Janusz Donizak

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 .

Experimental analysis of enclosure aspect ratio influence on thermo-magnetic convection heat transfer

Experimental analysis of strong magnetic field influence on paramagnetic fluids convection in rectangular enclosures with aspect ratios (AR=height/width) 0.5 and 2.0 was conducted. For this purpose, enclosure filled with paramagnetic fluid was placed inside superconducting magnet in Rayleigh-Benard configuration and temperature measurements of the fluid were performed, with and without magnetic field induction. On the basis of performed research, analysis of heat transfer and character of the flow was conducted. Obtained results allowed characterization of fluid behavior and demonstrated that the aspect ratio has an immense influence on quantitative heat transfer in the system.

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.

Influence of a strong magnetic field on a paramagnetic fluid's convection in systems with different aspect ratios

Influence of a strong magnetic field gradients on a natural convection of a paramagnetic fluid in enclosures with aspect ratios (AR=height/width) 0.5 and 2.0 was investigated. Performed experiments allowed to determine the impact of strong magnetic field on heat transfer and the nature of the flow, showing that strong magnetic field enhances Nusselt number and rapidly changes the character of the flow. Conducted Fast Fourier analysis also allowed to determine the aspect ratio influence on investigated systems.