Doctoral Degrees (Applied Mathematics)

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Browsing Doctoral Degrees (Applied Mathematics) by Subject "Foamed materials"

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    Mathematical pore-scale modelling of kinematic and geometric properties of fibrous porous media
    (Stellenbosch : Stellenbosch University, 2023-12) Maré, Esmari; Fidder, Sonia; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics Division.
    ENGLISH ABSTRACT: This study involves the mathematical modelling of permeability ( of both the Darcy and Forchheimer flow regimes) and specific surface area of fibre-type and foamlike porous media using geometric models. Several existing models for predicting these properties have been studied in the literature, with the Representative Unit Cell (RUC) model being of particular interest due to its simple rectangular geometry and good performance compared to other models and experimental data from the literature. This study includes a comparative analysis of the permeability and specific surface area prediction of different versions of the RUC model for fibrous media involving the 2D RUC models for in-plane and through plane flow, the 3D RUC model, the two-strut RUC models for in-plane and through plane flow, and the three-strut RUC model. It furthermore incorporates novel contributions such as the adaptation of the three-strut ( or foam) RUC model by adding solid material to account for the observed lump at the intersection of struts in actual metal and ceramic foams. The RUC models are also adapted analytically to take secondary effects such as compression or variable rectangular geometry into account. Additionally, the models are adapted to include changes in the predictions of the permeability due to the Klinkenberg effect, an effect that accounts for the increase in the permeability of gas flow as opposed to that of a liquid. The novelty of this study lies in the incorporation of these effects into the model predictions, which extends the range of applicability of the proposed models beyond those available in the literature. In order to ensure the user-friendliness of the analytical models provided, the predictive equations are expressed in terms of measurable macroscopic parameters. Furthermore, the models are evaluated through comparison with other models from the literature as well as available experimental and numerical data, which yield results that are satisfactory. The findings contribute positively towards industrial applications such as filtration and heat transfer processes, facilitating their effective operation by means of analytical modelling and analysis of the physical flow processes involved.