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This paper aims to present development and application of the Bayesian inverse approach for retrieving parameters of non-linear diffusion coefficient based on the integral information.

The Bayes formula was used to construct posterior distribution of the unknown parameters of non-linear diffusion coefficient. The resulting aposteriori distribution of sought parameters was integrated using Markov Chain Monte Carlo method to obtain expected values of estimated diffusivity parameters as well as their confidence intervals. Unsteady non-linear diffusion equation was discretised with the Global Radial Basis Function Collocation method and solved in time using Crank–Nicholson technique.

A number of manufactured analytical solutions of the non-linear diffusion problem was used to verify accuracy of the developed inverse approach. Reasonably good agreement, even for highly correlated parameters, was obtained. Therefore, the technique was used to compute concentration dependent diffusion coefficient of water in paper.

An original inverse technique, which couples efficiently meshless solution of the diffusion problem with the Bayesian inverse methodology, is presented in the paper. This methodology was extensively verified and applied to the real-life problem.

The purpose of this paper is to present a numerical and mathematical model of a moulding process of a dry electrical transformer. Moreover, the calculated results are reported and compared with experimental measurements.

An experimental rig, for carrying out and monitoring a moulding process, has been designed and built. Two experiments were preformed. First was an isothermal experiment in which an analog liquid was used. The second experiment was a non‐isothermal one in which an epoxy resin was used. For the rig geometry, the numerical mesh, with the use of the commercial code Gambit, was built. All necessary physical properties, including viscosity, surface tension and contact angle of fluids used in the experiments were measured.

The Euler approach for modelling multiphase flow with a free surface is addressed in the presented work. Comparison of the computational results with measurements on the designed experimental rig revealed good agreement. Comparison was carried out through measurements of free surface characteristic features captured with a digital camera and through temperature measurements for the nonisothermal case. Richardson extrapolation method was successfully applied to estimate the numerical discretisation error, proving that a grid independent solution was obtained.

This paper is useful for researchers and industrialists involved in the modelling of moulding processes, giving guidance on the available mathematical models appropriate for this kind of problem. Moreover, it provides valuable information as to how to perform validation and verification procedures for such real‐life processes.

The purpose of this paper is to overview successful approaches to the computational simulation of real fluid (R744 – carbon dioxide (CO₂)) flow within an ejector is presented. Important issues such as the ejector geometry and its optimisation, the adapted equations of state and the proposed models of the process, fluid parameters, etc., are examined and critically discussed. Whenever possible, the discussed models are experimentally validated. In the conclusion, some trends in future research are pointed out.

Flow within CO₂ ejector is generally transcritical and compressible. Models existing in the literature are shortly described and critically compared. Whenever possible, those models were validated against the experimental data. In a model validation process, the primary and secondary mass flow rates as well as the pressures at the selected points in the mixing section and diffuser were compared, showing a satisfactory agreement between experimental and computational results.

Developed CO₂ ejector flow models are tested in few industrial applications. All these initiatives bring solutions which are interesting and very promising from technological point of view.

This is an extensive overview of successful approaches to computational simulation of the real fluid (R744 – CO₂) flow within ejector. It brings many useful information.