48 research outputs found

    Diffusion Induced Chaos in a Closed Loop Thermosyphon

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    This is the published version, also available here: http://dx.doi.org/10.1137/S0036139996304184.The dynamics of a closed loop thermosyphon are considered. The model assumes a prescribed heat flux along the loop wall and the contribution of axial diffusion. The well-posedness of the model which consists of a coupled ODE and PDE is shown for both the case with diffusion and without diffusion. Boundedness of solutions, the existence of an attractor, and an inertial manifold is proven, and an exact reduction to a low-dimensional model is obtained for the diffusion case. The reduced systems may have far fewer degrees of freedom than the reduction to the inertial manifold. For the three mode models, equivalence with the classical Lorenz equations is shown. Numerical results are presented for five mode models

    Diffusion induced chaos in a closed loop thermosyphon

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    The dynamics of a closed loop thermosyphon are considered. The model assumes a prescribed heat flux along the loop wall and the contribution of axial diffusion. The well-posedness of the model which consists of a coupled ODE and PDE is shown for both the case with diffusion and without diffusion. Boundedness of solutions, the existence of an attractor, and an inertial manifold is proven, and an exact reduction to a low-dimensional model is obtained for the diffusion case. The reduced systems may have far fewer degrees of freedom than the reduction to the inertial manifold. For the three mode models, equivalence with the classical Lorenz equations is shown. Numerical results are presented for five mode models

    Effects of thermal spread on the space charge limit of an electron beam

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    An asymptotic analysis is carried out to calculate the effects of a small thermal spread in the injection energy of an electron beam on its space charge limit. It is found that the space charge limit is lowered proportionally to the beam temperature T near T = O

    Asymptotic Behavior of a Viscoelastic Fluid in a Closed Loop Thermosyphon: Physical Derivation, Asymptotic Analysis, and Numerical Experiments

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    Fluids subject to thermal gradients produce complex behaviors that arise from the competition with gravitational effects. Although such sort of systems have been widely studied in the literature for simple (Newtonian) fluids, the behavior of viscoelastic fluids has not been explored thus far. We present a theoretical study of the dynamics of a Maxwell viscoelastic fluid in a closed-loop thermosyphon. This sort of fluid presents elastic-like behavior and memory effects. We study the asymptotic properties of the fluid inside the thermosyphon and the exact equations of motion in the inertial manifold that characterizes the asymptotic behavior. We derive, for the first time, the mathematical derivations of the motion of a viscoelastic fluid in the interior of a closed-loop thermosyphon under the effects of natural convection and a given external temperature gradient

    Analytical description of chaotic oscillations in a toroidal thermosyphon

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    Multiple time scales and singular perturbation techniques are used to describe the ordinary and the chaotic oscillations due to natural convection in a fluid loop subject to a known external heat flux. The turbulent flow in the loop is modelled using the hydraulic approximation with a quadratic friction law. No steady solutions exist if the heat is added mainly to the top half and extracted from the bottom half of the loop, and two steady convective solutions may exist if one proceeds otherwise; these convective solutions may loose stability when the heat input is shifted from the side toward the bottom. The instability leads, first, to a periodic convective flow and then, after a period doubling Feigenbaum cascade, to a chaotic motion. An intermittent type transition from limit cycles to chaos is also found in the analysis. The transition to chaos can be described in terms of a non-invertible return map, obtained by singular perturbation techniques for loops with long length, when the system becomes strongly dissipative

    Two Phase Flow, Phase Change and Numerical Modeling

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    The heat transfer and analysis on laser beam, evaporator coils, shell-and-tube condenser, two phase flow, nanofluids, complex fluids, and on phase change are significant issues in a design of wide range of industrial processes and devices. This book includes 25 advanced and revised contributions, and it covers mainly (1) numerical modeling of heat transfer, (2) two phase flow, (3) nanofluids, and (4) phase change. The first section introduces numerical modeling of heat transfer on particles in binary gas-solid fluidization bed, solidification phenomena, thermal approaches to laser damage, and temperature and velocity distribution. The second section covers density wave instability phenomena, gas and spray-water quenching, spray cooling, wettability effect, liquid film thickness, and thermosyphon loop. The third section includes nanofluids for heat transfer, nanofluids in minichannels, potential and engineering strategies on nanofluids, and heat transfer at nanoscale. The forth section presents time-dependent melting and deformation processes of phase change material (PCM), thermal energy storage tanks using PCM, phase change in deep CO2 injector, and thermal storage device of solar hot water system. The advanced idea and information described here will be fruitful for the readers to find a sustainable solution in an industrialized society

    Heat Transfer in Energy Conversion Systems

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    In recent years, the scientific community’s interest towards efficient energy conversion systems has significantly increased. One of the reasons is certainly related to the change in the temperature of the planet, which appears to have increased by 0.76 °C with respect to pre-industrial levels, according to the Intergovernmental Panel on Climate Change (IPCC), and this trend has not yet been stopped. The European Union considers it vital to prevent global warming from exceeding 2 °C with respect to pre-industrial levels, since this phenomenon has been proven to result in irreversible and potentially catastrophic changes. These climate changes are mainly caused by the emissions of greenhouse gasses related to human activities, and can be drastically reduced by employing energy systems, for both heating and cooling of buildings and for power production, characterized by high efficiency levels and/or based on renewable energy sources. This Special Issue, published in the journal Energies, includes 12 contributions from across the world, including a wide range of applications, such as HT-PEMFC, district heating systems, a thermoelectric generator for industrial waste, artificial ground freezing, nanofluids, and others

    Heat Transfer

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    Over the past few decades there has been a prolific increase in research and development in area of heat transfer, heat exchangers and their associated technologies. This book is a collection of current research in the above mentioned areas and describes modelling, numerical methods, simulation and information technology with modern ideas and methods to analyse and enhance heat transfer for single and multiphase systems. The topics considered include various basic concepts of heat transfer, the fundamental modes of heat transfer (namely conduction, convection and radiation), thermophysical properties, computational methodologies, control, stabilization and optimization problems, condensation, boiling and freezing, with many real-world problems and important modern applications. The book is divided in four sections : "Inverse, Stabilization and Optimization Problems", "Numerical Methods and Calculations", "Heat Transfer in Mini/Micro Systems", "Energy Transfer and Solid Materials", and each section discusses various issues, methods and applications in accordance with the subjects. The combination of fundamental approach with many important practical applications of current interest will make this book of interest to researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modelling, inverse problems, implementation of recently developed numerical methods in this multidisciplinary field as well as to experimental and theoretical researchers in the field of heat and mass transfer
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