Numerical Simulation of Convective-Radiative Heat Transfer

This book presents numerical, experimental, and analytical analysis of convective and radiative heat transfer in various engineering and natural systems, including transport phenomena in heat exchangers and furnaces, cooling of electronic heat-generating elements, and thin-film flows in various technical systems. It is well known that such heat transfer mechanisms are dominant in the systems under consideration. Therefore, in-depth study of these regimes is vital for both the growth of industry and the preservation of natural resources. The authors included in this book present insightful and provocative studies on convective and radiative heat transfer using modern analytical techniques. This book will be very useful for academics, engineers, and advanced students

The physics of twisted magnetic tubes rising in a stratified medium: two dimensional results

The physics of a twisted magnetic flux tube rising in a stratified medium is studied using a numerical MHD code. The problem considered is fully compressible (no Boussinesq approximation), includes ohmic resistivity, and is two dimensional, i.e., there is no variation of the variables in the direction of the tube axis. We study a high plasma beta case with small ratio of radius to external pressure scaleheight. The results obtained can therefore be of relevance to understand the transport of magnetic flux across the solar convection zone.Comment: To be published in ApJ, Vol. 492, Jan 10th, 1998; 25 pages, 16 figures. NEW VERSION: THE PREVIOUS ONE DIDN'T PRINT CORRECTLY. The style file overrulehere.sty is include

On the oscillatory hydrodynamic instability of gravitational thermal flows of liquid metals in variable cross-section containers

Natural convective flows of liquid metals in open or closed ducts and containers play a relevant role in a variety of applications in mechanical, materials and nuclear engineering. This analysis follows and integrates the line of inquiry started in past authors’ work about the typical properties of these flows and associated hierarchy of bifurcations in rectangular geometries. The Navier Stokes and energy equations are solved in their time-dependent and non-linear formulation to investigate the onset and evolution of oscillatory disturbances and other effects breaking the initially unicellular structure of the flow. It is shown that a kaleidoscope of oscillatory patterns is made possible by the new degree of freedom represented by the opposite inclination of the walls with respect to the horizontal direction. Even minute variations in the geometry and/or initial conditions can cause significant changes. Multiple states exist which can replace each other in given sub-regions of the space of parameters. Observed regimes include: stationary convection, weakly oscillating rolls, coalescing rolls, traveling waves, and modulated (pulso-traveling) disturbances. Most interestingly, traveling waves can propagate either in the downstream or the upstream direction according to whether the walls are converging or diverging

Understanding growth rate limitations in production of single-crystal cadmium zinc telluride (CZT) by the traveling heater method (THM)

University of Minnesota Ph.D. dissertation. March 2017. Major: Material Science and Engineering. Advisor: Jeffrey Derby. 1 computer file (PDF); viii, 118 pages.Cadmium telluride (CdTe) and cadmium zinc telluride (CZT) are important optoelectronic materials with applications ranging from medical imaging to nuclear materials monitoring. However, CZT and CdTe have long been plagued by second-phase particles, inhomogeneity, and other defects. The traveling heater method (THM) is a promising approach for growing CZT and other compound semiconductors that has been shown to grow detector-grade crystals. In contrast to traditional directional solidification, the THM consists of a moving melt zone that simultaneously dissolves a polycrystalline feed while producing a single-crystal of material. Additionally, the melt is highly enriched in tellurium, which allows for growth at lower temperatures, limiting the presence of precipitated tellurium second-phase particles in the final crystal. Unfortunately, the THM growth of CZT is limited to millimeters per day when other growth techniques can grow an order of magnitude faster. To understand these growth limits, we employ a mathematical model of the THM system that is formulated to realistically represent the interactions of heat and species transport, fluid flow, and interfacial dissolution and growth under conditions of local thermodynamic equilibrium and steady-state growth. We examine the complicated interactions among zone geometry, continuum transport, phase change, and fluid flow driven by buoyancy. Of particular interest and importance is the formation of flow structures in the liquid zone of the THM that arise from the same physical mechanism as lee waves in atmospheric flows and demonstrate the same characteristic Brunt--V ais al a scaling. We show that flow stagnation and reversal associated with lee-wave formation are responsible for the accumulation of tellurium and supercooled liquid near the growth interface, even when the lee-wave vortex is not readily apparent in the overall flow structure. The supercooled fluid is posited to result in morphological instability at growth rates far below the limit predicted by the classical criterion by Tiller et al. for constitutional supercooling

Convective effects and traveling waves in transparent oxide materials processed with the floating zone technique

Zone melting (or zone refining or floating zone process, FZ) is a group of similar methods, specifically conceived for the purification of crystals, in which thermally-driven flows of both gravitational and surface-tension natures are typically produced when the considered material is processed. Since the melt never comes into contact with anything but vacuum (or inert gases), there are no contaminants that the melt may incorporate. Even though compounds with higher purity and improved quality can be obtained with this technique, a typical drawback is represented by the defects potentially induced in the crystalline structure by the unavoidable convection emerging in the fluid phase. In the present chapter, special attention is paid to a specific category of materials known as transparent oxides. A range of conditions is explored, differing in the dominant effect (buoyancy or Marangoni flow), the thermal conditions (heating being provided along the radial or axial direction) and the relative direction of gravity and applied temperature gradient. The hallmark of the entire chapter is our commitment to identify situations in which “waves” are produced and provide a systematic classification of such convective instabilities together with a description of related features based on advanced numerical simulations

Convective motions in the scrape-off layer of magnetically confined plasmas

Magnetic confinement devices utilize magnetic fields to confine hot plasma with the aim of generating thermonuclear fusion. At the plasma edge, in the so-called scrape-off layer (SOL), turbulent motions are responsible for transporting plasma from the core confinement region towards the material surfaces. It has been universally observed that SOL turbulence is characterised by large, intermittent fluctuations, often called filaments or blobs, which dominate the particle transport and enhance the plasma interaction with the surrounding material boundaries. This is problematic as plasma-wall interaction can potentially damage plasma-facing components and shorten the life-time of the device. A full understanding of filament dynamics is therefore essential for the successful operation of future fusion experiments and reactors. The dominant mechanism behind the generation of turbulent motions at the plasma edge is thought to be the interchange instability, due to pressure gradients and magnetic field curvature. In this thesis we study a two-dimensional interchange model based on the Braginskii fluid equations, in an effort to shed light on the fundamental properties of the onset of instability. We study interchange dynamics in two different settings: first, we restrict our attention solely to the dynamics in the SOL; next, we extend our considerations to the coupled interaction between the core plasma and the SOL. In both cases we characterise the onset of instability and perform an extensive analysis to describe how the behaviour of the system varies as a function of plasma parameters

Modeling of directional solidification of multicrystalline silicon in a traveling magnetic field

Melt flow plays an important role in directional solidification of multicrystalline silicon influencing the temperature field and the crystallization interface as well as the transport of impurities. This work investigates the potential of a traveling magnetic field (TMF) for an active control of the melt flow. A system of 3D numerical models was developed and adapted based on open-source software for calculations of Lorentz force, melt flow, and related phenomena. Isothermal and non-isothermal model experiments with a square GaInSn melt were used to validate the numerical models by direct velocity measurements. Several new 3D flow structures of turbulent TMF flows were observed for different melt heights. Further numerical parameter studies carried out for silicon melts showed that already a weak TMF-induced Lorentz force can stir impurities near to the complete mixing limit. Simultaneously, the deformed temperature field leads to an increase of the deflection of crystallization interface, which may exhibit a distinct asymmetry. The numerical results of this work were implemented in a research-scale silicon crystallization furnace. Scaling laws for various phenomena were derived allowing a limited transfer of the results to the industrial scale