R-3 Repository :: Browsing by Author "Bayazitoglu, Yildiz"

Browsing by Author "Bayazitoglu, Yildiz"

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A fundamental study of spray evaporative cooling
(1979) Grissom, William M.; Wierum, Frederic A.; Chapman, Alan J.; Bayazitoglu, Yildiz
"Spray evaporative cooling" is defined as the mode of spray cooling heat transfer for which no liquid film would form on a heated surface of infinite extent. The heat flux during this mode is simply that required to vaporize all of the impinging spray. The lower surface temperature range limit for the existence of spray evaporative cooling is determined experimentally to be an essentially linear function of the impinging spray mass flux. This suggests a conduction-controlled droplet evaporation mechanism. An analytical model of this form gives fairly good agreement with the experimental measurements at atmospheric pressure. The effect of lowering the surrounding pressure appears to be a decreased "wettability" of the liquid (distilled water) upon the aluminum surface. This would account for the correspondingly lower droplet evaporation times observed. "Spray film cooling" is defined as the mode of spray cooling heat transfer for which a liquid film would exist upon the heated surface. An analysis of this mode is of importance in determining several characteristics of the spray evaporative cooling mode. At atmospheric pressure the mechanism governing spray film cooling appears to be quite similar to that of ordinary pool boiling with little or no dependence upon the liquid film thickness. At vacuum pressures spray film cooling appears to be governed by the simple mechanism of heat conduction through the liquid film, and very much dependent upon the liquid film thickness. The "Leidenfrost State" is defined as the mode in which impinging droplets rebound off of the surface. The initiation of the Leidenfrost state imposes: the upper range limit for the existence of spray evaporative cooling. The surface temperature at which this state is initiated is found to be very much a function of the surrounding pressure. Interestingly, this variation with pressure is such that it counteracts the variation of the lower range limit with pressure, resulting in essentially the same maximum possible heat flux during spray evaporative cooling for all surrounding pressures.
An analytical model for near-infrared light heating of a slab by embedded gold nanoshells
(2006) Tjahjono, Indra Kurniawan; Bayazitoglu, Yildiz
Exposed to spectral and uniform light, a one-dimensional, conducting and radiatively participating medium due to embedded absorbing and scattering gold nanoshells is solved. P1 Approximation method is used to solve the radiative transfer equation and finite difference explicit method is used to find the temperature distribution having both boundaries subjected to convection. The host medium was transparent to spectral radiation and the temperature distribution is obtained when the temperature of the irradiated boundary reaches the desired temperature such that any temperature in the medium does not exceed the melting temperature of the host medium. Variation of the concentration and configuration of gold nanoshells are found to change the radiative transfer spectrum that leads to an alteration in the local heat generation spectrum and the desired temperature distribution.
An efficient computational scheme for solving nonlinear, two-point boundary-value problems via the method of adjoint variables
(1981) Coker, Estelle M.; Miele, Angelo; Bayazitoglu, Yildiz; Wierum, Frederic A.
A method for solving nonlinear differential equations of the form x - (x,t) =, £ t <_ 1, subject to boundary conditions of the form w(x()) = , ÿ(x(l)) = / is developed. It is assumed that t is a scalar, x and are n-vectors, u is a p-vector, and ^ is a q-vector, with p + q ** n. The method is based on the consideration of the performance index P, the cumulative error in the differential equations and the boundary conditions. The differential equations and the boundary conditions are linearized about a nominal function x(t); the linearized system is embedded into a more general system by means of a scaling factor a, <_ a <_ 1, applied to each forcing term. The variations per unit stepsize A(t) = Ax(t)/a are governed by a system of n linear differential equations, subject to p separated initial conditions and q separated final conditions. Then, the system is solved employing the method of adjoint variables. The scaling factor a is determined by a bisection process, starting from a = 1, so as to ensure the decrease of the performance index P. Convergence to the desired solution is achieved when the inequality P £ e is met, where e is a small, preselected number. Two updating schemes are considered, called Scheme (a) and Scheme (b) for easy identification. In Scheme (a), the initial point x() is updated according tox(O) =x() +aA(), and the new nominal function x(t) is obtained by forward integration of the nonlinear differential equations. In Scheme (b), the function xCt) is updated according to x(t) = x(t) + aA(t). Four numerical examples are solved using the ITEL AS/6 computer of Rice University. The computational scheme developed here for the method of adjoint variables is particularly efficient, in that it minimizes the algorithmic work per iteration, namely, the number of integrations to be performed in order to solve the linear, two-point boundary-value problem. In the method developed by Roberts and Shipman (Ref. 4), the number of integrations is n, where n is the number of state variables. In this thesis, we show that the number of integrations can be reduced to q, where q < n is the number of final conditions.
Analysis of a Liquid Droplet Radiator by Galerkin's method with an improved profile
(1989) Krause, Paul John; Bayazitoglu, Yildiz
The Liquid Droplet Radiator is a proposed lightweight radiator for the dissipation of waste heat generated by power plants in space. The hot working fluid is sprayed into space as coherent streams of tiny, discrete droplets, which then cool by transient radiative heat transfer, and are later collected for recirculation. An improved, hybrid trial function is presented for the solution by Galerkin's method of the equation of radiative transfer, which governs the emission, scattering, and absorption within the layer formed by the droplet streams. The trial function compensates for the effects of the particular solution corresponding to the inhomogeneous source term. The method of analysis is demonstrated for a source function having a polynomial profile. The improved-profile Galerkin solution is then applied to a non-dimensional analysis of gray, isotropically, scattering droplet layers which are asymmetrically heated by normal, isotropic, external radiation. The analysis identifies a critical value for the magnitude of external radiation. Droplet layers exposed to external radiation greater than this critical value will heat initially, and then either recover and cool, or for magnitudes sufficiently stronger than the critical value will achieve a state of equilibrium.
Carbon nanotubes thermal conductivity analysis using molecular dynamics simulations
(2010) Toprak, Kasim; Bayazitoglu, Yildiz
Non-equilibrium molecular dynamics simulations are used to determine the thermal conductivities of (5,5) single wall carbon nanotubes. By fixing the temperatures of opposing ends of an armchair single wall carbon nanotube with a Nose-Hoover thermostat, the length dependence of thermal conductivities of single wall carbon nanotubes were studied in vacuum. Specifically, single wall carbon nanotubes of 12.3 nm, 24.6 nm, and 36.9 nm lengths with varying fixed end temperatures were analyzed to determine thermal conductivities. In addition, the fixed end temperature lengths of single wall carbon nanotubes were varied to see convergence of the temperature profiles. The equivalent thermal resistance of single wall carbon nanotube bundle in water was modeled using the one dimensional heat conduction equation. The preliminary effective thermal conductivity of the system was calculated with different nanotube structures for a length ranging from 500 nm to 3000 nm to observe effective thermal conductivity variations. The effective thermal conductivity increases when the volume fraction of SWNTs and the nanotube length increase.
Combined Convection of Packer Fluid Flow between Vertical Parallel Plates
(2017-04-20) Xu, Heqi; Bayazitoglu, Yildiz
Packer fluid whose function is to prevent or tremendously reduce the heat transfer rate which would occur from the production tubing area to the production casing region is being studied in recent decades because of its wide applications in Oil & Gas Industry. Reduction of heat transfer rate can lead to the minimization of trapped annular pressures and reduction of contents of hydrates resolvable in production fluids. This paper utilizing ANSYS Fluent gives numerical solution for the combined convection problem of this packer fluid. Because of the geometry of the tubing-to-casing annulus, it is modeled as vertical and long parallel plates in ANSYS Fluent geometry part where the width of the duct is small comparable to the length of the duct. The flow is assumed to lie in laminar region and ANSYS Fluent laminar flow model is utilized. How different parameters including aspect ratio, temperature difference and inlet velocity will have effects on the convective heat transfer rate are analyzed respectively by measuring and calculating dimensionless parameters including Nusselt number, Reynolds number, Prandtl number, Grashof number and Rayleigh number. Numerical results characterize the convective heat transfer performance of the packer fluid.
Containerless mixing of metals and polymers with fullerenes and nanofibers to produce reinforced advanced materials
(2008-01-29) Barrera, Enrique V.; Bayazitoglu, Yildiz; Rice University; United States Patent and Trademark Office
The present invention relates to fullerene, nanotube, or nanofiber filled metals and polymers. This invention stems from a cross-disciplinary combination of electromagnetic and acoustic processing and property enhancement of materials through fullerene or nanofiber additives. Containerless processing (CP) in the form of electromagnetic field enduced and/or acoustic mixing leads to controlled dispersion of fullerenes, nanotubes, or nanofibers in various matrices. The invention provides methods of mixing that highly disperse and align the fullerenes, nanotubes, or nanofibers within the matrices of metals and polymers. The invention provides new compositions of matter and multifunctional materials based on processing, composition, and degree of in situ processing.
Convective heat transfer in microchannel gaseous slip flow
(2002) Tunc, Gokturk; Bayazitoglu, Yildiz
A new set of slip boundary conditions is developed to be used beyond the slip flow-early transition by using more accurate representation of the velocity and temperature gradients at the wall. The new model agrees well with the results from the solution of the Boltzman equation. The effect of rarefaction on steady-state heat transfer in microchannels in the slip flow regime is investigated by the integral transform technique with the implementation of the first order slip boundary conditions. Uniform temperature and/or uniform heat flux boundary conditions are considered for flow between two parallel plates, in circular and rectangular channels and annular sections. Thermal entrance length is solved as well as the fully developed region. Transient effects are obtained by performing the analysis for a cylindrical pipe with a sudden wall temperature change. Two characteristics of rarefaction namely the velocity slip and the temperature jump have opposite effects on heat transfer. It is found that the Nusselt number decreases with increasing rarefaction. Viscous heat dissipation is also included in the analyses and the change in the heat transfer due to this effect is clarified. Viscous heating may increase or decrease the heat transfer coefficient depending on the direction of the external heat transfer.
Critical point pressure sensitivity
(2002) Wagner, Howard Andrew; Bayazitoglu, Yildiz
A new means of heat transfer known as the piston effect was identified in 1989. The piston effect is where the expanding thermal boundary layer acts like a piston which compresses the bulk fluid. An examination of the equations for the conservation of mass, momentum, and energy identified the significant thermophysical properties as the thermal conductivity, the volume expansivity, and the isothermal compressibility. The thermal conductivity and the volume expansivity determine the thickness of the thermal boundary layer. The isothermal compressibility of the bulk fluid determines the pressure response of the bulk fluid to a given volume change. Previous researchers used only the van der Waals equation of state at conditions within mK of the critical point. The research described herein focuses on the pressure response of a fluid near the critical point to a sudden change in the boundary temperature. The use of the van der Waals equation of state for numerical simulation of the piston effect results in underpredicting the magnitude of the pressure wave by approximately 30 percent while overpredicting the acoustic heating by approximately 15 percent compared to using all fluid properties from a real gas equation of state. When evaluating the piston effect at conditions typical of cryogenic storage systems the pressure response of the fluid was observed to be six orders of magnitude larger than had been previously reported. The extent of the acoustic heating resulted in temperature increases in the bulk fluid that were four orders of magnitude larger. The real gas equation of state was used to compare the pressure and temperature response of oxygen and hydrogen due to a thermal disturbance at the boundary. The pressure rise in hydrogen after five acoustic time periods was only 17% of the pressure rise in oxygen. The temperature increase in hydrogen was only 30% of the temperature rise in oxygen. On the diffusion time scale the pressure rise in the oxygen is an order of magnitude larger than the pressure rise in hydrogen for the same thermal penetration depth. The temperature rise in oxygen is four times greater than the temperature rise in hydrogen.
Design of a methanol to hydrogen micro-reformer for fuel cell applications
(2007) Gernand, Jeremy Michael; Bayazitoglu, Yildiz
A new design for a microchannel methanol-steam reformer has been developed to provide power in conjunction with a micro fuel cell for a portable, low-power device. The design is optimized for low pumping power and rapid operation as well as thermal efficiency, overall size, and complete generation of the available hydrogen. An iterative, implicit, finite element solution code, which locates the boundaries between liquid, two-phase, and gaseous flow, provides a complete solution of the fluid and heat transfer properties throughout the device. The solution employs experimentally verified microchannel fluid dynamics relations to develop accurate results, but this is the first application of those relations to a methanol-water mixture. Based on this analysis, the proposed microreformer design will have an efficiency of 42%, with a theoretical maximum of 70%.
Dielectric Dispersion Measurement, Its Field Data Evaluation, and The Development of Two-Dimensional Nuclear Magnetic Resonance Inversion
(2018-10-02) Shehab, Fouad; Bayazitoglu, Yildiz; Myers, Mike
Dielectric logging was first deployed in Oil & Gas industry as part of operations in the early 1970’s and 1980’s with Schlumberger being the first company to attempt to do so. Its operational deployment then was primarily detecting freshwater zones in oil and gas bearing formations. That was due to the fact that there is low resistivity contrast between hydrocarbon and fresh water bearing formations, resulting in resistivity tools alone being of no value in such reservoirs. This paved the way for technical development and deployment of the dielectric logging tool which provides contrast in its real part, permittivity, between water and hydrocarbons. The first has a dielectric constant of 76-80 for fresh water and can go as low as 45 depending on salinity, temperature and pressure, meanwhile hydrocarbons have a permittivity of 1 in case of gas and 2-2.5 in case of oil. Such a large difference in value pushed for the release of these tools with motivation of identifying fresh water and hydrocarbon bearing zones when coupled with resistivity measurements. However, these earlier versions yielded the conclusion that the technology is immature and the tool requires further R&D, in both equipment design and measurement capabilities at borehole and lab scale. Moreover, further work is required to be done on the petrophysical modeling interpretation side to obtain mature and reliable desired petrophysical parameters such as water saturation. This resulted in failure of the dielectric logging program then. In the period of 2006 till present time, and with release of multi-frequency dielectric logging tools by Schlumberger and Baker Hughes, with new design and measurement capabilities that extend in both axial and radial directions as well as operating at multiple frequencies, the applications portfolio of this technology has expanded drastically to a variety of petrophysical applications. Some examples are the evaluation of water content and salinity in the shallow / invaded zones of unconventional shale reservoirs, heavy oil formations, and oil mobility studies across multiple depths of investigations when the formation type permits and estimating cementation exponents in both carbonate and sandstone reservoirs. The introduction of this recent generation multi-frequency tools has set new challenges that should be addressed for accurate understanding of tool current capabilities and future R&D requirements to achieve maximum potential. These are the studying of the reliability of these tools in the borehole and evaluating / developing interpretation models for the acquired data in the lab. This dissertation investigates the lab equipment development aspect by developing the measurement capability that matches the direction dependent measured complex relative permittivity in the borehole. Furthermore, it evaluates the current existing effective medium models that are an option to be used in interpreting the high frequency measured relative permittivity data, 10MHz-1.56GHz on multi-frequency log data. Finally, an attempt to solve another problem in the logging industry, in particular NMR logging tools for both wireline and MWD, was made. This thesis develops and presents a novel 2D NMR inversion scheme which removes one of the bottle necks of the current exiting inversion schemes, i.e. necessity of data compression and selection of singular values to retain enough dimensionality, yet solving the problem efficiently, both in speed and memory. This equips the industry with a more robust inversion mechanism with one less of an uncertainty parameter to tweak. This also paves the way for further future work of bridging dielectrics with NMR in unconventionals.
Dynamics of deformed droplets: Thermophysical property measurement using acoustic levitation
(2000) Fuentes, Arturo Alejandro; Bayazitoglu, Yildiz
A general theory for the dynamics of aspherical droplets useful to interpret frequency spectra more accurately for thermophysical property measurements was developed. The oscillations of a non-spherical droplet oscillating about an oblate spheroid subjected to external forces are considered. The effect of the static deformation and the interaction between the drop oscillation and the external field on the resonance are investigated. The analysis developed can be extended to consider different static shape deformation shapes. In order to validate the analytical predictions and to conduct further investigations, an experimental apparatus and a novel experimental procedure were developed. Experimental data and observations on the frequency splitting and surface tension, and the dynamics of the droplet in the experimental apparatus are presented. Finally, the effect of fullerenes on some dynamic features of levitated droplets is investigated.
Effectiveness of Polymer Composites as Radiation Shield against Galactic Cosmic Rays
(2019-04-19) Yang, Deng; Bayazitoglu, Yildiz
Currently spacecraft uses aluminum alloys for primary structures which do not provide sufficient radiation protection for both the spacecraft electronics and for the astronauts in cislunar space. This thesis evaluates the shielding effectiveness of several types of polymer composite materials against Galactic Cosmic Rays (GCRs). Because the galactic cosmic rays consist of high energy particles and produce neutrons while interacting with shielding materials, the purpose of this thesis is to assess new shielding materials that could be used to protect spacecraft electronics and the astronauts against both primary and secondary radiation. New type of composite shielding materials which are metal-doped polyacetylene with hydrogen are studied. Since the metal doped polyacetylene have large molecules, they are proposed to be ideal hydrogen storage materials for shielding purposes. The MULASSIS which is a one-dimensional Monte Carlo transport code is used for the dose equivalent calculations. This transport code demonstrated that the shielding effectiveness of the proposed materials in this thesis are better when compared with the currently used ones. In addition, the fluence analysis shows that Ti-decorated cis-polyacetylene with hydrogen content produces less neutrons when it interacts with GCR radiation and thus it naturally becomes very effective shielding material.
Energy Storage Capacity and Superconductivity of Nanosized Titanium Diboride, and Multifunctionality of Carbon-based Nanostructures: Development of Nano-engineered Solutions
(2019-09-30) Zhou, Zhou; Ajayan, Pulickel; Kono, Junichiro; Bayazitoglu, Yildiz
Nanotechnology has risen into prominence since the discovery of the “buckyball” in 1985,2 due to the enhanced tunability and performance of nanomaterials.3 Keenly awaited, scalable and facile application of nanotechnology, however, remains challenging. In petroleum industry, for instance, implementation barriers in scalability, controllability, and profitability have been hindering the advancement of nanotechnology innovations. The potential of fine tuning material properties and creating novel solutions is yet to be realized. Industrial friendly, scalable synthesis of nanosized titanium diboride and multifunctional nanostructures are exploited in this thesis, to include chemical vapor deposition, liquid exfoliation and electrochemical deposition. State of the art characterization techniques reveal atomic level properties in physical structure and chemical composition. After iterative material development cycles, the performance of prototypes are evaluated experimentally and theoretically. Lithium ion storage capacity and type II superconductivity are first time reported for nanosized titanium diboride. Remarkable theoretical capacity of 385.7 mAh/g and superconductive critical temperature of 5.8 K are attributed to the dimensional confinement of the nanoscale. Titanium diboride nanoparticles exhibit remarkable charge storage capacity, demonstrating great potential for applications as lithium ion battery anode and supercapacitor material. Their high energy storage capacity together with their newly discovered superconductivity manifest the distinctive material characteristics induced by dimensional confinement. Looking beyond the enhancement of material properties offered by the nanoscale, the multifunctionality of nanostructures are explored. Impelled by the virtues of carbon nanotubes and Fe@C core-shell nanoparticles, multifunctional, nano-engineered prototypes are designed and fabricated, combining hydrophobicity, mechanical and chemical resistance, and superparamagnetic, florescent and photocatalytic properties. The multifunctionality of infiltrated carbon nanotubes and Fe@C-CNx nanostructures appeal to various applications such as protective composite and reusable photocatalyst. Bridging the gap between academic research and industrial application, nano-engineering and design thinking approaches in this thesis develop nanostructures to solve explicit problems. Size confinement induced properties and innovative designs of nano-engineered structures are vital to convey the value of nanotechnology. The developed prototypes provide innovative solutions to various existing problems, including low durability of drilling tools, high friction in mechanical operations, critical environment energy storage and hazardous water waste.
Entrainment and turbulence characteristics of low-velocity isothermal and buoyant jets
(1991) Peterson, Jill Elizabeth; Bayazitoglu, Yildiz
The current study examined the transition region of axisymmetric isothermal and buoyant jets of low Reynolds number, directed vertically upwards into a stagnant, unstratified ambient. These flows were examined experimentally and numerically. The region in which measurements were obtained allows examination of two types of transition occurring in the jet: from nozzle exit dominated to fully developed, and from momentum to buoyancy dominated flow. Velocity data were acquired using a two channel Laser-Doppler Anemometer for isothermal Reynolds numbers of 850 to 7405, and buoyant Froude numbers of 12 to 6425 and Reynolds numbers from 525 to 6500. Curve fit approximations of the data were developed by assuming polynomial similarity profiles for the measured quantities. Correlation equations were developed which allow prediction of the downstream velocity flow field and turbulent flow field as a function of the Reynolds number, Froude number and density ratio at the nozzle exit. Profile width and entrainment increased at low Reynolds number. Axial and radial velocity fluctuations were found to increase at low Reynolds number. The buoyant cases studied were found to have lower velocity fluctuations and significantly lower Reynolds stresses than isothermal cases of similar Reynolds number. Once comprehensive correlation equations were developed predicting mean and turbulent flow quantities, the basis was formed for development of a new turbulence model, the analytic turbulence model. This method involved substitution of correlation equation approximations to the mean flow quantities into the boundary layer forms of the governing equations. The turbulent terms were then solved for explicitly. It was shown that this method predicts the fully developed boundary layer turbulent flow field, and can be used as a criterion for a flow attaining boundary layer form. Comparison of turbulent values predicted analytically with those measured empirically revealed that the transition flow examined experimentally had not fully developed to boundary layer form. Testing of the turbulent correlation equations was performed by using them as a turbulence model in a finite difference numerical solution. While the correlation equations were representative of the turbulent flow field, they did not produce correct results when used in a marching, boundary layer simulation. As verified by the analytic turbulence model, this occurred because the transition flow had not yet reached fully developed boundary layer form.
Evaporative cooling on a grooved surface
(1980) Yoder, Dwight; Wierum, Frederic A.; Chapman, Alan J.; Bayazitoglu, Yildiz
Spray evaporative cooling defines a mode of heat transfer where the drops evaporate on contact with the heated surface. Since no water accumulates on the surface, the term "dry wall" is used to described the surface condition. If while operating in the drywall mode the surface temperature is lowered, there will be a transition to a point where water will begin to accumulate on the surface. When water begins to accumulate the surface is said to be "flooded". Behavior at this transition point was investigated experimentally to determine the temperatures and corresponding heat flux at which this transition occurred. Several pressure ranges were considered including one below the triple point of water. Additionally, the results using a grooved surface were compared to those using a smooth surface. It was determined that a grooved surface has no effect on the heat transfer.
Experimental and analytical results for longitudinal electromagnetic levitation
(1997) Shampine, Rod William; Bayazitoglu, Yildiz
Electromagnetic levitation offers the possibility of working with metals in a containerless fashion. In order to realize this on a commercial basis, a solid theoretical understanding of the phenomena is needed, coupled with experimental work validating the theoretical models. In the case of the conventional conical electromagnetic levitator, models have been proposed for the forces, heating, and torque experienced by a levitated specimen. Experimental work has been primarily focused on measuring the forces. A new type of levitator is proposed in the first part of this work. The proposed levitator is suitable for use on earth as well as in micro gravity and it overcomes almost all of the drawbacks that are inherent in currently used levitation melting devices. This levitator can support samples that are an order of magnitude more massive than those that can be supported by existing devices. Further, it can levitate liquid metal samples of arbitrary shapes and provide control over the position, movement, and the rate of heat generation in them. The new levitator has the potential to become a "containerless" manufacturing process. An analysis of the currents induced in specimens supported in a longitudinal electromagnetic levitator is presented. Expressions for the forces, heating, and torque are developed. The predictions are compared with experimental measurements and are found to be in excellent agreement. Inductance, optimum specimen to coil size ratio, and effect of the number of poles are discussed in connection with the design of this class of levitator. Future directions for research with longitudinal levitators are discussed. These include finding the shape of the levitated specimen after it melts, levitation casting of significant quantities of metal, and demonstrating continuous processing of materials where only the molten portion is supported. The final part of this work fills in a significant gap in the understanding of conical electromagnetic levitators by presenting experimental results for the heating in spherical specimens, and compares these with theoretical predictions. It is found that the heating may be predicted with good accuracy, even using a simplified model.
Experiments in acoustic levitation: Surface tension and viscosity of deformed droplets
(1995) Mitchell, Garrick F.; Bayazitoglu, Yildiz
Acoustic levitation permits the observation of individual oscillating liquid droplets. Droplet shape oscillation data lead to thermophysical property measurements without the contaminating effects of a solid container. For spherical droplets, analysis has shown natural frequencies are a function of droplet size, mode number, and the surface tension and density of the liquid; the damping rate of oscillations has been correlated with the viscosity of the liquid. In terrestrial levitation, however, gravity serves to deform the droplet and split the frequency spectrum. In addition, droplet evaporation causes natural frequencies to change over time. This work compares experimental data on the frequency splitting of water and ethyl alcohol with theoretical predictions. With slight refinements to the theory, good agreement is found. Surface tension and viscosity were also measured; surface tension for distilled water came within 5% of the published value, and a new approach to the measurement of viscosity via levitation is described and tested.
Force and Heat Generation in a Conducting Sphere in an Alternating Magnetic Field
(1995) Sathuvalli, Udaya Bhaskar R.; Bayazitoglu, Yildiz; Chapman, Alan J.; Akin, John Edward.; Cox, Steven J.
The interaction of an electrically conducting sphere with a time varying magnetic ﬁeld is useful in the study of "containerless" processing methods such as electromagnetic levitation melting. The fundamental quantities of interest in this interaction are the rate of heat generation in the sphere, the Lorentz force and magnetic pressure on it. These quantities depend upon the nature of the current sources that create the magnetic field, and the material properties of the sphere. In this work, the Maxwell equations for the interaction of a sphere with an arbitrary external alternating magnetic ﬁeld are ﬁrst formulated. Then, the density of the induced currents in the sphere is found as a function of the external current sources and the material properties of the sphere. The current density is now used to calculate the heat generated in the sphere. Next, a method to calculate the Lorentz force on an electrically conducting sphere placed in an arbitrary sinusoidally varying magnetic ﬁeld is developed and a formula for the force on the sphere is given. This formula is used to derive the special case of a sphere in an axisymmetric system of circular current loops. Numerical results for the force on a sphere on the axis of a stack of loops are presented as a function of the stack geometry. The results for the heat generation and the Lorentz force obtained in this study are compared with the results obtained by a previously used model (known as the "homogeneous model") which assumes that the external magnetic ﬁeld is uniform and unidirectional. It is shown that the homogeneous model is a special case of the present model and that it underestimates heat generation signiﬁcantly, and overestimates the Lorentz force. In addition, as the size of the sphere decreases, the homogeneous model gives erroneous results, approaching an order of magnitude for heat generation in a very small sphere. Subsequently, a procedure to determine the magnetic pressure distribution on the surface of a levitated liquid metal droplet is developed. The pressure distribution is calculated in terms of the geometry of the coil that creates the ﬁeld. Finally, the magnetic ﬁelds of helical windings that are commonly used in the laboratory for levitation melting are calculated.
Heat conduction for dielectric thin films from the Casimir to diffusion limit
(1994) Polsky, Yarom; Bayazitoglu, Yildiz
The heat transfer in electrically insulating thin film materials is predominantly governed by phonons and is accurately described when the phonon mean free path is either much smaller than the order of the thickness of the material (the thick limit) or when there is no phonon scattering (the thin limit). The thick limit model, which is referred to as Fourier's equation, and the thin limit model, which is referred to as the Casimir limit, differ primarily in the distribution function used to describe the excitation state of phonons. This difference arises because scattering alters the excitation levels of the phonons. Whereas the Fourier's equation phonon distribution function is derived using the Boltzmann transport equation, the Casimir limit phonon distribution is given by the Bose-Einstein statistics. This paper first relates the elastic properties of a solid to the phonon description of a crystal's energy to obtain the phonon distribution using the Boltzmann Transport Equation. It will then explain why Fourier's equation breaks down at the nano/microscale level and develop a general heat flux equation which also describes the regime between the Casimir limit and Fourier's Equation.

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