The main aim of the work of this PhD was to investigate the need and the applicability of a fast and easy method in order to define quantities when transport phenomena are under investigation. After the introduction and the background review presented in the first chapter, Chapter 2 investigates the fundamental transport processes, affected by advection and diffusion, for all the used scales, microscopic, mesoscopic and macroscopic. Chapter 2 includes a brief but detailed discussion regarding the most widely used CFD models and the modules utilized by the selected CFD-ACE. A big part of this study, aims to develop a fast and easy method to match the macroscopic quantities (such as adsorption efficiency) during a scale transition process, from mesoscopic to macroscopic (scale-up), or to microscopic (scale-down) and vice versa, geometries. In order to be able to transit from one scale to another, the fundamental transport processes (laminar flow, convection, diffusion and heterogeneous reaction) were described in detail for all three scales, following the same flow conditions given by the use of the dimensionless Peclet number. Furthermore, a surface catalytic reaction on species mass fractions is analyzed. The reactants are consumed on the catalytic surface and their mass fraction as expected decreases as the exit of the porous media is reached. On the other hand, the steam and carbon dioxide are produced due to the oxidization reaction and their mass fractions increase towards the exit. It should be noted that, for the microscopic case (sphere-in-cell) and the mesoscopic scale (assemblage of spheres), which represent a more analytical view of the porous media, formed a gradient from the catalytic surface towards the pores due to the combinatory effect of the prevailing transport phenomena. Next, a method of matching the geometrical parameters when scale transition occurs is proposed, underlying the necessary steps that should be followed. As the first step the calculation of the geometrical characteristics of the detailed geometry is a necessity as it will be the base where the transition will be relied on. Then, the inlet mixture flow needs to be adjusted in order to preserve the Peclet number for all of the scales. Since the diffusion coefficients are practically constant, this adjustment can be made only by adapting the velocity to the necessary value. Finally, the last two most important adjustments are required to be made in order to have an identical characterization of the geometry without any discrepancies. The characteristic ratio, S/V of the porous material, is a measurement value of the available surface where the reaction may occur. After studying the scale transition problem, three case studies implementing the transport phenomena (as presented and discussed in Chapter 2) were analyzed. The three studies considered the applicability of the mathematical simulation of transport phenomena in the case of water remediation, heating of marine heavy oil and migration in packed foods. The first study simulates the case of water remediation, investigating the adsorption process from both experimental and theoretical (modeling) point of view. The adsorption process of phosphate onto Phoslock, is an increasingly used worldwide restoration tool aiming the control a minimization of phosphorus in natural water ecosystems. Bench-scale batch experiments were performed examining Phoslock’s efficiency as an adsorbent and detailed simulations were carried out, allowing a better understanding of the phosphate removal process. The second case study simulated the heat transfer case utilized in an industrial scale problem investigated a rather common marine practice. In marine industry, the use of superheated water in heating coils for heating up heavy fuel oil is essential. The goal of this study was to estimate the necessary size and length under the assumption of an insulated tank. A parametric analysis was also performed to identify the relative influence of each parameter on the process performance. The concept of migration from polymeric packaging materials to food and food simulants, under the environmental conditions expected during the food products' complete life cycle, was investigated for the third case study. The aim of this case study was to consider these models and weight them against their extensive use. After having identified the areas of their inadequacies in validating the migration during food process applications were found to potentially affect food quality rather than safety. This study outlined and proposed specific and eventually more complete directions, for future modeling approaches regarding the food–packaging interactions, comprehensively involving the storage environment in terms of both conditions and constituents. The outcome of this work is the proposal to go beyond the consideration of the diffusion process as being the single mechanism to describe the migration from packaging to foodstuffs, but rather to incorporate more complicated phenomena (sorption, surface reactions, etc.) to overcome the above‐mentioned discrepancies. Overall, in the present thesis the transport phenomena, were analytically studied from modelling point of view and it was proved that the use of simulation with a computerized mathematical model imitates the behavior of a real-world process or system over time. Simulations are used to describe and analyze the behavior of a system when asking "what-if" questions about real-life systems. Furthermore, mathematical models could be very helpful tools for designing artificial systems, while the easy and quick description of phenomena occurring in porous media could be feasible.