bluuebunny/crossref_metadata_2025 huggingface dataset:
Hydrodynamic Prediction of Peak Pool-boiling Heat Fluxes from Finite Bodies
Authors: Lienhard J. H. , Dhir V. K.
Published: November 2010

Since Zuber made a hydrodynamic prediction of the peak pool-boiling heat flux on an infinite flat plate, his general concept has been used to predict the peak heat flux in two finite heater configurations. These latter predictions have differed from Zuber’s in the introduction of a largely empirical variable—the thickness of the vapor escape path around the body. The present study shows how measurements of this thickness can be combined with the hypothesis that the vapor velocity within the vapor blanket must match the vapor velocity in the escaping jet above the heater. The result is a more exact description of the hydrodynamics of vapor removal. This idea is used to suggest the possibility of a universal value for the ratio of the cross-sectional area of escaping jets to the heater area for large finite heaters and for long slender heaters. A set of general ground rules is developed for predicting the peak heat fluxes on both large and small heaters. These rules are used in turn to predict the peak heat flux from horizontal ribbons. They are also used to correct the traditional prediction for infinite-flat-plate heaters. The predictions are supported with new data.
Stability and Oscillation Characteristics of Finite-Element, Finite-Difference, and Weighted-Residuals Methods for Transient Two-dimensional Heat Conduction in Solids
Authors: Yalamanchili R. V. S. , Chu S.-C.
Published: November 2010

The finite-element difference expression was derived by use of the variational principle and finite-element synthesis. Several ordinary finite-difference formulae for the La-placian term were considered. A particular finite-difference formula for the Laplacian term was chosen to bring the difference expressions of finite-element, finite-difference, and weighted-residuals (Galerkin) methods into the same format. The stability criteria were established for all three techniques by use of the general stability, von Neumann, and Dusinberre concepts. The oscillation characteristics were derived for all three techniques. The finite-element method is more conservative than the finite-difference method, but not so conservative as the Galerkin method in both stability and oscillation characteristics.
The Use of Singularity Programming in Finite-Difference and Finite-Element Computations of Temperature
Authors: Emery A. F.
Published: November 2010

This report contains a description of a numerical technique designed to overcome the difficulties associated with the usual solution of two-dimensional discretized thermal problems when there are singularities arising from point sources or discontinuous boundary conditions. The method is here applied to both the finite-difference and the finite-element approach by incorporating in the numerical computations the known analytical form of the singularities.
Vapor Flow in Cylindrical Heat Pipes
Authors: Bankston C. A. , Smith H. J.
Published: November 2010

Solutions of the complete axisymmetric Navier–Stokes equations for steady, laminar vapor flow in circular heat pipes with various lengths of evaporator and condenser have been obtained by finite-difference methods. In addition, a new series solution for the slow-motion case was obtained that is valid for arbitrary distributions of evaporation and condensation and that confirms the numerical result in the limit of low Reynolds number. For uniform evaporation and condensation, the motion in the evaporator is found to be described adequately by similar solutions in both limits, and in the transition from low to high Re, the flow is completely determined by the evaporator Reynolds number. The evaporator is very weakly coupled to the condenser. The conditions in the condenser are decidedly more complex, and similar solutions are of value only for small Reynolds numbers and long tubes. Reverse flows occur for condenser Reynolds numbers greater than two and occupy a substantial fraction of the condenser length. Complete flow descriptions for symmetrical and asymmetrical heat pipes were obtained, and practical results for the calculation of pressure losses in low-speed heat-pipe vapor flows are given.
Multistream Countercurrent Heat Exchangers
Authors: Bentwich M.
Published: November 2010

An idealized model multistream countercurrent exchanger is considered. It comprises a number of parallel two-dimensional streams in channels separated by thin conductive partitions. The streams on the two sides of any partition flow in opposite directions. Thus the heat contained in one set of co-directional currents, which enters the exchanger at a high temperature, is transferred through the partitions to the oppositely directed cooling streams. The analysis accounts for the entire temperature distribution in this model when the axial conduction in the streams and in the partitions is neglected. The solution is obtained by expressing the temperature field in terms of the inlet conditions and the flux across the partitions. The latter is represented by as many a priori unknown functions of the axial distance as there are partitions. They are governed by the same number of linear integral equations. Using a finite-difference technique, these are solved for a variety of cases that are of practical interest.
Methods for Evaluating the Performances of Compact Heat Transfer Surfaces
Authors: Cox B. , Jallouk P. A.
Published: November 2010

Methods are presented for evaluating the performances of compact surfaces based on their simultaneous heat transfer rates and pumping power expenditures. Calculations of approximate total costs and volume requirements for a heat exchanger are simplified with the aid of performance curves based on a unit of heat transfer surface area and a unit of exchanger volume. In certain cases, the minimum cost surface can be determined from a single plot and requires no specific cost information. Basic design data are presented for three plate-fin surfaces, each one having a different degree of heat transfer promotion. The attractiveness of each type of surface is shown to depend on the particular design specifications.
An SEM Study of Nucleation Sites in Pool Boiling From 304 Stainless Steel
Authors: Nail J. P. , Vachon R. I. , Morehouse J.
Published: November 2010

A Scanning Electron Microscope (SEM) was used to examine pool boiling nucleation sites on 304 stainless steel in contact with distilled, degassed water. Nucleation sites were located during the boiling process by noting the coordinates of the bubble locations on the surface. These locations were then magnified using the SEM and photographs made of the nucleation sites. The radii of the cavities varied from 14.8μ-in. to 180μ-in. and the widths of grooves varied from 75μ-in. to 154μ-in.
Local Nonsimilar Solutions for Natural Convection on a Vertical Cylinder
Authors: Minkowycz W. J. , Sparrow E. M.
Published: November 2010

The local nonsimilarity solution method has been applied to solve for natural convection on a vertical cylinder for conditions where there are large deviations from the flat plate results. To assess and insure the accuracy of the results, solutions were obtained for three levels of truncation of the governing equations. The solutions were carried out for Pr = 0.733 and for a range of cases extending from small deviations from the flat plate to a factor-of-four deviation between the local heat fluxes for the cylinder and the flat plate. The results provided by the local similarity solutions were found to be highly accurate over this range. Comparisons were made with available results for the local and surface-integrated heat transfer, and solution methods were identified which appear promising for application beyond the range studied here. A presentation of representative temperature and velocity profiles showed only small deviations between the local similarity solutions and those for the third level of truncation.
Boiling and Evaporation From Heat Pipe Wicks With Water and Acetone
Authors: Abhat A. , Seban R. A.
Published: November 2010

Heat transfer for pool boiling with flaxes in the range of 5 × 102 5 × 104 Btu/(ft2 hr) and the associated excess of wall over saturation temperatures are presented, primarily for atmospheric pressure, for vertical tubes in water, ethanol, and acetone, bare or wrapped with screen or felt metal. For the wrapped tubes, this performance is given also for evaporation into surrounding saturated vapor with the liquid being supplied by the wick: this is the significant mode in respect to heat pipe applications. For this mode maximum evaporation rates are also indicated and it is shown that this maximum can be rationalized either in terms of a partially full wick with conduction transfer to the evaporation surface or in terms of a full wick with vapor holes originating at nucleation sites on the tube surface.
Preliminary Measurements of Instantaneous Velocity in a Two-Meter Square Furnace Using a Laser Anemometer
Authors: Baker R. J. , Hutchinson P. , Whitelaw J. H.
Published: November 2010

The results of an exploratory investigation of the application of laser anemometry to the measurement of instantaneous velocity within industrial flames is reported. A laser anemometer was used to assess the viability of measurements within the 2 m-sq experimental furnace of the International Flame Research Foundation. Measurements were carried out, in the forward scattering real fringe mode, in a hot furnace without combustion and in gas, oil, and coal flames. The particle concentration was observed for each flow configuration and, where possible, the mean velocity value obtained from the laser anemometer was compared with that from a water cooled pitot probe. On the basis of this investigation, the value of laser anemometry to the improvement of furnace design is discussed.
Mean Temperature Difference for Heat Exchanger Design—A General Approximate Explicit Equation
Authors: Roetzel W. , Nicole F. J. L.
Published: November 2010

An approximate equation together with empirical coefficients is presented for the fast calculation of the mean temperature difference of nine countercurrent cross-flow arrangements, as applied in air-cooled heat exchangers. The same equation can be used for other flow systems, as demonstrated for one shell-and-tube arrangement.
Experimental Investigation of Combined Forced and Free Laminar Convection in Horizontal Tubes
Authors: Morcos S. M. , Bergles A. E.
Published: November 2010

The present study considers the effects of property variations on fully developed laminar flow heat transfer and pressure drop in horizontal tubes. A facility was developed to test electrically heated glass and stainless steel tubes, with distilled water and ethylene glycol as working fluids. The Nusselt number for fully developed flow depends primarily on Rayleigh number; however, the Prandtl number and a dimensionless tube wall parameter are also required to correlate the four sets of heat transfer data. This correlation agrees well with data of most previous investigations. The friction factor increases with increasing Rayleigh number; data are within the bounds of limiting analytical predictions.
Heat Transfer Augmentation in Laminar Fully Developed Channel Flow by Means of Heating From Below
Authors: Ostrach S. , Kamotani Y.
Published: November 2010

Results are reported of an experimental investigation of fully developed forced convection between two horizontal plates when the lower plate is heated and the upper one is cooled. The experiments covered a range of Rayleigh numbers between 100 and 13,500 and Reynolds numbers less than 100 using air. The heat transfer measurements show a sharp increase of heat transfer coefficient when longitudinal vortex rolls appear in the passage which indicates the considerable heat-transfer augmentation obtained in this way. Comparison of heat transfer coefficients for fully developed cases and those for confined cases indicates that there is no appreciable difference between them. Periodic spanwise temperature distributions created by vortex rolls are distorted by a second type of vortex rolls as the Rayleigh number increases. Because of the interaction the regular vortex structure disappears around Rayleigh number 8000.
Measurements of Drop-Size Distributions During Transient Dropwise Condensation
Authors: Tanaka H.
Published: November 2010

Instantaneous drop-size distributions were measured during transient dropwise condensation onto an initially bare surface which forms the constituent process of the so-called steady dropwise condensation on a vertical surface. The measured distributions agreed satisfactorily with the prediction from the previous author’s theory.
Theoretical Analysis of a Horizontal Condenser-Evaporator Elliptical Tube
Authors: Moalem D. , Sideman S.
Published: November 2010

The characteristics of the various parameters affecting the films and overall heat transfer coefficients of horizontal evaporator-condenser elliptical tubes are presented for a representative range of operating conditions. Effects of the axis ratio of the tube are analyzed and compared with the equivalent circular tube. The study indicates that the ratio of the vertical to the horizontal axis of about 4 approaches the asymptotic solution for a vertical plane of constant wall temperature and the average overall transfer rate decreases at axis ratios above 4. Effects of the intermittent removal of the condensate film from the wall are presented. The effect of homogeneously distributed noncondensables is accounted for.
Thermal Stability of Binary Gas Mixtures in a Porous Medium
Authors: Lawson M. L. , Yang Wen-Jei
Published: November 2010

Thermal instability of a thin horizontal layer of binary gas mixture subject to an adverse temperature gradient in a porous medium is experimentally determined by applying the Schmidt-Milverton principle for detecting the onset of convective currents. The binary gas mixture consists of helium and nitrogen gases at various composition, while a packed bed of tiny steel balls constitutes the porous medium. It is disclosed that the critical Rayleigh number for pure gas is lowered by the presence of another species of different molecular weight and has a minimum value at a certain composition of the binary mixture.
Field Controlled Charge and Heat Transfer Involving Macroscopic Charged Particles in Liquids
Authors: Dietz P. W. , Melcher J. R.
Published: November 2010

When an electric field is applied to a system of electrically conducting particles in an insulating liquid, the rates of charge and heat transfer are augmented. Charged during collisions in the field, the particles execute field-induced excursions between the electrodes interrupted by collisions with other particles. Thus a combination of particle migration and particle-induced fluid convection results in the increase in heat transfer. Experimental values for the Nusselt number are obtained for heat transfer across the parallel electrode configuration. The model developed using these results consists of a well-mixed central region with thermal boundary layers about one particle diameter thick near each electrode.
Thermal Performance Analysis of the Stationary Reflector/Tracking Absorber (SRTA) Solar Concentrator
Authors: Kreider J. F.
Published: November 2010

The performance of a novel solar energy concentrating system consisting of a fixed, concave spherical mirror and a sun-tracking, cylindrical absorber is analyzed in detail. This concentrating system takes advantage of the spherical symmetry of the mirror and its linear image which, when taken together, form a tracking, solar-concentrating system in which only the small cylindrical absorber need move. The effects of mirror reflectance, concentration ratio, heat transfer fluid flow rate, radiative surface properties, incidence angle, an evacuated absorber envelope, and insolation level upon thermal performance of the concentrator are studied by means of a mathematical model. The simulation includes first order radiation and convection processes between the absorber and its concentric glass envelope and between the envelope and the environment; radiation processes are described by a dual-band, gray approximation. The energy equations are solved in finite difference form in order that heat flux and temperature distributions along the absorber may be computed accurately. The results of the study show that high-temperature heat energy can be collected efficiently over a wide range of useful operating conditions. The analysis indicates that mirror surface reflectance is the single most important of the principal governing parameters in determining system performance. Efficiency always increases with concentration ratio although the rate of increase is quite small for concentration ratios above 50. High fluid flow rate (i.e., lower operating temperature), an evacuated envelope, or a highly selective surface can enhance performance under some conditions. The conclusion of the study is that high-temperature heat energy can be generated at high efficiency by the present concentrator with present technology in sunny regions of the world.
Effect of Nozzle—Surface Separation Distance on Impingement Heat Transfer for a Jet in a Crossflow
Authors: Sparrow E. M. , Goldstein R. J. , Rouf M. A.
Published: November 2010

Measurements were made of the local heat transfer coefficients resulting from the impingement of a turbulent jet which interacts with a crossflow. The experiments were performed for separation distances between the exit of the jet nozzle and the impingement surface ranging from 3 to 12 times the jet exit diameter. The ratio of jet to crossflow mass velocity was varied from 4 to 12. To evaluate the heat transfer coefficients, local recovery temperatures were also measured. The results for the larger mass velocity ratios indicated that as the separation distance is varied, the impingement point heat transfer coefficient attains a maximum when the separation distance is 5–6 times the jet diameter. On the other hand, at a smaller mass velocity ratio such as 4, the maximum is attained at a substantially smaller separation distance. Experiments were also performed to examine how the transfer coefficients are affected by the presence or absence of a simulated duct wall at the exit of the jet nozzle. The differences between the results for the two configurations were confined to dimensionless separation distances greater than 4, with the largest effects at low mass velocity ratios.
Heat and Mass Transfer From Freely Falling Drops
Authors: Yao Shi-Chune , Schrock V. E.
Published: November 2010

When a drop breaks free from a liquid film or feeding orifice and falls through an atmosphere of lower temperature it experiences a transient heat and mass transfer process involving acceleration, the development of hydrodynamic, thermal, and concentration boundary layers in the gas, oscillation of the drop shape, and the development of internal circulation within the drop. This problem, which is of importance in evaporative cooling systems, has been studied experimentally for water drops 3–6 mm in diameter falling through air. Study of a simplified set of governing equations indicates that similitude does not exist in this problem. However, it has been found that for this size range an approximate procedure based on the assumption of negligible internal thermal resistance and an empirical transient correction factor applied to the Ranz-Marshall [1] correlation could describe the data very well.
Behavior of Inert Gas Bubbles in Forced Convective Liquid Metal Circuits
Authors: Minkowycz W. J. , France D. M. , Singer R. M.
Published: November 2010

Conservation equations are derived for the motion of a small inert gas bubble in a large flowing liquid-gas solution subjected to large thermal gradients. Terms which are of the second order of magnitude under less severe and steady-state conditions are retained, thus resulting in an expanded form of the Rayleigh equation. The bubble dynamics is a function of opposing mechanisms tending to increase or decrease bubble volume while being transported with the solution. Diffusion of inert gas between the bubble and the solution is one of the most important of these mechanisms included in the analysis. The analytical model is applied to an argon gas bubble flowing in a weak solution of argon gas in liquid sodium. Calculations are performed for these fluids under conditions typical of normal and abnormal operation of a liquid metal fast breeder reactor (LMFBR) core and the resulting bubble radius, internal gas pressure, and mass of inert gas are presented in each case. An important result obtained indicates that inert gas bubbles reaching the core inlet of an LMFBR will always grow as they traverse the core under normal and extreme abnormal conditions and that the rate of growth is quite small in all cases.
Experimental Investigation of Natural Convection in Inclined Rectangular Regions of Differing Aspect Ratios
Authors: Arnold J. N. , Catton I. , Edwards D. K.
Published: November 2010

An experimental investigation of steady natural convection heat transfer was carried out for finite rectangular regions. The effect of angle of inclination on heat transfer across rectangular regions of several aspect ratios was measured for Rayleigh numbers between 103 and 106. The angle of inclination varied from 0 deg (heated from above) to 180 deg (heated from below) with aspect ratios of one, three, six, and twelve. Comparison is made with past theoretical work, and a simple scaling law is derived which is valid for angles of inclination from 0 to 90 deg (vertical).
A Model for Flame Propagation in Low Volatile Coal Dust-Air Mixtures
Authors: Krazinski J. L. , Buckius R. O. , Krier H.
Published: November 2010

A model describing steady, laminar flame propagation in low volatile coal dust-air mixtures is presented. The model includes radiative transport, a two-phase energy equation, and heterogeneous carbon gasification of the coal particles. The differential approximation (or method of spherical harmonics) was used to represent the one-dimensional radiant energy transport. The equations were numerically integrated and predictions of flame structure and the adiabatic flame speed are presented. The effects of radiation properties and coal particle size are presented and discussed. The influence on the temperature profiles of heat released in the solid phase is also described.
Experiments on the Onset of Longitudinal Vortices in Horizontal Blasius Flow Heated from Below
Authors: Gilpin R. R. , Imura H. , Cheng K. C.
Published: November 2010

Experiments were performed to confirm the occurrence and growth of longitudinal vortices in a laminar boundary layer developing in water over a heated horizontal flat plate with uniform surface temperature. Photographs of the vortices, measurements of the conditions of their onset, and measurements of their wavelength are presented. Comparisons are made with theoretical instability results for the critical Grashof number and wavelength. Temperature profiles across the boundary layer were measured for flows with and without vortices to show qualitatively the effect that the longitudinal vortices have on the heat transfer rate at the plate. Under conditions of thermal instability the longitudinal vortices were found to be the first stage of the laminar-turbulent transition process in a boundary layer heated from below.
A Numerical Study of Unsteady Laminar Forced Convection From a Circular Cylinder
Authors: Jain P. C. , Goel B. S.
Published: November 2010

A numerical investigation of an unsteady laminar forced convection from a circular cylinder is presented. The Navier-Stokes equations and the energy equation for an unsteady incompressible fluid flow are solved by the finite difference method. The results are obtained at Reynolds numbers 100 and 200. The temperature field around the cylinder is obtained throughout the region of computation and is shown by isotherms at different times. The variations of the local Nusselt number around the cylinder at different times are computed and shown by graphs. The mean Nusselt number and the Strouhal number are also calculated. The computed results are compared with the other available experimental and theoretical results and are found to be in good agreement with them.
Calculations of Combined Radiation and Convection Heat Transfer in Rod Bundles Under Emergency Cooling Conditions
Authors: Sun K. H. , Gonzalez-Santalo J. M. , Tien C. L.
Published: November 2010

A model has been developed to calculate the heat transfer coefficients from the fuel rods to the steam-droplet mixture typical of Boiling Water Reactors under Emergency Core Cooling System (ECCS) operation conditions during a postulated loss-of-coolant accident. The model includes the heat transfer by convection to the vapor, the radiation from the surfaces to both the water droplets and the vapor, and the effects of droplet evaporation. The combined convection and radiation heat transfer coefficient can be evaluated with respect to the characteristic droplet size. Calculations of the heat transfer coefficient based on the droplet sizes obtained from the existing literature are consistent with those determined empirically from the Full-Length-Emergency-Cooling-Heat-Transfer (FLECHT) program. The present model can also be used to assess the effects of geometrical distortions (or deviations from nominal dimensions) on the heat transfer to the cooling medium in a rod bundle.
“Heat-Valve” Effects in the Ground Thermal Regime
Authors: Gilpin R. R. , Wong B. K.
Published: November 2010

A one-dimensional model of a freezing and thawing ground with a seasonally varying surface cover was analyzed. Analytical and numerical techniques were used primarily to study the factors that produce differences between the yearly means of the air and ground temperatures. It was shown that the variation of the surface cover characteristics in phase with the annual air temperature wave can generate the heat-valve effect which is responsible for raising the average ground temperature above the average air temperature. This temperature difference was, however, very sensitive to changes to the surface cover properties indicating how disturbances to the surface cover could cause melting of a permafrost soil.
Axial Heat Conduction Effects on Thermal Instability of Horizontal Plane Poiseuille Flows Heated From Below
Authors: Cheng K. C. , Wu R.-S.
Published: November 2010

A linear stability analysis is used to study the effect of axial heat conduction on the onset of instability for longitudinal and transverse vortex disturbances for plane Poiseuille flow in the thermal entrance region of a horizontal parallel-plate channel heated from below with a constant temperature difference between two plates. The basic flow solution for temperature (Graetz problem) incorporates axial heat conduction effects and the fluid temperature is taken to be uniform at the far upstream location x = −∞ to allow for upstream heat penetration through the thermal entrance x = 0. Numerical results for the critical Rayleigh numbers are obtained for an entrance temperature parameter θ0 = 1 (T0 = T2) and Peclet numbers 1, 5, 10, 50. It is found that the transverse vortex disturbances are preferred over the longitudinal vortex disturbances for Pe ≲ 1 and Pr ≳ 1 (low Re) in the developing regions upstream and downstream of the thermal entrance. For other conditions, the longitudinal rolls have priority of occurrence. The Prandtl number effect on the onset of the longitudinal vortices is clarified.
A Solution of Freezing of Liquids of Low Prandtl Number in Turbulent Flow Between Parallel Plates
Authors: Shibani A. A. , O¨zis¸ik M. N.
Published: November 2010

The steady-state freezing of liquids of low Prandtl number in turbulent flow between parallel plates, the walls of which are kept at uniform temperature lower than the freezing temperature of the liquid, is solved by matched asymptotic technique. The location of the liquid-solid interface and the heat transfer rate are established as a function of the axial position along the channel.
Free Convection Boundary Layers on Cylinders of Elliptic Cross Section
Authors: Merkin J. H.
Published: November 2010

Numerical results are presented for free convection boundary layers over horizontal cylinders of elliptic cross section when the major axis is both horizontal and vertical and when the cylinder is isothermal and has constant heat flux. The particular case of a circular cylinder is considered and these results are compared with the various series expansions suggested for solving the equations.
The Use of the Milne-Eddington Absorption Coefficient for Radiative Heat Transfer in Combustion Systems
Authors: Felske J. D. , Tien C. L.
Published: November 2010

The applicability of the Milne-Eddington absorption coefficient approximation is discussed in relation to the calculation of radiative transport involving the two distinct types of species produced in combustion systems—gases and soot particles. The approximation is found to apply well to hydrocarbon soot particles and as a result analytical closed-form solutions are derived for the radiative heat transfer inside one-dimensional slab shaped soot clouds. (The applicability of the gray approximation to soot is also discussed.) For the calculation of total band radiation from gases, however, the Milne-Eddington approximation is found to be questionable. The meaning of its assumption is discussed in light of an established Curtis-Godson wide band scaling approximation. Its usefulness for real gases is then assessed through the calculation and comparison of slab radiation by both techniques.
Analysis of Melting in the Presence of Natural Convection in the Melt Region
Authors: Sparrow E. M. , Patankar S. V. , Ramadhyani S.
Published: November 2010

An analysis of multidimensional melting is performed which takes account of natural convection induced by temperature differences in the liquid melt. Consideration is given to the melt region created by a heated vertical tube embedded in a solid which is at its fusion temperature. Solutions were obtained by an implicit finite-difference scheme tailored to take account of the movement of the liquid-solid interface as melting progresses. The results differed decisively from those corresponding to a conventional pure-conduction model of the melting problem. The calculated heat transfer rate at the tube wall decreased at early times and attained a minimum, then increased and achieved a maximum, and subsequently decreased. This is in contrast to the pure conduction solution whereby the heat transfer rate decreases monotonically with time. The thickness of the melt region was found to vary along the length of the tube, with the greatest thickness near the top. This contrasts with the uniform thickness predicted by the conduction solution. These findings indicate that natural convection effects, although unaccounted for in most phase change analyses, are of importance and have to be considered.
Heat Transfer to Water in Downward Flow in a Uniform Wall Temperature Vertical Tube at Low Graetz Numbers
Authors: Mullin T. E. , Gerhard E. R.
Published: November 2010

This paper presents an experimental investigation of heat transfer to water in vertical tube flow. Results from both Heating in Upflow and Heating in Downflow with the Natural Convection Parameter (Gr Pr D/L)w held constant at a value of 5.5 × 105 are compared with the expression developed by Martinelli and Boelter. The Nusselt numbers for Heating in Downflow were slightly higher but, within experimental error, equivalent to those values obtained for Heating in Upflow. A description of the flowfield is presented for one set of conditions for Heating in Downflow.
Analysis of Effects of Free-Stream Turbulence on Heat Transfer and Skin Friction
Authors: Miyazaki H. , Sparrow E. M.
Published: November 2010

A model for the momentum eddy diffusivity induced by free-stream turbulence was constructed on the basis of measured turbulent velocity fluctuations. The thermal eddy diffusivity was obtained via the turbulent Prandtl number. The general eddy diffusivity model was applied at the stagnation point of a cylinder situated in a uniform crossflow. The expression for the eddy diffusivity contains a single unknown constant which was determined from experimental stagnation point heat transfer results. Nusselt numbers and friction factors were evaluated from solutions of the governing conservation equations, and comparisons were made with available data and other predictions. The present analytical results agree well with the data and exhibit a behavior whereby, in concert with the data, the Nusselt number (and friction factor) increases with the free-stream turbulence intensity but to a lesser extent as the turbulence intensity increases. The effect of free-stream turbulence on the friction factor is shown to be substantially less than the effect on the Nusselt number.
Convection in an Enclosure-Source and Sink Located Along a Single Horizontal Boundary
Authors: Clomburg L. A.
Published: November 2010

Laminar natural convection in a two-dimensional enclosure with both source (uniform heat flux density) and sink (temperature specified) located on the top horizontal boundary is investigated numerically. Temperature and velocity profiles are presented for a high Prandtl number fluid for length Rayleigh numbers in the range 107 to 109 for length to depth ratios of 1:1 to 4:1. To generalize the results, an order of magnitude analysis is used to determine the dependence of temperature, velocity, and boundary-layer thickness scales on aspect ratio and Rayleigh number. The numerical data are well correlated using these suggested scales. The analysis shows the Nusselt number and the maximum horizontal velocity to depend on the 1/6 and 1/3 powers of the Rayleigh number, independent of aspect ratio.
Free-Forced Convection in the Entry Region of a Heated Straight Pipe
Authors: Yao Lun-Shin
Published: November 2010

The developing flow in the entry region of a horizontal pipe whose temperature is held constant and higher than the entry fluid temperature is analyzed. The asymptotic solution of the developing flow near the entrance of the heated straight pipe, distance 0(a), is obtained by perturbing the solution of the developing flow in an unheated straight pipe. The displacement of the boundary layer induces radial-directional and downward motion of the fluid particles in the inviscid core flow. The combination of these two motions results in two vortices developing along the pipe. The temperature in the core flow equals the entry fluid temperature. The forced convection boundary layer is affected by the buoyancy force and the axial pressure gradient induced by the boundary-layer displacement, and so is the heat transfer rate. The axial velocity has a concave profile with its maximum off the center line near the entrance, and it grows toward a uniformly distributed profile downstream. The downward stream caused by the displacement of the secondary boundary layer forces the axial velocity profile to turn counterclockwise continuously along the pipe if the flow is from left to right. The competition of two displacement effects supplies the physical explanation of why the flow pattern and the temperature distribution in heated pipes differ due to different degrees of heating.
Laminar Mixed-Mode, Forced and Free, Diffusion Flames
Authors: Shih T. M. , Pagni P. J.
Published: November 2010

To explore the intersection of previous studies of inert mixed-mode flows and single-mode diffusion flames, this analysis describes a laminar, forced and free, mixed-mode diffusion flame adjacent to a vertically burning fuel slab. Shvab-Zeldovich variables, boundary-layer and local similarity approximations are used. Five flaming and chemical parameters are found necessary to describe this combusting system. The solution obtained herein includes profiles of velocity, Shvab-Zeldovich variables and thereby enthalpy and species, as well as surface fluxes, flame sheet locations and excess pyrolyzate. For comparison, the finite-difference method is also employed. The local similarity solution for surface gradients lies within 20 percent of the finite-difference results. Good agreement with the aforementioned simpler limiting cases is also obtained. The results indicate that the flow characteristics of a mixed-mode flame are more complicated than a simple superposition of the two limiting flame cases.
The Temperature Dependence of Surface Tension of Pure Fluids
Authors: Alamgir Md. , Lienhard J. H.
Published: November 2010

The temperature dependence of the surface tension of pure liquids, in contact with their vapors, is correlated using the law of corresponding states. Molecular form is characterized by the Pitzer acentric factor. The temperature dependence reduces to a form identical to that of the van der Waals limiting liquid superheat when the Pitzer factor reaches the van der Waals value. The correlation brings together data for 91 organic and inorganic—polar and nonpolar—substances, within a constant, over the ranges of temperature for which data exist. Only water requires special modification. The accuracy of the correlation is on the order of ± one percent. This correlation will give surface tension over almost the entire range of temperature if one measured value, and the Pitzer factor, are known.
Effect of Subcooling on Cylindrical Melting
Authors: Sparrow E. M. , Ramadhyani S. , Patankar S. V.
Published: November 2010

An analysis is made of the melting of a subcooled solid surrounding a heated circular cylinder. The solution is facilitated by coordinate transformations which immobilized both the moving interface between the melt region and the solid and the moving temperature wave that diffuses into the solid. The actual solutions were carried out numerically via a finite-difference procedure which circumvents the nonlinearity associated with the moving interface. Results were obtained for a wide range of a subcooling parameter and of the Stefan number. It was found that the subcooling can have a marked effect on the melting characteristics. Depending on the degree of subcooling, the surface heat transfer can be several times greater than that for no subcooling. Furthermore, at high levels of subcooling and at long melting times, the liquid layer thickness may be only a small fraction of that without subcooling. Subcooling also sharpens the differences between cylindrical and plane melting. The ratio of the heat flux for cylindrical melting to that for plane melting increases substantially due to subcooling, while the thickness of the cylindrical melt layer is only a fraction of that of a corresponding plane melt layer.
Laminar Boundary Layer Transfer over Rotating Bodies in Forced Flow
Authors: Lee Min-Hsiun , Jeng D. R. , De Witt K. J.
Published: November 2010

A procedure is described for the calculation of momentum and heat transfer rates through laminar boundary layers over rotating axisymmetric bodies in forced flow. By applying appropriate coordinate transformations and Merk’s type of series, the governing momentum equations can be expressed as a set of coupled ordinary differential equations that depend on a wedge parameter and on a rotation parameter. For the energy equation, a set of ordinary differential equations is obtained which depend explicitly on the Prandtl number and implicitly on the aforementioned parameters. These equations are numerically integrated for a range of parameter values for the special case of a rotating sphere, and the local friction coefficient and the local Nusselt number are presented for values of the rotation parameter B = 1, 4, and 10 with Prandtl numbers of 1, 10, and 100. These results are then compared with previous theoretical results. It is also shown how the flow and heat transfer characteristics for a rotating disk can be readily obtained as a special case from the formulation for the rotating sphere. The disk results are also compared with previous theoretical and experimental studies.
The Effect of Buoyancy on the Turbulence Structure of Vertical Round Jets
Authors: Tamanini F.
Published: November 2010

The paper presents an application of the algebraic stress modeling (ASM) technique to the prediction of the flow in a turbulent round buoyant jet. In the ASM approach, algebraic formulas are obtained for the Reynolds stresses, uiuj, and for the components of the turbulent heat flux, tui. In the model used here, transport equations are solved for the turbulence kinetic energy, k, its dissipation, ε, and the mean square temperature fluctuations, g. The study shows that buoyancy increases the rate of dissipation of g above the values indicated by previous recommendations for the modeling of that quantity. As a possible explanation for this result it is suggested that buoyancy introduces anisotropy in the fluctuations at the dissipation scale. The study shows that the contribution from the secondary components of the strain tensor to the production of k is non-negligible. In addition, between 12 and 17 percent of the longitudinal enthalpy flux is contributed by the turbulent fluctuations. Finally, it is observed that the modeling of buoyant flows still presents uncertainties and that additional work is necessary to properly account for the effect of buoyancy on the production of ε and the dissipation of g.
Potential Weather Modification Caused by Waste Heat Release from Large Dry Cooling Towers
Authors: Lee Jiin-lang
Published: November 2010

A numerical model of a cooling tower plume is employed to study the possible atmospheric effects of thermal plumes from natural draft dry cooling towers. Calculations are performed for both single and multiple towers, each of which can dissipate the waste heat from a nominal 1000 MWe power generating unit, and the results are compared with those for wet cooling towers associated with plants of the same generating capacity. Dry cooling tower plumes are found to have a higher potential for inducing convective clouds than wet cooling tower plumes, under most summertime meteorological conditions. This is due to the fact that both the sensible heat and momentum fluxes from a dry tower in summer are approximately one order of magnitude larger than those from a wet cooling tower.
Apparent Radiative Properties of an Isotropically Scattering Medium on a Diffuse Substrate
Authors: Crosbie A. L.
Published: November 2010

The apparent directional and hemispherical radiative properties of a finite scattering medium bounded by a diffuse substrate are investigated. The isothermal medium emits, absorbs and isotropically scatters radiation. Specifically, the emittance and reflectance are determined. Using the principle of superposition, exact but simple equations are developed which express the apparent properties in terms of the properties of a medium not bounded by a substrate. Any arbitrary directional distribution of incident radiation can be handled. Integro-differential equations of the initial value type for the radiative properties are developed and solved. In general, when the substrate emittance is less than the emittance of a semi-infinite scattering medium, the scattering layer acts as a source and increases the apparent emittance. Conversely when the substrate emittance is greater, the scattering layer acts as a shield and decreases the apparent emittance.
Laminar Transport Phenomena in parallel Channels with a Short Flow Construction
Authors: Bunditkul S. , Yang Wen-Jei
Published: November 2010

A finite-difference numerical analysis was conducted in [3] to investigate laminar transport phenomena in constricted parallel ducts with fully developed flow and temperature profiles. The same numerical procedure is employed to determine laminar transfer phenomena in parallel channels with a short flow constriction within which the flow is still developing. Two limiting thermal conditions are treated: uniform surface temperature and uniform surface heat flux. Theoretical results are obtained for the pressure, streamline, velocity and temperature distributions, the loss coefficients, the Fanning friction factor, and the local and average heat transfer coefficients. Two new dimensionless parameters are derived which describe the transfer performance in the ducts with a short flow constriction. Both the hydrodynamic and thermo-hydrodynamic effects at the entrance as well as the exit of the constricted flow geometry are determined. The numerical scheme is capable of treating high velocity flows up to the transition Reynolds number.
Numerical Solution of Solid Propellant Transient Combustion
Authors: Kooker D. E. , Nelson C. W.
Published: November 2010

Three thermal theories of solid propellant combustion, [1, 2, 3], all based on the quasi-steady flame assumption, were subjected to a rapidly rising external pressure field simulating a gun combustion chamber. Transient burning rates were computed by four different numerical solution methods; the best results were obtained with an invariant imbedding scheme. The numerical predictions show that (1) burning rate “runaway” is a numerical difficulty and is not a solution to the models, (2) the final state of an intrinsically unstable model at constant pressure is composed of repeating finite-amplitude spikes, and (3) the dynamic burning rate from a linearly-stable model can be many times greater than r = apn.
Small Reynolds Number Convection in Rotating Spherical Annuli
Authors: Douglass R. W. , Shaughnessy E. J. , Munson B. R.
Published: November 2010

A fourth order regular perturbation expansion in powers of the Reynolds number is used to investigate the steady convection of a stratified Boussinesq fluid in rotating spherical annuli. The results include the primary and secondary flow patterns, temperature distributions, total heat flux, and torque characteristics emphasizing their dependence on a wide range of radius and angular velocity ratios. Maximum usable Reynolds numbers were found and usually were larger than 10. The optimum configuration for convective heat transfer is a radius ratio of 0.35 and an angular velocity ratio of +1/3. This same configuration gives the largest torque as well.
Condensation on an Extended Surface
Authors: Patankar S. V. , Sparrow E. M.
Published: November 2010

An analysis is made of film condensation on a vertical fin which is attached to a cooled vertical plate or cylinder. This is a three-dimensional problem in which the condensation process on the fin surface is tightly coupled to conduction within the fin. A physically meaningful similarity solution of the problem was formulated and numerically evaluated. Beyond the range where the similarity solution is valid, a finite-difference marching solution of the governing partial differential equations was carried out. The heat transfer results from the similarity solution, which are represented by simple algebraic formulas, appear to be applicable for the operating range encountered in practice. It was found that the calculated fin heat transfer is markedly less than that which would be predicted by an isothermal fin model, so that the use of such a model substantially overestimates the performance of the fin.