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Fouling is a known dairy industry issue during thermal treatments using a plate heat exchanger (PHE) it directly affects not only energy costs and maintenance but also production, energy and water losses during cleaning operations. Therefore, a considerable attention has been paid to the modelling of the fouling phenomena in order to improve the PHE performances. In this paper, a mathematical model describing the steady state was established for the flow at the macroscopic scale; the model account for constant and turbulent flows between two flat parallel plates at imposed temperature in the presence of a porous medium. The closure k-ε model has been chosen and the conservation of equations has been developed. The numerical procedure adopted was based on the finite volume method on the Fluent CFD software. The accuracy of the Fluent software was validated by comparing our results with those previously published in the literature. The numerical results showed a good reliability of the developed code for both laminar and turbulent regimes of the studied phenomenon. It was able to capture the dynamic and the thermal aspects of the process. The maximum velocity at the output of the channel increased when the thickness of the porous medium was increased. An increase of the average temperature over the whole length of the channel was observed; while a decrease of the average temperature at the outlet of the channel was noticed. The deposit fouling caused additional thermal resistance. Finally, a decrease of the temperature gradient and Nusselt number in the medium of the channel was observed.

The purpose of this paper is to study and perform a numerical analysis of the simultaneous processes of mass and heat transfer during the condensation process of a steam in the existence of noncondensable gas (NCG) inside a descending vertical channel. In this study, the flow of the vapor-air mixture is laminar and the saturation conditions are prevailing at the inlet of the channel. The coupled control equations for liquid film, interfacial conditions, and mixture flow are solved together using the approach of finite volume. Detailed and valuable results are presented both in the liquid condensate film and in the mixing regions. These detailed results contain the dimensionless velocity and dimensionless temperature profiles in both phases, the dimensionless mass fraction of vapor, the axial variation of the dimensionless thickness of the film liquid δ⁎, and the accumulated condensate rate Mr as well the local Nusselt number Nuy. The relative humidity at the inlet varies from 60% to 100% and the inlet temperature from 40°C to 80°C. The results confirm that a decrease in the mass concentration of NCG by the increasing the inlet relative humidity has a direct influence on the liquid film layer, the local number of Nusselt, and the variation of condensation rate accumulated through the channel. The results also designate that an increase of the inlet relative humidity and the inlet temperature ameliorates the condensation process. The comparison made for the coefficient of heat transfer due to condensation process and the condensate liquid film thickness with the literature results is in good concordance which gives more credibility to our calculation model.

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The present work is devoted to the numerical study of steady and laminar mixed convection of nanofluid (water nanoparticles) in a horizontal channel provided with sources of heat at constant temperature, which simulate hot electronic components. The transport equations for continuity, momentum, and energy are solved with finite volume approach using the SIMPLE algorithm. The effective thermal conductivity and the dynamic viscosity of the nanofluid are calculated using, respectively, the Maxwell-Garnett and Brinkman model. The influence of the volume fraction of the nanoparticles 0%≤φ≤10%, Reynolds numbers 5≤Re≤75, the distance between the blocks 0≤d/H≤3, and the types of nanoparticles added (TiO2, Al2O3, CuO, Ag, Cu, and MgO) were investigated and discussed. It emerges from this simulation that the heat transfer increases with the increase in the volume fraction of the nanoparticles and the Reynolds number and decreases with the augmentation of separation distance between heated sources. Moreover, the study shows that the heat transfer is improved by 20% at a solid volume fraction of 10% of Cu nanoparticles.