bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of a Multifield Model to Reflooding of a Hot Vertical Tube: Part II—Analysis of Experimental Results
Authors: Kawaji M. , Banerjee S.
Published: October 2009

The two-fluid model equations developed for reflood calculations and discussed in Part I (Kawaji and Banerjee, 1987) are solved numerically with appropriately formulated constitutive relations to analyze the Inconel tube reflood experiments involving inverted annular and dispersed flow regimes downstream of the quench front. Constitutive relations are formulated separately for individual transfer mechanisms that are considered to be phenomenologically significant. For inverted annular flow, phasic pressure difference is incorporated into the momentum equations to predict the interfacial waves which enhance film boiling heat transfer. For dispersed flow, a size distribution of drops is considered and both single and multifield equations of motion are solved to calculate the droplet transport. Most of the important heat transfer and hydrodynamic aspects of the experimental results are predicted reasonably well, indicating the adequateness of the mechanisms considered. In particular, a wall–drop interaction heat transfer mechanism is determined to be essential in explaining the experimentally observed strong dependence of heat transfer rate on liquid volume fraction in the dispersed flow region. A sensitivity study is made to identify the weaknesses in the constitutive relations, but no single relation could be accounted for areas in need of further improvement. In comparison with the predictions of the single-field model, those of the multifield model showed improvement for some but not all experiments.
Effects of Size of Simulated Microelectronic Chips on Boiling and Critical Heat Flux
Authors: Park K.-A. , Bergles A. E.
Published: October 2009

Microelectronic chips were simulated with thin foil heaters supplied with d-c power and arranged in two vertical configurations: flush mounted on a circuit board substrate or protruding from the substrate about 1 mm. Heat transfer characteristics (midpoint) were obtained with varying height (1 mm to 80 mm) and width (2.5 mm to 70 mm) in R-113. Two types of incipient boiling temperature overshoot were observed with saturated boiling. The inception of boiling depended greatly on the location of the active boiling sites on the heater. For arrays, the inception of boiling for the top heater took place at lower superheat than for the bottom heater. Heater size had no effect on established boiling, in contrast to results reported previously in the literature. The critical heat flux for wide heaters increased with decreasing heater height, as expected. The critical heat flux also increased with decreasing width. Correlations are presented that describe these effects.
The Properties of Steam: Current Status
Authors: Hill P. G. , MacMillan R. D. C.
Published: October 2009

A review has been made of progress in the past two decades on measurement and correlation of the properties of steam. Data bases available in 1966 and 1986 for formulation and evaluation of equations of state are described and contrasted. Progress in the formulation of wide-ranging fundamental equations is outlined with particular reference to refinement in understanding of the critical region. Consistency of data sets is discussed and attention is drawn to areas where further work is needed. The results of continuing work on correlation of viscosity and thermal conductivity are cited.
Three-Dimensional Laminar Heat Transfer and Fluid Flow Characteristics in the Entrance Region of a Rhombic Duct
Authors: Asako Y. , Faghri M.
Published: October 2009

A solution methodology is developed to obtain three-dimensional fluid flow and heat transfer characteristics in the entrance region of a rhombic duct. Owing to the complexity of the geometry, the literature results are limited to the fully developed values. The numerical methodology is based on an algebraic coordinate transformation technique, which maps the complex cross section onto a rectangle, coupled with a calculation procedure for three-dimensional parabolic flows, which reduces the problem to a series of two-dimensional problems. The Nusselt number and friction factor results are obtained for boundary conditions of uniform wall heat flux and uniform wall temperature. The asymptotic values of the Nusselt numbers and friction factors approach the available fully developed results. The entry length results for the limiting case of φ = 90 deg are in perfect agreement with the available experimental and numerical results for a rectangular duct.
Buoyancy-Driven Exchange Flow Through Small Openings in Horizontal Partitions
Authors: Epstein M.
Published: October 2009

This paper describes an experimental study of the phenomenon of buoyancy-driven exchange (countercurrent) flow through openings in a horizontal partition. A density-driven exchange flow was obtained by using brine above the partition and fresh water below the partition. In the first part of the study, flow measurements were made with a single opening, for opening ratios L/D in the range 0.01 to 10.0, where L and D are the length of the opening (in the direction normal to the partition) and the diameter of the opening, respectively. Four different flow regimes are identified as L/D is increased through this range. As a result of the competition between two of these regimes, the exchange flow rate versus L/D relation exhibits a peak. The exchange flow rate was found, for all practical purposes, to be independent of viscosity, enabling a universal correlation between Froude number (dimensionless exchange flow rate) and L/D. The second part of the study was an experimental investigation of the same phenomenon, but with two openings in the horizontal partition. Two openings were observed to give rise to three different flow configurations involving both one-way and countercurrent flows within the openings.
Evaporative Cutting of a Semitransparent Body With a Moving CW Laser
Authors: Abakians H. , Modest M. F.
Published: October 2009

The formation of a groove by partial evaporation of a moving semi-infinite and semitransparent solid is considered. Evaporative removal of material is achieved by focusing a high-power, highly concentrated Gaussian laser beam of continuous wave (CW) onto the surface of the solid. Surface heat losses due to radiation and convection are assumed to be negligible, and conductive losses are treated in an approximate fashion using a simple integral method. The relevant nonlinear partial differential equations are solved numerically, and results for groove depth and shape are presented for a variety of laser and solid parameters.
Modeling of Vapor Channeling Behavior in Liquid-Saturated Debris Beds
Authors: Stubos A. K. , Buchlin J.-M.
Published: October 2009

The formation and evolution of vapor channels in a liquid-saturated and heatgenerating particulate bed is modeled. The effect of the sticking forces on the onset of channeling is considered. Simple experimental techniques are devised to support the model development. Satisfactory interpretation of the D10 in-pile test performed at Sandia Laboratories can be achieved with the present channel model.
A Parametric Study of Boiling Heat Transfer in a Horizontal Tube Bundle
Authors: Jensen M. K. , Hsu J.-T.
Published: October 2009

Boiling heat transfer outside of a section of a uniformly heated horizontal tube bundle in an upward crossflow was investigated using R-113 as the working fluid. The inline tube bundle had five columns and 27 rows with a pitch-to-diameter ratio of 1.3. Heat transfer coefficients obtained from the 14 instrumented tubes are reported for a range of fluid and flow conditions; slightly subcooled liquid inlet conditions were used. At most heat fluxes there was no significant variation in the local heat transfer coefficients throughout the tube bundle. However, at low heat fluxes and mass velocities, the heat transfer coefficient increased at positions higher in the tube bundle. As pressure and mass velocity increased so did the heat transfer coefficients. For the local heat transfer coefficient, a Chen-type correlation is compared to the data; the data tend to be overpredicted by about 20 percent. Reasons for the overprediction are suggested.
Recent Developments in Computational Heat Transfer
Authors: Patankar S. V.
Published: October 2009

Recent developments in computational methods for heat transfer and fluid flow are reviewed. Emphasis is given to the treatment of convection and diffusion and solution of flow equations. Also, some interesting applications of the methods are mentioned. Whereas many attractive methods have been formulated in recent years, there exists no clear consensus about a preferred method. Careful and controlled evaluations of different methods are required. This and other tasks for future research are outlined.
Analysis of Extended Surface
Authors: Kraus A. D.
Published: October 2009

Previous work, by the author and others, pertaining to parameterizations for individual fins is reviewed. These parameterizations are the thermal transmission matrices and ratios that were devised to facilitate the analysis of an assembly of individual fins into an array of extended surface. An elaboration of the usefulness of these parameters, particularly with regard to their superiority over the notion of fin efficiency or fin effectiveness, is made. The concept of reciprocity is developed and the representation of an individual fin as a connection of just three simple resistances is developed. A procedure for the nodal analysis of finned arrays is developed via a matrix-oriented approach.
Wavenumber Selection in Be´nard Convection
Authors: Catton I.
Published: October 2009

The results of three related studies dealing with wavenumber selection in Rayleigh–Be´nard convection are reported. The first, an extension of the power integral method, is used to argue for the existence of multi-wavenumbers at all supercritical wavenumbers. Most existing closure schemes are shown to be inadequate. A thermodynamic stability criterion is shown to give reasonable results but requires empirical measurement of one parameter for closure. The third study uses an asymptotic approach based in part on geometric considerations and requires no empiricism to obtain good predictions of the wavenumber. These predictions, however, can only be used for certain planforms of convection.
Natural Convection in Enclosures
Authors: Ostrach S.
Published: October 2009

There exists a great diversity of buoyancy flows in enclosures that are of interest in science and technology. These buoyancy flows pose new and challenging physical and mathematical problems. Emphasis is given to the complexities of the phenomena, viz., the coupling of the flow and transport and of the boundary-layer and core flows, the interaction between the flow and the driving force, which alters the regions in which the buoyancy acts, and the occurrence of flow sub-regions (cells and layers). The importance of scaling analysis and experiments to determine flow details are discussed and the essentials of scaling techniques are outlined. The implications of these for numerical methods are presented, and the inadequacies of purely numerical solutions are pointed out. Representative works covering a broad range of problems are discussed.
Recirculating Combined Convection in Laminar Pipe Flow
Authors: Morton B. R. , Ingham D. B. , Keen D. J. , Heggs P. J.
Published: October 2009

Investigations are conducted into situations where flow recirculation occurs in laminar combined convection flows in vertical circular tubes. Particular attention is given to flows in which finite sections of the tube wall are maintained at constant temperatures, which may be either hotter or colder than the temperature of the fluid at the entrance of the tube. A numerical study is carried out in which the governing elliptic partial differential equations are expressed in finite difference form and solved using a relaxation technique. The values of the governing parameters, namely the Reynolds, Prandtl, and Grashof numbers, and the thermal and viscous boundary conditions are chosen to correspond as closely as possible to an experimental investigation that involves water being forced along a perspex vertical circular tube, which is heated and/or cooled over finite sections. It is found that the numerical model is able to predict quite accurately the location, shape, and size of the recirculation regions observed in the experiments.
Band Radiation From a Fluctuating Medium
Authors: Nelson D. A.
Published: October 2009

A simple model of band radiation from a fluctuating medium, which emulates fluctuations in a turbulent diffusion flame, has been studied to determine the relative importance of the many mean and fluctuation parameters. The importance of fluctuations is largely confined to variation in the Planck function, which is strongly dependent upon the mean and variance of the mixture fraction and upon the band fundamental wavenumber.
Reduction of Computing Time and Improvement of Convergence Stability of the Monte Carlo Method Applied to Radiative Heat Transfer With Variable Properties
Authors: Kobiyama M.
Published: October 2009

A modified Monte Carlo method is suggested to reduce the computing time and improve the convergence stability of iterative calculations without losing other excellent features of the conventional Monte Carlo method. In this method, two kinds of radiative bundle are used: energy correcting bundles and property correcting bundles. The energy correcting bundles are used for correcting the radiative energy difference between two successive iterative cycles, and the property correcting bundles are used for correcting the radiative properties. The number of radiative energy bundles emitted from each control element is proportional to the difference in emissive energy between two successive iterative cycles.
Sensible and Latent Heat Transfer in Cross-Counterflow Gas-To-Gas Heat Exchangers
Authors: Holmberg R. B.
Published: October 2009

Simultaneous heat and mass transfer during condensation in cross-counterflow gas-to-gas heat exchangers has been analyzed. The coupled heat and mass transfer equations are derived for boundary-layer controlled heat and mass transfer and include longitudinal heat conduction in the exchanger wall. A numerical method of the finite-difference type is applied to the steady-state performance. Temperature and absolute humidity distributions are calculated for exchanger parameters that are typical in air conditioning systems. Temperature and humidity efficiencies together with frosting limits are evaluated for different inlet air conditions.
An Extension to the Irreversibility Minimization Analysis Applied to Heat Exchangers
Authors: Aceves-Saborio S. , Ranasinghe J. , Reistad G. M.
Published: October 2009

The irreversibility minimization method of heat exchanger optimization is extended to include a term to account for the exergy of the material of construction of the heat exchanger. The method permits physically realistic optimization to be conducted with the resulting optimum designs providing conceptually beneficial guideposts, which do not change with time or location. Such optima are in contrast to the optima obtained by presently advocated methods, which on one hand indicate unrealistic infinite area heat exchangers, and on the other hand point to optima that may change dramatically with location and time. Although the analysis presented here does not represent a “cure-all” for heat exchanger analysis (economic optimization is still recommended), it does provide valuable conceptual insights and nonchanging guideposts for optimal design. Accompanying exergetic efficiency expressions using the same type of material exergy term show physically more realistic values than the usual expressions.
Experiments on Forced Convection From a Horizontal Heated Plate in a Packed Bed of Glass Spheres
Authors: Renken K. J. , Poulikakos D.
Published: October 2009

This paper presents an experimental investigation of boundary-layer forced convective heat transfer from a flat isothermal plate in a packed bed of spheres. Extensive experimental results are reported for the thermal boundary-layer thickness, the temperature field, and the local wall heat flux (represented by the local Nusselt number). Theoretical findings of previous investigations using the Darcy flow model as well as a general model for the momentum equation accounting for flow inertia and macroscopic shear with and without variable porosity are used to evaluate the theoretical models. Several trends are revealed regarding the conditions of validity of these flow models. Overall, the general flow model including variable porosity appears to perform better, even though the need for serious improvements in modeling becomes apparent.
Transfer Functions for Efficient Calculation of Multidimensional Transient Heat Transfer
Authors: Seem J. E. , Klein S. A. , Beckman W. A. , Mitchell J. W.
Published: October 2009

Finite difference or finite element methods reduce transient multidimensional heat transfer problems into a set of first-order differential equations when thermal physical properties are time invariant and the heat transfer processes are linear. This paper presents a method for determining the exact solution to a set of first-order differential equations when the inputs are modeled by a continuous, piecewise linear curve. For long-time solutions, the method presented is more efficient than Euler, Crank–Nicolson, or other classical techniques.
Analysis of Order of the Sequential Regularization Solutions of Inverse Heat Conduction Problems
Authors: Scott E. P. , Beck J. V.
Published: October 2009

Various methods have been proposed to solve the inverse heat conduction problem of determining a boundary condition at the surface of a body from discrete internal temperature measurements. These include function specification and regularization methods. This paper investigates the various components of the regularization method using the sequential regularization method proposed by Beck and Murio (1986). Specifically, the effects of the regularization order and the influence of the regularization parameter are analyzed. It is shown that as the order of regularization increases, the bias errors decrease and the variance increases. Comparatively, the zeroth regularization has higher bias errors and the second-order regularization is more sensitive to random errors. As the regularization parameter decreases, the sensitivity of the estimator to random errors is shown to increase; on the other hand, the bias errors are shown to decrease.
Wave Characteristics of Heat Conduction Using a Discrete Microscopic Model
Authors: Cheng K. J.
Published: October 2009

The wave properties of heat conduction are studied using a discrete velocity microscopic model. In this model, molecules move with two possible speeds along one of six allowable directions, and the molecular dynamics are governed by the Boltzmann transport equation. Macroscopic quantities such as temperature and density are extracted from the distribution of molecules among various possible states. It is found that at a low degree of rarefaction (low Knudsen number), an initial temperature pulse simply spreads out with time without exhibiting any wavelike behavior. But at a high degree of rarefaction (high Knudsen number), an initial temperature pulse propagates as a highly damped temperature ripple at almost constant speed. The thermal propagation speed thus obtained agrees with the value predicted from macroscopic equations. This propagation of temperature pulse is then compared with the propagation of density disturbance (sound wave) using the same model.
Thermal Constriction Resistance of Sphere/Layered Flat Contacts: Theory and Experiment
Authors: Fisher N. J. , Yovanovich M. M.
Published: October 2009

The effect of surface layers on the thermal constriction resistance of contacts is of interest to the thermal analyst. This paper investigates analytically and experimentally the thermomechanical problem of a sphere in elastic contact with a flat coated with a layer. An approximate solution is developed that utilizes the solution to the thermal portion of the problem and the Hertzian limits of the mechanical portion. The approximation shows good agreement with the full solution for two examples that represent extremes in elastic properties for common metallics. Thermal constriction resistance measurements for a steel sphere contacting a nickel flat coated with a silver layer are compared to theoretical predictions. Resistance predictions from both full and approximate solutions show good agreement with measurements for light loads within the elastic load range. For heavy loads, the resistance is over-predicted due to plastic yielding of the nickel substrate.
Theory of Rolling Contact Heat Transfer
Authors: Bejan A.
Published: October 2009

This paper addresses the fundamentals of the phenomenon of steady heat transfer by rolling contact between two bodies at different temperatures. The contact region is modeled according to the classical Hertz theory, by which the bodies undergo elastic deformation and the contact area has the shape of an ellipse. In the first part of the study it is shown that when the two bodies make contact continuously over the elliptical area, the overall heat transfer rate is proportional to the square root of the Peclet number based on the ellipse semiaxis parallel to the tangential (rolling) velocity. In the same case the heat transfer rate increases as the square root of the normal force (F) between the two bodies. The second part of the study treats the case when the rolling contact is made through a large number of asperities (contact sites) distributed over the elliptical contact area. The heat transfer rate is again proportional to the square root of the Peclet number. When the asperities are distributed randomly, the heat transfer rate increases as F5/6. In the case of regularly distributed asperities that undergo elastic deformation, the heat transfer rate is proportional to F13/18. The high Peclet number domain covered by this study is discussed in the closing section of the paper.
An Experimental Determination of the Thermal Conductivity of a 304L Stainless Steel Powder Metallurgy Material
Authors: Agapiou J. S. , DeVries M. F.
Published: October 2009

The thermal conductivity of a 304L stainless steel powder metallurgy (P/M) material was experimentally determined to support research aimed at understanding the poor machining characteristics of P/M austenitic stainless steels. Thermal conductivity measurements were made on samples having relative densities ranging between 64 and 90 percent of theoretical density since workpieces requiring machining are often fabricated in that density range. The measurements were also made over a temperature range of 50 to 300°C since workpiece temperatures can attain levels this high during the machining operation. The thermal conductivity was measured using an apparatus having a design based on the comparative method. The experimentally determined thermal conductivities were modeled by mathematical models found in the technical literature and modified for the present study. The thermal conductivity of this material increases with increasing relative density and temperature; it is also dependent on the matrix structure for a given porosity.
Multipass Plate Heat Exchangers—Effectiveness-NTU Results and Guidelines for Selecting Pass Arrangements
Authors: Kandlikar S. G. , Shah R. K.
Published: October 2009

Plate heat exchangers are classified on the basis of number of passes on each side and the flow arrangement in each channel, taking into account the end plate effects. This results in four configurations each for the 1–1 (1 Pass–1 Pass), 2–1, 2–2, 3–3, 4–1, 4–2, and 4–4 arrangements, and six configurations for the 3–1 arrangement. These arrangements are analyzed using the Gauss–Seidel iterative finite difference method; the plate arrangement that yields the highest effectiveness in each pass configuration is identified. Comprehensive results are presented in tabular form for the temperature effectiveness P1 and log-mean temperature difference correction factor F as functions of the number of transfer units NTU1, the heat capacity rate ratio R1, and the total number of thermal plates. On the basis of these results, specific guidelines are outlined for the selection of appropriate plate heat exchanger configurations.
Asymptotic Effectiveness-NTU Formulas for Multipass Plate Heat Exchangers
Authors: Kandlikar S. G. , Shah R. K.
Published: October 2009

The effectiveness of a plate heat exchanger with a finite number of plates is affected by the end channels, and the channels between two adjacent passes. These effects become less significant as the number of thermal plates becomes large, N > 40, as shown by Kandlikar and Shah (1989). In the present paper, closed-form equations are derived for plate heat exchangers with N = ∞ in terms of temperature effectiveness P1 as a function of the capacity rate ratio R1 and the number of transfer units NTU1 for the following pass arrangements: 1–1, 2–1, 2–2, 3–1, 3–2, 3–3, 4–1, 4–2, 4–3, and 4–4.
Thermal Stability of Horizontally Superposed Porous and Fluid Layers
Authors: Taslim M. E. , Narusawa U.
Published: October 2009

The results of stability analyses for the onset of convective motion are reported for the following three horizontally superposed systems of porous and fluid layers: (a) a porous layer sandwiched between two fluid layers with rigid top and bottom boundaries, (b) a fluid layer overlying a layer of porous medium, and (c) a fluid layer sandwiched between two porous layers. By changing the depth ratio dˆ from zero to infinity, a set of stability criteria (i.e., the critical Rayleigh number Rac and the critical wave number ac) is obtained, ranging from the case of a fluid layer between two rigid boundaries to the case of a porous layer between two impermeable boundaries. The effects of k/km (the thermal conductivity ratio), δ (the square root of the Darcy number), and α (the nondimensional proportionality constant in the slip condition) on Rac and ac are also examined in detail. The results in this paper, combined with those reported previously for Case (a) (Pillatsis et al., 1987), will provide a comprehensive picture of the interaction between a porous and a fluid layer.
Effect of Solid Subcooling on Natural Convection Melting of a Pure Metal
Authors: Beckermann C. , Viskanta R.
Published: October 2009

A combined experimental and numerical study is reported of melting of a pure metal inside a vertical rectangular enclosure with natural convection in the liquid and conduction in the solid. The numerical model is successfully verified by conducting a series of experiments covering a wide range of hot and cold wall temperatures. It is found that solid subcooling significantly reduces the melting rate when compared to melting with the solid at the fusion temperature. Because the cooled wall is held below the fusion temperature of the metal, the solid/liquid interface eventually reaches a stationary position. For moderate values of the subcooling parameter the steady-state interface is almost vertical and parallel to the cold wall. Strong subcooling results in an early termination of the melting process, such that natural convection in the relatively small liquid region cannot fully develop. For moderate subcooling, correlations have been derived for the steady-state volume and heat transfer rates. While many aspects of melting with solid subcooling appear to be similar to ordinary nonmetallic solids, important differences in the local flow structures and heat transfer mechanisms are observed.
Combined Convection–Conduction–Radiation Boundary Layer Flows Using Optimal Control Penalty Finite Elements
Authors: Utreja L. R. , Chung T. J.
Published: October 2009

Numerical solutions for combined convection and radiation in a laminar boundary layer on an isothermal wall are obtained using optimal control penalty (OCP) finite elements. The integro-differential energy equation is solved without any limitation of optical thickness. The expression for the divergence of radiation flux containing integral terms is written in terms of a one-dimensional radiation field for a flat plate geometry. The radiation interaction effect on the temperature distribution in the boundary layer is described. The solution of the integro-differential energy equation is then compared with known solutions in the limits of optical thickness.
A Detailed Examination of Gas and Liquid Phase Transient Processes in Convective Droplet Evaporation
Authors: Haywood R. J. , Nafziger R. , Renksizbulut M.
Published: October 2009

A finite volume numerical technique has been used to model the evaporation of an n-heptane droplet with an initial Reynolds number of 100 in air at 800 K, 1 atm. The effects of variable thermophysical properties, liquid phase motion and heating, and transient variations in droplet size and velocity are included in the analysis. With appropriate corrections for the effects of variable properties and liquid phase heating, quasi-steady correlations are shown to predict accurately the transient histories of the drag coefficient and Nusselt and Sherwood numbers. For the case investigated here, the transient effects of importance were the variation in droplet velocity, the decline in the liquid phase velocities, and the rise in the droplet surface and volume average temperatures. In spite of the transient rise in the droplet temperature, the nature of the liquid phase heating, as characterised by the liquid Nusselt number, was found to remain constant during most of the droplet lifetime.
A Theoretical Model of Film Condensation in a Bundle of Horizontal Low Finned Tubes
Authors: Honda H. , Nozu S. , Takeda Y.
Published: October 2009

The previous theoretical model of film condensation on a single horizontal low finned tube is extended to include the effect of condensate inundation. Based on the flow characteristics of condensate on a vertical column of horizontal low finned tubes, two major flow modes, the column mode and the sheet mode, are considered. In the column mode, the surface of the lower tubes is divided into the portion under the condensate column where the condensate flow is affected by the impinging condensate from the upper tubes, and the portion between the condensate columns where the condensate flow is not affected by the impinging condensate. In the sheet mode, the whole tube surface is assumed to be affected by the impinging condensate. Sample calculations for practical conditions show that the effects of the fin spacing and the number of vertical tube rows on the heat transfer performance is significant for R-12, while the effects are small for steam. The predicted value of the heat transfer coefficient for each tube row compares well with available experimental data, including four fluids and five tube bundles.
Subsonic Pressure Recovery in Cylindrical Condensers
Authors: Busse C. A. , Loehrke R. I.
Published: October 2009

A method is presented for predicting laminar, subsonic flow in axisymmetric cylindrical heat pipe condensers. The method involves the use of the boundary layer approximation and a noncontinuous power series to describe the velocity profile under conditions including strong axial flow reversal. A comparison between laminar predictions and measurements indicates that transition to turbulent flow in the condenser begins when the absolute value of the radial Reynolds number exceeds 6. The condenser pressure recovery in the turbulent regime can be calculated from the momentum flow at the condenser inlet and an empirical wall-friction parameter.
Improved Liquid-Crystal Thermometry Excluding Human Color Sensation
Authors: Akino N. , Kunugi T. , Ichimiya K. , Mitsushiro K. , Ueda M.
Published: October 2009

A new liquid-crystal thermometry method is described to determine an isothermal map on a heat transfer surface coated with a cholesteric liquid-crystal layer that changes color according to temperature. This method is based on the use of a set of sharp band-pass optical filters, one of which is attached to a black-and-white video camera to take a monochromatic image having a specified color. From the image, an isothermal line was drawn with the aid of a digital image processing technique that excludes human color sensation. We obtain as many isothermal lines as band-pass filters and can determine an isothermal map. An experiment is presented as an application of the present method to measure temperature distributions on a heated surface cooled by air flow and disturbed by a short attached cylinder.
Numerical and Analytical Solutions for Two-Dimensional Gas Distribution in Gas-Loaded Heat Pipes
Authors: Peterson P. F. , Tien C. L.
Published: October 2009

This work presents a two-dimensional axisymmetric diffusion model for the non-condensable gas distribution in gas-loaded heat pipes and thermosyphons. The new model, based on an integral analysis, has major advantages over existing, computationally time consuming, two-dimensional models. It has equal accuracy while using only the computational effort required for the cruder one-dimensional model, and also includes the effects of wall conduction and spatial variation of the condenser heat transfer coefficient. To simplify design calculations further an analytic two-dimensional solution is established, which gives excellent results over a wide range of parameters.
Finite Analytic Solution of Convective Heat Transfer for Tube Arrays in Crossflow: Part II—Heat Transfer Analysis
Authors: Chen Ching Jen , Wung Tzong-Shyan
Published: October 2009

The convective heat transfer and pressure drop in flow past two types of tube array are solved numerically by the Finite Analytic Method in this investigation. The tube arrays considered are an in-line tube array and a staggered tube array with longitudinal and transverse pitch of two. The flow field solution is obtained and analyzed in Part I of the study. In the present Part II, the temperature field, heat transfer characteristics, and pressure drop are investigated. The fluid and tubes are considered to be at the same temperature, except for the array tube, which is heated or cooled. The solution domain covers three pitches of tube arrays in order to simulate accurately the non-periodic behavior of the temperature field downstream of the heated tube. In general, the heat transfer in a staggered array of tubes is found to be higher than that in an in-lined array of tubes. However, the pressure drop in a staggered array arrangement is also higher. Local heat transfer varies between in-line and staggered tube arrays and depends on Reynolds number and Prandtl number. At high Reynolds number, the local heat transfer tends to peak at the upstream surface of the heated tube but away from the stagnation point and becomes minimum at the separation point. Heat transfer in recirculation zones are, in general, small.
High Rayleigh Number Laminar Natural Convection in an Asymmetrically Heated Vertical Channel
Authors: Webb B. W. , Hill D. P.
Published: October 2009

Experiments have been performed to determine local heat transfer data for the natural convective flow of air between vertical parallel plates heated asymmetrically. A uniform heat flux was imposed along one heated wall, with the opposing wall of the channel being thermally insulated. Local temperature data along both walls were collected for a wide range of heating rates and channel wall spacings corresponding to the high modified Rayleigh number natural convection regime. Laminar flow prevailed in all experiments. Correlations are presented for the local Nusselt number as a function of local Grashof number along the channel. The dependence of both average Nusselt number and the maximum heated wall temperature on the modified Rayleigh number is also explored. Results are compared to previous analytical and experimental work with good agreement.
Induction Electrohydrodynamic Pump in a Vertical Configuration: Part 2—Experimental Study
Authors: Seyed-Yagoobi J. , Chato J. C. , Crowley J. M. , Krein P. T.
Published: October 2009

An induction electrohydrodynamic (EHD) pump in axisymmetric, vertical configuration was designed and built. The flow rates were measured for various temperature profiles and several values of frequency, voltage, wavelength, and electric conductivity. The experimental data are generally in good agreement with the theoretical model presented in Part 1. With the present apparatus at relatively low voltages, velocities four times higher than natural circulation velocity are easily obtained. The external pressure load and entrance temperature profile play important roles on the operation of the pump and must be considered carefully in the design.
Combined Forced and Free Upward-Flow Convection in the Entrance Region Between Inclined Parallel Plates
Authors: Naito E. , Nagano Y.
Published: October 2009

The effects of buoyancy on upward-flow laminar convection in the entrance region between inclined parallel plates are studied by a numerical method. Solutions are given for three thermal conditions of parallel plates: lower wall heated and upper wall insulated; vice versa; and both walls heated equally. Results are presented to show how the developing upward-flow and thermal field in the entry region are affected by buoyancy in terms of the various inclination angles of parallel plates. Correlation equations applicable in practice are also developed for the skin-friction coefficient and the local Nusselt number.
A Heat Transfer Analysis for Solidification of Slabs, Cylinders, and Spheres
Authors: Prud’homme M. , Nguyen T. Hung , Nguyen D. Long
Published: October 2009

The method of strained coordinates is applied to the inward solidification problem. Constant thermal properties are assumed throughout the analysis for the liquid, which is initially at the fusion temperature. A unified approach is adopted that allows the simultaneous treatment of the problem in plane, cylindrical, and spherical geometries for three different types of boundary condition. A general recurrence formula is derived for the determination of the series solutions up to any desired order of the Stefan number. A comparison is made with numerical and regular perturbation solutions in the plane case to illustrate the usefulness and the validity of the method.
An Experimental Investigation of Binary Solidification in a Vertical Channel With Thermal and Solutal Mixed Convection
Authors: Bennon W. D. , Incropera F. P.
Published: October 2009

Experimental measurements and photographic observations are presented for the solidification of a binary, aqueous ammonium chloride solution in a vertical channel. Transient liquidus front progressions and temperature measurements are used to characterize the influences of flow rate, superheat, composition, and chill wall temperature on binary phase-change behavior. Experimental results are compared with previously reported model predictions and discrepancies are used to critically assess model assumptions and limitations.
Microelectronic Cooling by Enhanced Pool Boiling of a Dielectric Fluorocarbon Liquid
Authors: Anderson T. M. , Mudawar I.
Published: October 2009

An experimental study of boiling heat transfer from a simulated microelectronic component immersed in a stagnant pool of the dielectric Fluorinert (FC-72) is presented. Various enhancement surfaces were attached to an electrically heated copper calorimeter bar having a vertically oriented heat transfer surface area of 12.7×12.7 mm2. A number of enhancement schemes aimed at a reduction of the incipience temperature overshoot were tested, employing various arrangements of fins, studs, grooves, and vapor-trapping cavities. Atmospheric pressure testing revealed a variation in the magnitude of boiling curve incipience temperature excursion as a function of both macro- and microcharacterization of the surface geometry and initial conditions (pressure and temperature history) prior to boiling. Increased incipience temperatures accompanied prolonged periods of nonboiling. It is assumed that this is due to vapor embryos within surface cavities collapsing to smaller radii. Large artificially created cavities (0.3 mm diameter) were found incapable of maintaining a stable vapor embryo for time periods greater than 10 min. In comparison to flat surfaces, low-profile surface geometries having a structure scale of the order of one bubble departure diameter resulted in significant enhancement of nucleate boiling while drilled surfaces had minimal effectiveness. Surface finish and artificial cavities had no effect on CHF, but levels of critical heat flux computed on base area were strongly dependent on macrogeometry, due in part to increased surface area.
A Study of Heat Transfer and Particle Motion Relative to the Modified Chemical Vapor Deposition Process
Authors: Choi M. , Greif R. , Baum H. R.
Published: October 2009

Heat transfer and particle motion relative to the modified chemical vapor deposition process have been studied for general values of the torch speed. Three-dimensional temperature fields have been obtained over the entire cross section of the tube and the effects of tube rotation and localized torch heating in the axial and circumferential directions have been studied. The particle trajectories have been calculated from a formulation that includes the contributions from forced flow, i.e, Poiseuille flow in the axial direction, rigid body rotation about the tube axis, and thermophoretic contributions in the axial, radial, and angular directions. The particle trajectories are helices and are shown to be strongly dependent on the tube rotation.
Single- and Two-Phase Convective Heat Transfer From Smooth and Enhanced Microelectronic Heat Sources in a Rectangular Channel
Authors: Maddox D. E. , Mudawar I.
Published: October 2009

Experiments have been performed to assess the feasibility of cooling microelectronic components by means of single-phase and two-phase forced convection. Tests were conducted using a single heat source flush mounted to one wall of a vertical rectangular channel. An inert fluorocarbon liquid (FC-72) was circulated upward through the channel at velocities up to 4.1 m/s and with subcooling up to 46°C. The simulated microelectronic heat sources tested in this study include a smooth surface and three low-profile microstud surfaces of varying stud height, each having a base area of 12.7×12.7 mm2. Correlations were developed for the single-phase convective heat transfer coefficient over the Reynolds number range from 2800 to 1.5 × 105, where Reynolds number is based on the length of the heater. The results demonstrate that the low thermal resistances required for cooling of microelectronic heat sources may be achieved with single-phase forced convection by using high fluid velocity coupled with surface enhancement. Experiments were also performed to understand better the parametric trends of boiling heat transfer from the simulated microelectronic heat source. It was found that increased velocity and subcooling and the use of microstud surfaces enhance nucleate boiling, increase the critical heat flux, and reduce the magnitude of temperature overshoot upon the inception of nucleation.
Condensation on Coherent Turbulent Liquid Jets: Part I—Experimental Study
Authors: Kim S. , Mills A. F.
Published: October 2009

Condensation on coherent turbulent liquid jets was investigated experimentally in order to obtain a data base for the liquid side heat transfer coefficient. Jet breakup was identified by means of high-speed photography. Nozzles were formed from smooth and roughened glass tubes to define the initial turbulence level in the jets. Jet diameters of 3–7 mm and lengths of 2–12 cm were tested at jet velocities of 1.4–12 m/s giving Reynolds numbers of 6000–40,000. Viscosity and surface tension were varied by using ethanol, and water from 277–300 K, as test liquids. The Stanton number was found to be essentially independent of jet diameter, but to decrease with length to the power of −0.57, velocity to the power of −0.20, surface tension to the power of −0.30, and viscosity to the power of −0.1.
Performance Characteristics of a Concentric Annular Heat Pipe: Part II—Vapor Flow Analysis
Authors: Faghri A.
Published: October 2009

The solutions of the equations of fluid motion for compressible and incompressible flow in a concentric annular heat pipe have been analyzed. In addition, a similarity solution is presented that can predict the pressure losses in all the segments of the concentric annular heat pipe as well as conventional heat pipes. A theoretical analysis to predict the sonic limit for this new heat pipe is also presented.
Proposed Method for Measuring Local Heat Transfer Coefficients of Isothermal Surfaces
Authors: Kumada T.
Published: October 2009

A method has been proposed for measuring local heat transfer coefficients. The method uses the change of a wet surface temperature by radiation heating and can be applied to isothermal conditions and with large variations of the local heat transfer coefficients along the surface of a body. The present method is based on the heat balance equation, which expresses a simple relationship between humidity and wet-bulb temperatures. An experiment was devised to measure the local heat transfer coefficient along a flat plate. The results confirmed the effectiveness of the present method to measure local and overall heat and mass transfer coefficients with reasonable accuracy.
Heat Transfer, Temperature, and Velocity Measurements Downstream of an Abrupt Expansion in a Circular Tube at a Uniform Wall Temperature
Authors: Baughn J. W. , Hoffman M. A. , Launder B. E. , Lee Daehee , Yap C.
Published: October 2009

Detailed heat transfer, temperature, and velocity data are reported for the turbulent flow downstream of an abrupt increase in tube diameter (2.5:1) in which the downstream tube is maintained at a uniform elevated temperature. The heat transfer experiments cover downstream Reynolds numbers ranging from 4300 to 44,500, the flow being fully developed at the exit of the small tube (i.e., the abrupt expansion step). Maximum local heat transfer coefficients are proportional to the upstream Reynolds number to the power 2/3 with the location of the maximum moving upstream slightly as the Reynolds number is increased. Heat transfer data at a Reynolds number of 17,300 are supplemented by velocity and temperature profiles, which are especially informative. They bring out clearly that the viscous sublayer, despite the thinning that is believed to occur in the vicinity of the reattachment point, still provides the major resistance to heat transfer. The correct prediction of the Nusselt–Reynolds number relation in reattaching flows is thus crucially dependent on the variation of turbulent diffusivity in the “buffer” region of the flow.
An Experimental Investigation of Natural Convection From an Isothermal Horizontal Plate
Authors: Clausing A. M. , Berton J. J.
Published: October 2009

An investigation of natural convection from a heated, upward-facing, square, horizontal plate to a surrounding gas medium is described in this paper. The results of the experimental investigation provide an improved correlation for the natural convection regime by accounting for variable property effects and extend the applicable Rayleigh number (Ra) range of the correlation over previous research. The large Rayleigh number regime is emphasized. The value of the Richardson number (Ri) at which combined convection influences become important is also determined. The ratio of the plate wall temperature Tw to the ambient temperature T∞ is incorporated into the Nusselt number correlation in order to account for variable property influences. A cryogenic heat transfer tunnel, with test section temperatures that are varied between 80 K and 310 K, is used to help deduce the influences of the relevant parameters. The ranges of the dimensionless parameters investigated are 2 × 108 < Ra < 2 × 1011 and 1 < Tw/T∞ < 3.1.