies on the fuel reforming process on an Ni/YSZ catalyst. Nickel is widely known as a catalyst material for Solid Oxide Fuel Cells. Because of its prices and catalytic properties, Ni is used in both electrodes and internal reforming reactors. However, using Ni as a catalyst carries some disadvantages. Carbon formation is a major problem during a methane/steam reforming reaction based on Ni catalysis. Carbon formation occurs between nickel and metal-support, creating fibers which damage the catalytic property of the reactor. To prevent carbon deposition, the steam-to-carbon ratio is kept between 3 and 5 throughout the entire process. To optimize the reforming reactors, detailed data about the entire reforming process is required. In the present paper kinetics of methane/steam reforming on the Ni/YSZ catalyst was experimentally investigated. Measurements including different thermal boundary conditions, the fuel flow rate and the steam-to-methane ratios were performed. The reforming rate equation derived from experimental data was used in the numerical model to predict synthetic gas composition at the outlet of the reformer.Copyright