The standard dielectric barrier discharge (DBD) plasma actuator, in which an asymmetric arrangement of electrodes leads to momentum coupling into the surrounding air, has already demonstrated its capability for flow control. The effect of some parameters such as dielectric thickness, dielectric temperature, voltage amplitude, driving frequency, different configurations and arrangements on actuator performance are examined. The new configuration of DBD which uses multiple encapsulated electrodes (MEE) has been shown to produce a superior and more desirable performance over the standard actuator design. As the number of encapsulated electrodes increases and other variables such as the driving frequency and voltage amplitude are considered, finding the optimum actuator configuration for increasing the induced velocity becomes a challenge. The surrogate modelling optimisation provides a cheap and yet efficient method for systematically investigating the effect of different parameters on the performance of the plasma actuator. The effect of the optimum actuator configuration on the aerodynamic performance of an aerofoil under leading edge separation and wake interaction conditions is examined. The plasma actuator is placed at the leadingedge of a symmetric NACA 0015 aerofoil which corresponds to the location of the leading edge slat. The aerofoil is operated at a chord Reynolds number of 0.2×10 6. Surface pressure measurements along with the mean velocity profile of the wake using pitot measurements are used to determine the lift and drag coefficients, respectively. Particle image velocimetry (PIV) is also utilised to visualise and quantify the induced flow field. In comparison with reported literature on the standard DBD configuration, the MEE setup employed here is shown to provide a better means of flow control for the control of aerofoil separation. The characteristicsof a DBD plasma actuator when exposed to an unsteady flow generated by a shock tube is also investigated. This type of flow, which is often used in different studies, contains a range of flow regimes from sudden pressure and density changes to relatively uniform high-speed flow regions. A small circular shock tube is employed along with the schlieren photography technique to visualise the flow. The voltage and current traces of the plasma actuator are monitored throughout, and using the well established shock tube theory the change in the actuator characteristics are related to the physical processes which occur inside the shocktube. The results show that not only is the shear layer outside of the shock tube affected by the plasma but the passage of the shock front and high-speed flow behind it also greatly influences the properties of the plasma.

The research, which is described in the following chapters is designed to continue the studies made by Jordinson into the behaviour of small disturbances of constant frequency in the Blasius boundary layer over a flat plate. In his work a numerical method due to Osborne was used to solve the problem of the nonlinearly occurring eigenvalue which is associated with the Orr- Sommerfeld equation in the case of space amplification. A digital computer, the Edinburgh University KDF 9, performed the calculations. The present thesis first of all extends the Orr- Sommerfeld equation to include the effect of the growing thickness of the boundary layer upon the eigenvalues, and then it discusses a possible stage where the disturbance grows to such a size that the linearised theory no longer completely represents its behaviour. Following a chapter of introduction a mathematical model is devised which is based upon a Fourier Series expansion of the flow stream function in terms of frequency harmonics. This model is intended to represent the beginnings of finite disturbance development by showing the presence of second harmonic oscillations and the effect of the transfer of energy and momentum between the perturbation and the mean flow. The third chapter analyses the importance of the normal component terms of the Blasius mean flow from an empirical viewpoint. These are the terms which are responsible for the thickening of the boundary layer and it is shown, that in order to be consistent with the assumptions of boundary layer theory their retention is necessary. The topic of a linear disturbance is then discussed and the Orr-Sommerfeld equation, together with the contribution due to boundary layer thickening, is derived. In addition a proof is sketched which demonstrates that the boundary conditions of the differential equation are unaltered by the presence of the extra terms. Since the eigenvalue character of the linearised problem is of the same nature as Jordinson's problem, the same method of solution is used and the details are given in the fourth chapter. A rational discretisation of the differential equation is performed in order to reduce the truncation error of the approximation. This is followed by a discussion of Osborne's method. Tests carried out by varying the data parameters, the discrete step length, and the range of integration demonstrate remarkable stability. The results given in the fifth chapter show that the boundary layer is rendered slightly less stable if the effect of growing thickness is included, and that the curve of neutral stability is enlarged. This enlargement is in itself not sufficient to account for the differences existing between the predictions of theory and the results of experiment, particularly at lower Reynolds Numbers, but an argument later developed explains why these differences occur. The non-linear investigations ere discussed in the next two chapters. In the first of these the Fourier-Series mathematical model is studied more closely and details are given of the deter¬ mination of second harmonic oscillation values, distorted mean flow components and Reynolds stress. The effect of finite dis¬ turbance development upon the first harmonic of a perturbation. arises in the form of a set of coupled differential equations which are solved by a straightforward iterative procedure. The results of the investigations which are all given for a fixed fre¬ quency, show first of all that the Reynolds stress distribution begins to oscillate as the Reynolds Number increases and that its amplitude is increased. They also show that a perturbation of fixed signal size has a far greater effect at higher Reynolds Number upon mean flow and first harmonic component distortion Results of the distribution of first and second harmonic values are also given. The final chapter discusses a futuro research topic and summarises the preceding work. The computer programs for the calculation were developed from Jordinson's program and were run initially on the KDF 9 computer and latterly on the IBM 360/5C and Systems 4/75 computers in Edinburgh University. Details of the extensions to the existing subroutines are given in the Appendix.

The dispersed phase that accompanies enclosure fires, for example, soot, ash, sprinkler droplets and extinguishing powder, could exert a significant influence on the dynamics of the background fluid. In this thesis, the results of a numerical study into the effects of this dispersed phase on the flow in a fire compartment are presented. A two-dimensional computational fluid dynamics solver, with appropriate approximations for low Mach number flows and mathematical sub-models for two­phase flows, has been developed in order to simulate fire induced convective motions in planar compartments. The description of the dispersed particulate is based on a two­continuum approach, whereby the dispersed phase and the gaseous phase are assumed to be two mutually interacting and penetrating continua. In this thesis, two 'passive' models and an 'active' model of the dispersed phase are considered. In the passive models the particulate acts as a tracer only and has no hydrodynamical influence on the gas phase. The second passive model differs from the first in that the production of gases in the fire compartment, for example arising from combustion or propellant gases due to extinguishment of the fire, is taken into account. This second passive model more accurately predicts the growth of pressure in a sealed fire compartment for weak fires. As the volume fraction of the particulate increases the spatial-temporal hydrodynamic influence exerted on the gaseous flow by the dispersed phase becomes significant and, under certain conditions, a passive representation is insufficient. An active one­temperature and one-velocity model is proposed which is appropriate for the description of a hydrodynamically active particulate with an instantaneous velocity and thermal relaxation time. In this thesis, computational fluid dynamics is used as a tool in order to characterise the applicability of the passive models and the active model. The ability of the passive models to accurately predict the growth of pressure in a compartment for 'surface' fires, for example smouldering combustion and weak fires, is investigated. The active model is used to study the hydrodynamics of powder extinguishing media in a compartment with an open doorway.

Ce travail de thèse porte sur l’instabilité de Faraday qui résulte de l’oscillation verticale d’une couche de liquide. L’objectif est d’apporter une vérification expérimentale précise des résultats issus d’une analyse de stabilité linéaire. À basse fréquence, la longueur d'onde caractéristique de cette instabilité est de l'ordre des dimensions de la cellule expérimentale. Théoriquement les longueurs d'onde associées aux modes disponibles sont discrétisées selon le confinement latéral. Mathématiquement, la condition qui facilite les calculs est une condition limite pariétale sans contrainte, ce qui est irréaliste en raison des couches limites visqueuses et de l’hystérésis capillaire au point de contact du fluide avec les parois. Ici, nous présentons l'étude expérimentale d'un système de basse fréquence conçu pour se rapprocher d’une condition pariétale sans contrainte, par un choix judicieux de liquides. Le système a permis d’obtenir expérimentalement des seuils d’apparition de l’instabilité très proches des prédictions théoriques basées sur une analyse de stabilité linéaire. Les différences observées sont associées au ménisque formé par le liquide sur la paroi ainsi qu’au film liquide se formant à la paroi lors de l'excitation des ondes. Les écarts avec la théorie dû à ces imperfections semblent être fonction de la structure du mode et la périodicité des ondes. De plus, les ondes générées par le ménisque conduisent à des seuils inférieurs aux prévisions. Ceci indique une résonance mixte entre l'instabilité paramétrique et les oscillations forcées du ménisque où chaque contribution peut être contrôlée par un forçage caractérisé par deux fréquences. / This work is an inquiry into the current understanding of experimental single-mode Faraday waves, from the perspective of linear stability theory. At low frequency, the characteristic wavelength is of the order of the cell dimensions, and theoretically the wavelengths associated with the modes available for excitation are discretized by the sidewall boundary condition. Mathematically, the condition which eases manipulation is a stress-free sidewall condition, which is unrealistic due to viscous boundary layers and capillary hysteresis. We report the experimental investigation of a low frequency system designed to approximate this condition, by careful choice of the fluid liquids and thereby increasing the relative importance of the interior damping. The design has permitted close connection between the experimental thresholds and the predictions, contrasting the traditional approach of phenomenologically measuring the mode dissipation and treatment as a single degree of freedom system. Non-ideal behavior of the sidewall persists, evident by the contact meniscus and the sidewall film which is formed during wave excitation. The presence of these non-idealities is translated to trends in the deviation between the observed and predicted thresholds, depending upon the mode structure and wave periodicity. The presence of harmonically excited waves from the meniscus seems to result in observation of amplitudes consistently lower than the predictions, indicating a mixed resonance between the parametric instability and the forced meniscus oscillations. Furthermore, it is seen this interaction can be adjusted by excitation with two commensurate parametric frequencies.

Σε έναν μεγάλο αριθμό βιομηχανικών διεργασιών απαιτείται η διαδικασία της μίξης δύο ή περισσοτέρων υλικών για την παρασκευή του τελικού προιόντος.Ο πιο συνηθισμένος τρόπος μίξης είναι η ανάδευση ενός ή περισσοτέρων υλικών σε μια δεξαμενή. Η δεξαμενή καθώς και ο υπόλοιπος απαραίτητος εξοπλισμός όπως το στροφείο που πραγματοποιεί την ανάδευση, πρέπει να είναι με τέτοιο τρόπο σχεδιασμένος ώστε να είναι σε θέση αφ’ενός να φέρει εις πέρας την διαδικασία της μίξης και την παραγωγή του τελικού αποτελέσματος, τηρώντας κάποιες προδιαγραφές, αφ’εταίρου να είναι μηχανικά ευσταθής και ασφαλής. Λόγω διαφόρων αναγκών κατά την παραγωγική διαδικασία είναι απαραίτητη η αντικατάσταση των σωληνώσεων για την μεταφορά ενός υγρού από μια δεξαμενή επεξεργασίας ή αποθήκευσης σε άλλη, με την χρησιμοποίηση συστημάτων μεταφοράς της δεξαμενής. Άλλοι λόγοι επιβάλλουν την ταυτόχρονη μεταφορά και ανάδευση υλικών σε μια δεξαμενή, ή η δεξαμενή ανάδευσης να είναι στερεωμένη σε μεταλλικά ικριώματα ή να είναι στερεωμένη πάνω σε μεταλλικούς δοκούς. Έτσι, στην περίπτωση του συστήματος μεταφοράς μιας δεξαμενής από ένα σημείο σε κάποιο άλλο πρέπει κανείς να εξετάσει τις διαταραχές που υφίσταται το υγρό που περιέχει η δεξαμενή για παράδειγμα, εξαιτίας της κίνησης της δεξαμενής, για την αποφυγή υπερχείλισης του υγρού. Επιπλέον στην περίπτωση όπου τα υλικά που περιέχει μια δεξαμενή αναδεύονται κατά την μεταφορά της ή αυτή είναι στερεωμένη σε μεταλλικά ικριώματα, πρέπει να εξετάσει κανείς τις επιδράσεις της ανάδευσης στην σταθερότητα της δεξαμενής, και συνεπώς και στο σύστημα στήριξης ή μεταφοράς της ώστε να παρέχεται η αξιοπιστία και η ασφάλεια του συστήματος. Στην παρούσα εργασία χρησιμοποιήθηκε μια δεξαμενή ανάδευσης που περιείχε νερό, και μελετήσαμε τις επιδράσεις που είχε η ανάδευση του νερού, στην ισορροπία της δεξαμενής, καταγράφοντας την κατανομή του βάρους της. Στο πρώτο κεφάλαιο δίνονται διάφοροι ορισμοί και εξισώσεις που περιγράφουν ένα ρευστό και την κίνησή του. Στο δεύτερο κεφάλαιο περιγράφονται οι μονάδες που απαρτίζουν ένα σύστημα ανάδευσης, και στο τρίτο τα αποτελέσματα των φορτίσεων της δεξαμενής κατά την ανάδευσή της, στην πειραματική διάταξη που πραγματοποιήθηκε. / In a large number of industrial processes the mixing of two or more materials is necessary for the production of a final product. The most common form of mixing is the stirring of one or more materials in a mixing tank. The tank as well as the rest of the necessary equipment, for example the impeller which is responsible for the stirring process, must be designed in such a way that it is able to successfully complete the mixing process and produce the final product, according to certain specifications, while keeping mechanical stability and safety. Different needs may arise during the production of a final product. One of these may be the need to replace the pipes which are responsible for transferring one liquid material placed in a tank to another tank, with the use of a transferring system for the tank. Another need may be the simultaneous transfer and stirring of materials in a tank or the stirring tank may need to be stabilized on metal beams. In all these cases, one must evaluate the disturbances and the vibrations which effect the liquid and the tank, in order to ensure the efficiency, stability and safety of the mixing and transfer systems. In the present experimental thesis paper, a stirring tank was used that contained water, and the effects of the stirring of the water on the stability of the tank were studied and analyzed, through the recording of the distribution of the weight during the mixing. The first chapter contains definitions and equations that describe the motion of a fluid. The next chapter describes the parts that comprise a stirring system. Lastly, the third chapter contains the results, the analysis, and the conclusions of the experimental process.

Ce travail de thèse est une contribution à l’analyse de bifurcation des écoulements fluides avec prise en compte des interactions fluide-structure. Les phénomènes d’instabilité en interaction fluide-structure apparaissent dans de nombreux domaines de la vie courante ou industriels comme, par exemple : le flottement d’un drapeau dans le vent ou bien l’écoulement au sein d’échangeurs thermiques sur les sites de production d’énergie, l’écoulement autour des câbles sous-marins pour l’extraction de matières premières ou la fixation des plateformes off-shore, l’écoulement autour des structures aéronautiques ou navales. Dans ces situations, un phénomène complexe de vibration des structures induite par vortex peut se produire. L’objectif de la thèse est de proposer un algorithme permettant l’analyse de stabilité de tels systèmes. Ainsi, le couplage original d’une méthode de perturbation d’ordre élevé (Méthode Asymptotique Numérique - MAN) à une discrétisation spatiale permettant la prise en compte des interactions fluide-structure est proposée. À cet effet, une description purement eulérienne du mouvement est retenue. L’interaction fluide- structure est décrite au moyen d’une méthode de frontières immergées (MFI) à forçage continu (méthode de pénalisation) et discret (méthode Ghost-Cell). La présence d’obstacles au sein de l’écoulement est obtenue au moyen de la méthode de Level-Set. En complément, un intégrateur temporel des équations du mouvement associant la MAN, la MFI et une technique d’homotopie est proposé. L’ensemble de ces algorithmes est appliqué à des problèmes d’écoulement incompressible, à faible nombre de Reynolds, d’un fluide visqueux newtonien en présence d’obstacles solides rigides (fixes ou mobiles). L’analyse de stabilité d’un écoulement dans une conduite avec expansion/contraction soudaine (bifurcation stationnaire), et autour d’un cylindre (bifurcation de Hopf) est traitée. L’analyse transitoire d’un écoulement autour d’un cylindre rigide et mobile est également proposée. Les résultats obtenus permettent d’évaluer la précision et la performance des algorithmes proposés. Ainsi, les résultats de cette thèse permettent de conclure sur le bien-fondé de l’approche et constituent une première étape vers l’analyse de stabilité d’écoulements en présence de structures complexes, représentatifs de situations réelles / This thesis is a first contribution to the bifurcation analysis of fluid flows by taking into account fluid-structure interactions. Instability with fluid-structure interactions appears in many areas of everyday life or industry such as, for example: flag floating in the wind, flow within heat exchangers for energy production, flow around submarine cables for the extraction of raw materials or the fixing of off-shore platforms, flow around aeronautical or naval structures. In these situations, complex vortex-induced vibrations of the structures can occur. The aim of the thesis is to propose an algorithm allowing stability analysis of such systems. Thus, an original coupling of a high order perturbation method (Asymptotic Numerical Method - ANM) to a spatial discretization which takes into account fluid-structure interactions is proposed. For this purpose, a purely Eulerian description of the motion is retained. Fluid-structure interaction is described using an immersed boundary method (IBM) with continuous forcing (penalization method) and discrete (Ghost-Cell method) forcing. The presence of bodies within the flow is obtained by means of the Level-Set method. In addition, a time integrator of the governing equations associating ANM, IBM and homotopy technique is proposed. All these algorithms are applied to analyse incompressible flows, at low Reynolds number, of a Newtonian viscous fluid in the presence of rigid solids (fixed or moving). Bifurcation analysis of flows in a channel with sudden expansion / contraction (stationary bifurcation), or around a cylinder (Hopf bifurcation) are carried out. Transient analysis of a flow around a moving rigid cylinder is also proposed. Our results make it possible to evaluate accuracy and performance of the proposed algorithms. Thus, thesis results allow to conclude on the validity of the proposed approach. Finally, this thesis work constitutes a first step towards flow stability analysis in the presence of complex structures, representative of real situations.

Particles within an ultrasonic standing wave experience an acoustic force causing the particles to move to certain positions within the acoustic field. This phenomenon can be used to manipulate particles and so provides a means to separate, concentrate or trap particles, cells or spores. The work described is applied to a micro-engineered flow-through device for processing small samples and incorporates a fluid filled chamber of depth typically between 100 and 200μm, and therefore approaches microfluidic dimensions. The successful design and subsequent performance of such devices rely on the predictability of particle trajectories which are influenced predominantly by acoustic and fluid flow fields. Therefore, the majority of this research seeks an understanding of the nature of these fields and, in turn, reliable simulation of particle trajectories. Computational fluid dynamics (CFD) modelling is used to develop a robust 2-dimensional model of the device’s microchannels and is used to predict the presence of eddy regions, associated with the etch fabrication techniques, which are likely to disrupt the separation process. Based on a geometric study, simulations and subsequent test results on a fabricated device have revealed geometric modifications which minimise these eddy flows and promote the existence of laminar flow within the main channel of the device. Finite element analysis (FEA) provides a method to investigate the 2-dimensional characteristics of the acoustic field and reveals variations in acoustic pressure across the width of the device, giving rise to lateral radiation forces frequently reported in similar ultrasonic devices. This work investigates acoustic enclosure modes in 2 or 3-dimensions as a possible cause of these lateral variations, with modelled results matching well with experiment. A particle force model has also been developed which predicts the motion of particles through the device, and by which concentration and separation performance may be calculated. This tool is used to investigate acoustic design, operating conditions and separation performance for both the micro-engineered device and a device based on a quarter-wavelength, providing valuable insight into various trends observed. The novelty in this work is the application of macro-scale numerical techniques to microengineered ultrasonic particle manipulators and the execution of an extensive analysis of the design and operation of such devices. These analyses have demonstrated, and therefore have explained, various phenomena associated with the fluid and acoustic fields, and how they influence particle separation performance. The development of similar devices can be aided by the use of the numerical simulation methods featured throughout this thesis.

This thesis is concerned with the modelling of miscible fluid flow through porous media, with the intended application being the displacement of oil from a reservoir by a solvent with which the oil is miscible. The primary difficulty that we encounter with such modelling is the existence of a fingering instability that arises from the viscosity and the density differences between the oil and solvent. We take as our basic model the Peaceman model, which we derive from first principles as the combination of Darcy’s law with the mass transport of solvent by advection and hydrodynamic dispersion. In the oil industry, advection is usually dominant, so that the Péclet number, Pe, is large. We begin by neglecting the effect of density differences between the two fluids and concentrate only on the viscous fingering instability. A stability analysis and numerical simulations are used to show that the wavelength of the instability is proportional to Pe^−1/2, and hence that a large number of fingers will be formed. We next apply homogenisation theory to investigate the evolution of the average concentration of solvent when the mean flow is one-dimensional, and discuss the rationale behind the Koval model. We then attempt to explain why the mixing zone in which fingering is present grows at the observed rate, which is different from that predicted by a naive version of the Koval model. We associate the shocks that appear in our homogenised model with the tips and roots of the fingers, the tip-regions being modelled by Saffman-Taylor finger solutions. We then extend our model to consider flow through porous media that are heterogeneous at the macroscopic scale, and where the mean flow is not one dimensional. We compare our model with that of Todd & Longstaff and also models for immiscible flow through porous media. Finally, we extend our work to consider miscible displacements in which both density and viscosity differences between the two fluids are relevant.

Cette thèse porte sur deux problèmes différents d'interaction fluide-structure dans le cas tridimensionnel: dans le premier problème, on effectue une étude théorique d'un problème d'interaction entre une structure déformable et un fluide Newtonien incompressible (Chapitre 2); dans le deuxième problème, on considère un problème inverse géométrique associé à un système fluide-corps rigide (Chapitre 3). Pour le premier problème nous démontrons un résultat d'existence et d'unicité des solutions fortes, en utilisant, pour la structure élastique, une approximation des équations de l'élasticité linéaire par un système de dimension finie. Dans le deuxième problème, nous démontrons le caractère bien-posé du système associé et nous montrons un résultat d'identifiabilité: la forme d'un corps convexe et sa position initiale sont identifiées par la mesure, en un temps positif, du tenseur de Cauchy du fluide sur une partie ouverte de la frontière extérieure. De plus, un résultat de stabilité pour ce problème est abordé. / This thesis deals with two different fluid-structure interaction problems in the three dimensional case: in the first problem, we make a theoretical analysis of a problem of interaction between a deformable structure and an incompressible Newtonian fluid (Chapter 2); in the second problem, we consider a geometrical inverse problem associated to a fluid-rigid body system (Chapter 3). For the first problem, we prove a result of existence and uniqueness of strong solutions by using, for the elastic structure, an approximation of the equations of linear elasticity by a finite-dimensional system. In the second problem, we prove the well-posedness of the corresponding system and we show an identifiability result: the form of a convex body and its initial position are identified by the measurement, at a positive time, of the Cauchy force of the fluid on an open part of the exterior boundary. Moreover, a stability result for this system is tackled.

Η εν λόγω διπλωματική εργασία αναφέρεται σε κάποια γενικά στοιχεία των μεθόδων ελέγχου του οριακού στρώματος και εστιάζεται στον έλεγχο του οριακού στρώματος με εφαρμογή της μεθόδου απορρόφησης – έγχυσης. Πιο συγκεκριμένα, στο πρώτο κεφάλαιο, με γενικό τίτλο “Οριακό Στρώμα”, αναφέρονται κάποια σύντομα ιστορικά στοιχεία και εισάγεται η έννοια του οριακού στρώματος. Στη συνέχεια, και αφού αποσαφηνιστεί η έννοια του οριακού στρώματος με τη βοήθεια εικόνων και γραφικών, εισάγονται τα χαρακτηριστικά μεγέθη αυτού. Το κεφάλαιο κλείνει με μια περιγραφή του φαινομένου της αποκόλλησης του οριακού στρώματος και των συνεπειών που η αποκόλληση αυτή επιφέρει στη ροή. Στο δεύτερο κεφάλαιο, με γενικό τίτλο “Έλεγχος του Οριακού Στρώματος”, περιγράφονται συνοπτικά οι βασικές μέθοδοι ελέγχου του οριακού στρώματος καθώς και τα πιο διαδεδομένα πεδία εφαρμογής της κάθε μιας εξ’ αυτών. Συγκεκριμένα, αναφέρονται οι μέθοδοι Κίνησης του Στερεού Ορίου (Motion of the Solid Wall), Επιτάχυνσης του Οριακού Στρώματος (Acceleration of the Boundary Layer - Blowing), Ψύξης του Τοιχώματος (Cooling of the Wall), Έγχυσης Διαφορετικού Αερίου (Injection of a Different Gas), Πρόληψης της μετάπτωσης της ροής σε τυρβώδη με κατάλληλη διαμόρφωση της γεωμετρίας του στερεού (Laminar Aerofoils) και η παράγραφος κλείνει με μια πιο εκτενή περιγραφή της μεθόδου της Απορρόφησης (Suction). Στο τρίτο κεφάλαιο, που φέρει το γενικό τίτλο “Εξισώσεις Κίνησης και Εξισώσεις Οριακού Στρώματος για Ομογενή, Ασυμπίεστα, Πραγματικά Ρευστά”, παρατίθενται οι εν λόγω εξισώσεις, ώστε να χρησιμοποιηθούν στη συνέχεια, και γίνεται μια σύντομη αναφορά στον τρόπο που, ιστορικά, αυτές παρήχθησαν. Το τέταρτο κεφάλαιο, με τίτλο “Θεωρητική Μελέτη της Μεθόδου της Απορρόφησης”, προχωράει τη μελέτη της μεθόδου απορρόφησης/έγχυσης σε επίπεδο μαθηματικών εξισώσεων. Πιο συγκεκριμένα, εισάγονται τα βασικά στοιχεία της θεωρίας και στη συνέχεια, με ένα συνδυασμό αναλυτικών και αριθμητικών διαδικασιών, πραγματοποιείται η μελέτη της απορρόφησης σε δύο συγκεκριμένα παραδείγματα. Τέλος, στο πέμπτο κεφάλαιο, με τίτλο “Εφαρμογή Απορρόφησης/Έγχυσης σε Μαγνητοϋδροδυναμική Συμπιεστή Ροή Στρωτού Οριακού Στρώματος”, μελετάται η μόνιμη, στρωτή, διδιάστατη, μαγνητοϋδροδυναμική ροή, συμπιεστού οριακού στρώματος που δημιουργείται πάνω από λεπτή, επίπεδη επιφάνεια (πλάκα), με αντίξοη βαθμίδα πίεσης και μεταφορά θερμότητας και μάζας, καθώς και τα αποτελέσματα της εφαρμογής απορρόφησης ή έγχυσης στο παραπάνω πρόβλημα. Πιο συγκεκριμένα, μετά από μια σύντομη ιστορική εισαγωγή επί του θέματος, ακολουθεί η περιγραφή του προβλήματος, καθώς και η αδιαστατοποίηση των εξισώσεων που το διέπουν. Στη συνέχεια, ακολουθεί η περιγραφή της αριθμητικής μεθόδου που χρησιμοποιείται για την επίλυση των αδιαστατοποιημένων εξισώσεων και παρατίθενται τα αποτελέσματα που προκύπτουν από τη διαδικασία αυτή της αριθμητικής επίλυσης. Το κεφάλαιο κλείνει με μια συνοπτική παράθεση των συμπερασμάτων της μελέτης του κεντρικού προβλήματος του κεφαλαίου. / This master thesis refers to some general elements of boundary layer control methods and focuses on the method of suction-injection. In particular, in Chapter I, which is simply entitled “Boundary Layer”, a short reference to some historical facts associated with this subject is being made and the general idea of boundary layer is being introduced. Following, the idea of boundary layer is being clarified with the aid of some pictures and some graphics. The chapter ends with an introduction to the phenomenon of boundary layer separation. In Chapter II, carrying the general title “Boundary Layer Control”, a short description of some of the most basic methods of boundary layer control is given and the general conditions under which each method is more effective are being briefly stated. In particular, the methods which are brought up are Motion of the Solid Wall, Acceleration of the Boundary Layer – Blowing, Cooling of the Wall, Injection of a Different Gas, Laminar Aerofoils, and the chapter ends with a more extensive description of the method of Suction. In Chapter III, entitled “Equations of Motion and Boundary Layer Equations for Homogenous, Non-Compressible, Real Fluids”, the above equations are described, with the purpose of further use in the following chapters and a short reference to the way those equations were historically introduced is being made Chapter IV, with the general title “Theoretical Study of the Method of Suction”, carries the study of the method of suction-injection to the context of mathematical equations. More specifically, basic elements of the theory are being introduced and, after that, with a combination of analytical and arithmetical techniques, two simple examples are being studied. Finally, in Chapter V entitled “Application of Suction-Injection to Magnetohydrodynamic Compressible Flow of a Laminar Boundary Layer”, the steady, laminar, two dimensional, magnetohydrodynamic flow of the compressible boundary layer which is formed over a thin flat plate, with an adverse pressure gradient and mass and heat transfer is being studied along with the results of suction-injection in the above problem. In particular, after a short historical introduction follows the description of the problem and the normalization of the equations which describe it. Then follows the description of the arithmetical method and the program being used, and the results of this procedure are stated in the next paragraph. The chapter closes with a brief description of the facts which result from the general study of the main problem of this chapter.