12 research outputs found

    Series Solutions for Marangoni Convection on a Vertical Surface

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    The problem of steady, laminar, thermal Marangoni convection flow of Newtonian fluid over a flat surface is investigated. The boundary layer equations for the momentum and energy equations are transformed with the similarity solutions to ODEs to obtain the analytical approximate solutions. The analysis assumes that the temperature variation is a power law function of the location. The approximate solutions to the similarity equations are obtained by exponential series. The effects of the power law exponent and Prandtl number on the velocity and temperature profiles are presented

    Advanced Topics in Mass Transfer

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    This book introduces a number of selected advanced topics in mass transfer phenomenon and covers its theoretical, numerical, modeling and experimental aspects. The 26 chapters of this book are divided into five parts. The first is devoted to the study of some problems of mass transfer in microchannels, turbulence, waves and plasma, while chapters regarding mass transfer with hydro-, magnetohydro- and electro- dynamics are collected in the second part. The third part deals with mass transfer in food, such as rice, cheese, fruits and vegetables, and the fourth focuses on mass transfer in some large-scale applications such as geomorphologic studies. The last part introduces several issues of combined heat and mass transfer phenomena. The book can be considered as a rich reference for researchers and engineers working in the field of mass transfer and its related topics

    Complex Patterns in Extended Oscillatory Systems

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    Ausgedehnte dissipative Systeme können fernab vom thermodynamischen Gleichgewicht instabil gegenüber Oszillationen bzw. Wellen oder raumzeitlichem Chaos werden. Die komplexe Ginzburg-Landau Gleichung (CGLE) stellt ein universelles Modell zur Beschreibung dieser raumzeitlichen Strukturen dar. Diese Arbeit ist der theoretischen Analyse komplexer Muster gewidmet. Mittels numerischer Bifurkations- und Stabilitätsanalyse werden Instabilitäten einfacher Muster identifiziert und neuartige Lösungen der CGLE bestimmt. Modulierte Amplitudenwellen (MAW) und Super-Spiralwellen sind Beispiele solcher komplexer Muster. MAWs können in hydrodynamischen Experimenten und Super-Spiralwellen in der Belousov-Zhabotinsky-Reaktion beobachtet werden. Der Grenzübergang von Phasen- zu Defektchaos wird durch den Existenzbereich der MAWs erklärt. Mittels der selben numerischen Methoden wird Bursting vom Fold-Hopf-Typ in einem Modell der Kalziumsignalübertragung in Zellen identifiziert

    Spacelab Science Results Study

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    Beginning with OSTA-1 in November 1981 and ending with Neurolab in March 1998, a total of 36 Shuttle missions carried various Spacelab components such as the Spacelab module, pallet, instrument pointing system, or mission peculiar experiment support structure. The experiments carried out during these flights included astrophysics, solar physics, plasma physics, atmospheric science, Earth observations, and a wide range of microgravity experiments in life sciences, biotechnology, materials science, and fluid physics which includes combustion and critical point phenomena. In all, some 764 experiments were conducted by investigators from the U.S., Europe, and Japan. The purpose of this Spacelab Science Results Study is to document the contributions made in each of the major research areas by giving a brief synopsis of the more significant experiments and an extensive list of the publications that were produced. We have also endeavored to show how these results impacted the existing body of knowledge, where they have spawned new fields, and if appropriate, where the knowledge they produced has been applied

    Symmetry-based stability theory in fluid mechanics

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    The present work deals with the stability theory of fluid flows. The central subject is the question under which circumstances a flow becomes unstable. Instabilities are a frequent trigger of laminar-turbulent transitions. Stability theory helps to explain the emergence of structures, e.g. wave-like perturbation patterns. In this context, the use of Lie symmetries allows the classification of existing and the construction of new solutions within the framework of linear stability theory. In addition, a new nonlinear eigenvalue problem (NEVP) is presented, whose derivation is completely based on Lie symmetries. In classical linear stability theory, a normal ansatz is used for perturbations. Another ansatz that has been shown in early work is the Kelvin mode ansatz. In the work of Nold and Oberlack (2013) and Nold et al. (2015) it was shown that these ansätze can be traced back to the Lie symmetries of the linearized perturbation equations. Interestingly, knowledge of the symmetries also allows for the construction of new ansatz functions that go beyond the known ansätze. For a plane rotational shear flow, in addition to the normal mode ansatz, an algebraic mode ansatz with algebraic behavior in time t^s (eigenvalue s) can be constructed. The flow is stable according to Rayleigh's inflection point criterion, which is also confirmed by the algebraic mode ansatz. Furthermore, exact solutions of the eigenfunctions can be found and new stable modes can be determined by asymptotic methods. Thereby, spiral-like structures of the vorticity can be recognized, which propagate in the region with time. Another key result of this work is the formulation and solution of an NEVP based on the Lie symmetries of the Euler equation. It can is shown that an NEVP can be formulated for a class of flows with a constant velocity gradient. These include, for example, linear shear flows, strained flows, and rotating flows. The NEVP for linear shear flows shows a relation to experimental data from turbulent shear flows. It can be theoretically shown that the turbulent kinetic energy scales exponentially with the eigenvalue of the NEVP. The eigenvalue is determined numerically using a parallel spectral solver. Initially, nonlinear terms are neglected. The determined eigenvalues are in the range of known literature values for turbulent shear flows. Furthermore, the NEVPs for plane flows with pure rotation and pure strain are solved. It is shown that the flow is invariant to rotation, while oscillatory eigenfunctions are found in the case of strain. In addition, an algorithm to solve the NEVP including the nonlinear terms is presented. The results allow an exciting insight into a new stability theory and form the basis for further investigation and understanding of the full nonlinear dynamics of the fluid flows based on the NEVP

    MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

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    Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

    Generalized averaged Gaussian quadrature and applications

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    A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

    Proceedings of the Second International Colloquium on Drops and Bubbles

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    Applications of bubble and drop technologies are discussed and include: low gravity manufacturing, containerless melts, microballoon fabrication, ink printers, laser fusion targets, generation of organic glass and metal shells, and space processing. The fluid dynamics of bubbles and drops were examined. Thermomigration, capillary flow, and interfacial tension are discussed. Techniques for drop control are presented and include drop size control and drop shape control
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