A new meshless numerical approach for studying heat conduction in particulate systems was developed that allows the efficient computation of the temperature distribution and the effective thermal conductivity in particle aggregates. The incorporation of the discretization-corrected particle strength exchange operator in meshless local Petrov–Galerkin calculations is suggested here, which was shown to perform better than previously tested trial functions, regarding the speed of convergence and accuracy. Moreover, an automated algorithm for node refinement was developed, which avoids the necessity for user intervention. This was quite important in the study of particle aggregates due to the appearance of multiple points of contact between particles. An alternative approach for interpolation is also presented, that increased the stability of the methods and reduced the computational cost. Test case models, commercial computational fluid dynamics software, and experimental data were used for validation. Heat transport in various aggregate morphologies was also studied using sophisticated aggregation models, in order to quantify the effect of aggregate fractal dimension on the nanofluid conductivity, targeting eventually the optimization of heat transfer applications. A trend of effective conductivity enhancement upon reduction of the fractal dimension of the aggregate was noted.

A novel dual-time hierarchical approach is developed to link the plasma process to macroscopic transport phenomena in the interior of a dielectric barrier discharge (DBD) reactor that has been used for soil remediation (Aggelopoulos et al 2016 Chem. Eng. J. 301 353–61). The generation of active species by plasma reactions is simulated at the microseconds (µs) timescale, whereas convection and thermal conduction are simulated at the macroscopic (minutes) timescale. This hierarchical model is implemented in order to investigate the influence of the plasma DBD process on the transport and reaction mechanisms during remediation of polluted soil. In the microscopic model, the variables of interest include the plasma-induced reactive concentrations, while in the macroscopic approach, the temperature distribution, and the velocity field both inside the discharge gap and within the polluted soil material as well. For the latter model, the Navier–Stokes and Darcy Brinkman equations for the transport phenomena in the porous domain are solved numerically using a FEM software. The effective medium theory is employed to provide estimates of the effective time-evolving and three-phase transport properties in the soil sample. Model predictions considering the temporal evolution of the plasma remediation process are presented and compared with corresponding experimental data.

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