bluuebunny/crossref_metadata_2025 huggingface dataset:
A Method for the Determination of the Local Turbulent Friction Factor and Heat Transfer Coefficient in Generalized Geometries
Authors: Aranovitch E.
Published: November 2010

A method is presented for the determination of the distributions of velocity, local friction, and heat transfer coefficients in a forced axial turbulent flow with an arbitrary cross section. The method uses as basis the characteristics of the laminar flow. A comparison is made with some experimental results concerning different geometries.
Laminar Film Condensation on Plane and Axisymmetric Bodies in Nonuniform Gravity
Authors: Dhir Vijay , Lienhard John
Published: November 2010

Expressions are developed for the condensate film thickness and the local Nusselt number on arbitrary axisymmetric bodies, including vertical plates and cylinders. The expressions are the same as the Rohsenow-Nusselt expressions except that they are based on an “effective gravity” that corrects both for variable gravity and for the form of the body. The limitations on the expressions are: that radii of curvature greatly exceed the film thickness, that Prandtl numbers are never much less than unity, and that the ratio of sensible to latent heats is not large. These criteria include almost all practical situations. Several applications are developed.
Efficient Solution Processes for Finite Element Analysis of Transient Heat Conduction
Authors: Gallagher R. H. , Mallett R. H.
Published: November 2010

Systematic procedures are presented for reducing the order of a matrix differential equation governing transient heat conduction in solids. Two principal aspects of this development are a condensation of the set of gridpoint temperature degrees of freedom using steady-state relations and the introduction of generalized (modal) temperature degrees of freedom to achieve a further reduction. These processes are illustrated in an elementary one-dimensional transient heat conduction problem.
Forced Convection Heat Transfer From a Cylinder in Carbon Dioxide Near the Thermodynamic Critical Point
Authors: Green J. R. , Hauptmann E. G.
Published: November 2010

In an attempt to determine the heat transfer rates in forced flow normal to a heated cylinder and to provide some insight into the mechanisms in heat transfer in the critical region, heat transfer rates have been measured for both free and forced flow of supercritical carbon dioxide normal to a horizontal heated cylinder. The 0.006-in-dia cylinder was held at various constant temperatures by a feedback circuit. The effects of bulk fluid temperature, bulk fluid pressure, and surface temperature were studied for a range of bulk fluid temperatures and pressures from 0.8 to 1.4 times the critical temperature and pressure, and free-stream velocities from 0 to 3 fps. The temperature difference between the heated cylinder and the bulk fluid was varied from 1 to 300 deg F. Several photographs of the flow field are presented. In a supercritical fluid the heat transfer rate increases smoothly and monotonically with increasing temperature difference, increasing velocity, and increasing pressure. In fluid with the bulk temperature below the pseudo-critical temperature the heat transfer coefficient shows large peaks when the cylinder temperature is near the pseudo-critical temperature. The heat transfer coefficient decreases with increasing temperature difference when the bulk fluid temperature is above the pseudo-critical temperature. Supercritical forced convection does not exhibit the characteristic maximum in heat transfer rate shown in forced-flow nucleate boiling. Heat transfer rates at larger temperature differences are very similar in forced-flow film boiling and supercritical forced-flow heat transfer. With this horizontal constant-temperature cylinder, no “bubble-like” or “boiling-like” mechanisms of heat transfer were observed in supercritical free or forced convection.
Partially Ionized Gas Flow and Heat Transfer in the Separation, Reattachment, and Redevelopment Regions Downstream of an Abrupt Circular Channel Expansion
Authors: Back L. H. , Massier P. F. , Roschke E. J.
Published: November 2010

Heat transfer and pressure measurements obtained in the separation, reattachment, and redevelopment regions along a tube and nozzle located downstream of an abrupt channel expansion are presented for a very high enthalpy flow of argon. The ionization energy fraction extended up to 0.6 at the tube inlet just downstream of the arc heater. Reattachment resulted from the growth of an instability in the vortex sheet-like shear layer between the central jet that discharged into the tube and the reverse flow along the wall at the lower Reynolds numbers, as indicated by water flow visualization studies which were found to dynamically model the high-temperature gas flow. A reasonably good prediction of the heat transfer in the reattachment region where the highest heat transfer occurred and in the redevelopment region downstream can be made by using existing laminar boundary layer theory for a partially ionized gas. In the experiments as much as 90 percent of the inlet energy was lost by heat transfer to the tube and the nozzle wall.
Calibration of Constant-Temperature Hot-Wire Anemometers at Low Velocities in Water with Variable Fluid Temperature
Authors: Hollasch K. , Gebhart B.
Published: November 2010

Calibration of hot-wire probes operated in a constant-temperature mode in water at low velocities is discussed. Operation under circumstances where natural convection effects are important is considered. A method of calibrating a constant-temperature hot-wire probe for variations in fluid temperature is presented. The method consists of varying wire overheat during calibration at a constant fluid temperature. A relation is derived analytically relating anemometer output with a variable overheat resistance to anemometer output with fluid temperature variations. An experimental study to verify the analysis is presented.
Spectral Radiation from Alumina Powder on a Metallic Substrate
Authors: Bergquam J. B. , Seban R. A.
Published: November 2010

Normal spectral radiation was measured in the range of 1 to 10 μ from layers of 0.3-μ alumina powder of various thicknesses and compactions resting on a platinum substrate. The substrate was heated and the layer lost heat from its upper surface by radiation and free convection. The measurements are compared to the predictions obtained from the two-flux theory applied on a spectral basis, in combination with the equation of conduction. Qualitative correspondence is indicated but the magnitudes of the predicted and measured radiation differ by as much as 40 percent. The inference is that the specification of optical properties is not quite correct and that the thermal conductivity of the powder layer is substantially less than expected.
Cryo-Immunology: The Antigenic Properties of the Male Rabbit Reproductive System as Studied by Selective Freezing of Its Components
Authors: Shulman S. , Zappi E.
Published: November 2010

Immunologic analysis of antisera and comparative studies of their properties provide important data about the number and the localization of antigens in the various organs of the reproductive system of the rabbit. The advantages of cryostimulation for eliciting immune responses in the reproductive system of the male rabbit are discussed in this paper, and examples are given of the study of such antisera through different immunologic techniques.
Mathematical and Experimental Modeling of the Circulation Patterns in Glass Melts
Authors: Noble J. J. , Clomburg L. A. , Sarofim A. F. , Hottel H. C.
Published: November 2010

Natural convection currents in a rectangular two-dimensional enclosure representative of the longitudinal section of an industrial glass-melting furnace have been established by both model experiments and numerical calculation. For the latter a finite-difference method has been employed to solve the time-dependent coupled flow and energy equations. The highly generalized mathematical model makes allowance for buoyancy, temperature-dependent viscosity, and diffusive radiation. Generalized boundary conditions are employed to permit specification of any combination of temperature, flux, or mixed thermal boundary conditions. Representative temperature and flow contour maps obtained from the calculations are shown to agree well with experimental results obtained with a 1/20 scale model in which glycerine was employed as the modeling fluid.
Response of Finite-Thickness Gardon Heat-Flux Sensors
Authors: Kirchhoff Robert H.
Published: November 2010

The temperature–time response of a Gardon heat-flux sensor of finite thickness has been calculated by the integral-transform technique. Through the introduction of the aspect ratio, results are presented which characterize the response of a finite-thickness probe compared to a probe of zero thickness.
Condensation on a Downward-facing Horizontal Rippled Surface
Authors: Markowitz Avram , Mikic B. B. , Bergles A. E.
Published: November 2010

An analytical investigation is presented for film condensation on a downward-facing horizontal doubly rippled surface. Small undulations having constant radius of curvature are combined with larger cylindrical grooves designed to aid condensate runoff. A direct expression for the condensate film thickness at the top of an undulation crest, as well as on a small-diameter horizontal cylinder, is derived. An upper-bound expression for the condensation rate on the rippled surface is then obtained which predicts that the condensation rate will be five times the rate attainable on a flat horizontal surface of the same projected area. This analytical expression is compared with experimental data.
Laminar Counterflow Exchangers: An Approximate Account of Wall Resistance and Variable Transfer Coefficients
Authors: Seban R. A. , Hsieh T. C. , Greif R.
Published: November 2010

There is considered the calculation of the average value of the overall heat-transfer coefficient for counterflow between parallel plates or in concentric tubes when the flows are laminar and the thermal entry lengths for one or both streams extend over a significant part of the exchanger length. It is shown that if this length is at least less than the total length for one of the fluids, the average value of the overall coefficient can be calculated with adequate accuracy from the average values of the individual coefficients by means of the usual definition of the overall coefficient. When both thermal entry lengths exceed the exchanger length, then a special calculation is needed to obtain suitable average overall values. This result is given in graphical form and supported by more exact results from the literature and as obtained here.
Experiment and Analysis of Directional Effects on Radiant Heat Transfer
Authors: Toor J. S. , Viskanta R.
Published: November 2010

Validity of the commonly used simplified models for predicting local and overall radiant heat interchange among real surfaces is critically examined. The spectral local irradiation was measured at wavelengths of 3.08 and 4.51 μ in a configuration consisting of three plane parallel surfaces of finite extent. The test surfaces were gold with mechanical roughness and temperature varying from 0.02 to 7.1 μ and 77 to 760 deg K respectively. Comparisons between experimental data and predictions for six different models ranging from the simple diffuse to the most detailed diffuse-plus-specular-directional-property model with specular component calculated according to Beckmann are presented. It is shown that the calculation of the overall irradiation using appropriate constant-property models agrees well with the experimental data to within combined experimental and analytical uncertainty. In general it is concluded that for accurate prediction of local irradiation the directional characteristics of the surfaces must be considered.
An Analysis of Laminar Free and Forced Convection between Finite Vertical Parallel Plates
Authors: Quintiere J. , Mueller W. K.
Published: November 2010

Approximate analytical solutions are presented for constant-property laminar free- and forced-convection flows between finite vertical parallel plates. For free convection, the thermal boundary conditions considered include the thermally symmetric channel with uniform wall temperature or step change in wall temperature and the unsymmetric channel with uniform but unequal wall temperatures. For forced convection and combined free and forced convection, the thermally symmetric and uniform thermal boundary condition is considered. Where possible, results are compared with available numerical and experimental results. Particular attention is given to heat-transfer results, which cover a wide range of Rayleigh and Prandtl numbers. For combined convection the heat-transfer results are related to the impressed pressure difference and flow rate.
Combined Free- and Forced-Convective Heat Transfer and Fluid Flow in Rotating Curved Rectangular Tubes
Authors: Miyazaki H.
Published: November 2010

A theoretical study is presented for combined free- and forced-convective heat transfer and fluid flow in curved rectangular tubes rotating about an axis through the center of curvature of the tube. The analysis is performed under the conditions that the flow is thermally and hydrodynamically fully developed, and the axial wall heat flux is uniform with a peripherally uniform wall temperature. The governing equations are solved numerically, and effects of the aspect ratio, radius ratio, Prandtl number, a nondimensional parameter representing the effects of Coriolis forces, Grashof number, and Dean number on the flow and heat-transfer characteristics are presented for velocity and temperature distributions, streamlines and isotherms, local and mean friction factors f and Nusselt numbers Nu. The effects of the first two geometrical parameters are minor. However, an increase in the last three force parameters enhances both f and Nu greatly. An effect characteristic of the Coriolis forces is that they cause a great increase in f, while the enhancement of Nu is much less remarkable.
The Thermal Properties of Human Blood during the Freezing Process
Authors: Wessling F. C. , Blackshear P. L.
Published: November 2010

This paper presents calculations of the density, thermal conductivity, and enthalpy of blood during the freezing process. The calculations are based upon the premise that blood freezes similarly to a mixture of fats, proteins, and sodium chloride in a water solution and freezes so that ice crystals align themselves with the direction of heat flow. The properties were checked by calculating the theoretical temperature–time history of blood freezing in a Teflon-coated stainless-steel tube and comparing the results with experiments. The agreement was within 10 percent over the entire ranges of temperature and time. Hence the derived thermal properties are concluded to be good approximations to the real properties.
Void Fraction and Vapor and Liquid Temperatures: Local Measurements in Two-Phase Flow Using a Microthermocouple
Authors: Delhaye J. M. , Semeria R. , Flamand J. C.
Published: November 2010

A technique is described which enables the detection of the phase (liquid or vapor) in steam-water two-phase flow and the temperature measurement of each phase, using the hot junction of a microthermocouple. The signals are processed with a multichannel analyzer in order to obtain the amplitude histograms of the temperature. Significant results are obtained in pool boiling, forced convection subcooled boiling, and flashing flow of water.
Radiative Cooling of a Turbulent Flame Front
Authors: Edwards D. K. , Balakrishnan A.
Published: November 2010

Temperature profiles arising from simultaneous radiation and turbulent diffusion in combustion gas products in the vicinity of a turbulent flame front are obtained analytically. Account is taken of the highly nongray nature of the gas absorption and emission by use of band absorption properties and slab band absorptance functions. Radiative cooling is shown to be quite effective, not by acting directly upon the eddies themselves at the flame front, but by acting indirectly to cool greatly the gases in the vicinity of the flame front, which in turn cool the eddies through turbulent mixing. Generalized dimensionless results, as well as particularized examples, are presented. It was found that CO2, being an intense emitter, reduces flame front temperature to a greater degree than H2O, a less intense emitter, even though the total emissivity of H2O exceeds that of CO2. For this reason flue gas recirculation appears more advantageous than water or steam injection in achieving radiative cooling.
An Exact Solution for Flow Transients in Two-Phase Systems by the Method of Characteristics
Authors: Gonzalez-Santalo J. M. , Lahey R. T.
Published: November 2010

One of the important design considerations in modern water-cooled nuclear reactors is their thermal performance during hypothetical accident situations. However, an accurate analysis of the system thermal-hydraulics is required before the thermal margins can be appraised. In this paper, an analysis based on the method of characteristics has been developed by which the exact solution to flow decay transients in homogeneous two-phase systems can be obtained. The exact solution presented yields the system flow and quality at each point in space and time during an exponential flow decay transient. These parameters can then be combined with an appropriate CHF correlation to predict the occurrence of transient CHF.
Peak Pool Boiling Heat-Flux Measurements on Finite Horizontal Flat Plates
Authors: Lienhard J. H. , Dhir V. K. , Riherd D. M.
Published: November 2010

Experimental data obtained at both earth-normal and elevated gravity, in a variety of organic liquids and water, are used to verify the hydrodynamic theory for the peak pool boiling heat flux on flat plates. A modification of Zuber’s formula, which gives a 14 percent higher peak heat flux, is verified as long as the flat plate is more than three Taylor wavelengths across. For smaller heaters, the hydrodynamic theory requires a wide variation in heat flux owing to discontinuities in the number of escaping jets. Data for smaller plates bear out this predicted variation with heat fluxes that range between 40 percent and 235 percent of Zuber’s predicted value. Finally, a method is suggested for augmenting the peak heat flux on large heaters, and shown experimentally to be viable.
Augmentation of Heat Transfer in Tubes by Use of Mesh and Brush Inserts
Authors: Megerlin F. E. , Murphy R. W. , Bergles A. E.
Published: November 2010

This paper summarizes the results of a study to determine the heat transfer and pressure drop characteristics of two types of tube inserts developed specifically for augmenting heat transfer and accommodating high heat fluxes. The best performing mesh-insert tubes exhibited heat transfer coefficients nine times the coefficients with empty tubes while brush-insert tubes had coefficients averaging five times the empty tube values, both comparisons being made at equal mass velocity. Both inserts produced very large pressure drops. Subcooled boiling curves and burnout points are presented; burnout heat fluxes are two to three times the empty tube values at equal mass velocity. For single-phase conditions and for burnout, the mesh and brush tubes have favorable performance characteristics, based on pumping power, which suggest use of these inserts in certain special cooling systems.
The Thermal Diffusivity of Highly-Filled Rubber
Authors: Schapery R. A. , Martin R. E.
Published: November 2010

The influence of strain and temperature on the thermal diffusivity of solid propellant is investigated. Starting with the classical heat conduction equation for constant thermal properties, a simple procedure for experimentally determining the diffusivity and checking the validity of this equation is described. Existing theoretical bounds on the conductivity of composites with voids are then reviewed. Following a description of the experimental program, transient temperatures in two different solid propellants, covering the temperature range −320 deg F to 140 deg F and strain range 0 to 20 percent, are given and compared with theory. The diffusivity is found to vary noticeably with both strain and temperature.
Mass Transfer Cooling of Laminar Flow Between Parallel Porous Plates
Authors: Walker G. , Terrill R. M.
Published: November 2010

The limiting temperature and mass concentration profiles and the limiting wall Nusselt number are obtained for the laminar nonisothermal flow in a two-dimensional porous channel. Results are reported for a uniform rate of injection at the wall of a foreign component of higher thermal capacity than the fluid in the channel. An exact solution of the diffusion equation is found while numerical and analytic solutions of the energy equation are discussed for small injection rates. It is shown that the enthalpy transport resulting from the diffusion process has an effect equivalent to increasing the Prandtl number. It is also found that for a given injection velocity at the wall, the limiting Nusselt number is significantly reduced by the injection of a foreign component of high thermal capacity.
Heat Transfer in the Separated and Reattached Flow on a Blunt Flat Plate
Authors: Ota Terukazu , Kon Nobuhiko
Published: November 2010

Heat transfer measurements are made in the separated, reattached, and redeveloped regions of the two-dimensional air flow on a flat plate with blunt leading edge. The flow reattachment occurs at about four plate thicknesses downstream from the leading edge and the heat transfer coefficient becomes maximum at that point and this is independent of the Reynolds number which ranged from 2720 to 17900 in this investigation. The heat transfer coefficient is found to increase sharply near the leading edge. The development of flow is shown through the measurements of the velocity and temperature in the separated, reattached, and redeveloped regions.
Two-Dimensional Radiative Equilibrium of a Gray Medium in a Plane Layer Bounded by Gray Nonisothermal Walls
Authors: Modest M. F.
Published: November 2010

Radiative equilibrium temperature and surface heat flux distributions are calculated for an absorbing-emitting gray medium in an infinite plane layer bounded by gray diffuse walls with arbitrary temperature distributions. Superposition is used to obtain the solution for the differential approximation, which yields good accuracy for the optically thick medium. To also obtain accurate results for optically thin and intermediate regimes, the differential approximation is subsequently improved by a number of geometrical parameters, which are derived from the exact expression for the intensity. As an example, the case of constant temperature at the upper wall and a temperature step at the lower wall without heat generation in the medium is presented. Comparison with other available results shows excellent agreement.
Erosion of Metals by High Pressure Combustion Gases: Inert and Reactive Erosion
Authors: Plett E. G. , Alkidas A. C. , Shrader R. E. , Summerfield M.
Published: November 2010

An experimental and theoretical investigation of the erosion of various metals by high temperature, high pressure flows of combustion gases is described. The erosion process was categorized as either inert or a combination of inert and reactive erosion. Experimental results indicated the existence of two thresholds, the first represents the onset of erosion and the second the transition from purely inert to inert plus reactive erosion. Inert erosion was modeled by means of the melt and wipe-off theory. Experimental results are presented to demonstrate various erosion regimes and to identify the conditions for inert and reactive erosion.
Laser Interferometric Investigation of the Microlayer Evaporation Phenomenon
Authors: Voutsinos C. M. , Judd R. L.
Published: November 2010

An experimental investigation is presented in which the growth and evaporation of the microlayer underlying a bubble forming on a glass heater surface has been studied using laser interferometry and high speed photography. The results presented for a single bubble indicate that the microlayer thickness is of the order of 5 μm. Subsequent analysis of these results confirms that the microlayer evaporation phenomenon is a significant heat transfer mechanism, representing approximately 25 percent of the total nucleate boiling heat transfer rate for the conditions investigated.
Analysis of Conduction-Controlled Rewetting of a Vertical Surface
Authors: Tien C. L. , Yao L. S.
Published: November 2010

The present paper presents a two-dimensional analysis of conduction-controlled rewetting of a vertical surface, whose initial temperature is greater than the rewetting temperature. The physical model consists of an infinitely extended vertical slab with the surface of the dry region adiabatic and the surface of the wet region associated with a constant heat transfer coefficient. The physical problem is characterized by three parameters: the Peclet number or the dimensionless wetting velocity, the Biot number, and a dimensionless temperature. Limiting solutions for large and small Peclet numbers obtained by utilizing the Wiener-Hopf technique and the kernel-substitution method exhibit simple functional relationships among the three dimensionless parameters. A semi- empirical relation has been established for the whole range of Peclet numbers. The solution for large Peclet numbers possesses a functional form different from existing approximate two-dimensional solutions, while the solution for small Peclet numbers reduces to existing one-dimensional solution for small Biot numbers. Discussion of the present findings has been made with respect to previous analyses and experimental observations.
A Phenomenological Turbulence Model and its Application to Heat Transport in Infinite Rod Arrays With Axial Turbulent Flow
Authors: Ramm H. , Johannsen K.
Published: November 2010

The “turbulence-model” approach has been applied to solve the Reynolds equations of momentum and energy for an incompressible, steady-state, one-directional, hydrodynamically fully developed, turbulent internal flow. To close the turbulence equations, a phenomenological model of turbulent motion and energy transport has been developed which includes anisotropy effects. Predictions made for the turbulent diffusivities of heat in turbulent flow in a plain tube are found to be in good agreement with the experimental data over a wide range of Reynolds and Prandtl numbers. Corresponding results for infinite rod arrays with in-line flow also compare favorably with the few reliable data available.
An Elementary Analysis for Predicting the Momentum- and Heat- Transfer Characteristics of a Hydraulically Rough Surface
Authors: Lewis M. J.
Published: November 2010

A simple model is presented which approximates the turbulent shear flow over a well-defined rough surface as a series of attached and separated flow regions. An elementary analysis applied to the model provides values for the well-known momentum- and heat-transfer roughness functions R(h+) and g(h+, Pr), respectively. In order to use the calculation method the exact shape and distribution of the roughness elements are required together with a form drag coefficient and a characteristic separation length. These may be found in the literature for many roughness shapes of interest.
Heat Transfer in Free Swirling Flow in a Pipe
Authors: Hay N. , West P. D.
Published: November 2010

The local heat transfer coefficient, for air flowing through a pipe with a swirling motion, was measured at various stations downstream of the swirling air inlet. The swirling motion of the air was produced by a single tangential slot, initially at 90 deg to the pipe axis, through which the air was introduced. The dimensions of the slot and the angle of tangency were varied and the resultant flow field inside the pipe was measured and expressed in the form of local “swirl numbers”. The augmentation of heat transfer was found to be a function of the swirl number and a correlation for this function is presented. At some locations, the augmentation can be as much as eight times the value for fully developed nonswirling turbulent flow.
Liquid Crystal Thermography and Its Application to the Study of Convective Heat Transfer
Authors: Cooper T. E. , Field R. J. , Meyer J. F.
Published: November 2010

A thermographic technique is presented that allows visual determination of both qualitative and quantitative heat transfer and fluid flow information to be obtained on heated objects placed in forced convection environments. The technique employs cholesteric liquid crystals as the temperature sensing agent. The liquid crystals indicate temperature by exhibiting brilliant changes in color over discrete, reproducible temperature ranges. The technique has been used to quickly and easily obtain information on the variation of the Nusselt number on a right circular cylinder placed in a crossflow of air. In addition to yielding precise quantitative heat transfer information, the liquid crystal thermographic technique afforded the opportunity to visually observe the effects of flow separation, the separation bubble region, the turbulent boundary layer, and the turbulent wake on the surface temperature of the heated cylinder. The experimental results obtained using the liquid crystal thermographic technique are in close agreement with results obtained by other investigators who have used standard measuring techniques.
Scaling of Heat Exchanger Tubes by Calcium Carbonate
Authors: Watkinson A. P. , Martinez O.
Published: November 2010

Scaling of copper heat exchanger tubes has been studied under conditions that promote rapid and severe scaling. Artificially hardened water of high dissolved and suspended solids is recirculated through a heated test section operated at constant steam temperature. The effects of flow velocity, tube diameter, and bulk temperature on the asymptotic fouling resistance have been determined. Results are interpreted in terms of mathematical models of the scaling process.
Analysis of Multipass Heat Exchangers With Variable Properties and Transfer Rate
Authors: Kao S.
Published: November 2010

This paper presents a matrix solution technique for multishell, multitube-pass heat exchangers with variable heat transfer film coefficients and heat capacity rates. Using this method, a series of case studies has been made, whose results are used to check the validity of certain facets of the normal design practice. Some parameters have been examined and discussed in details including the applicable range of Colburn’s caloric temperature factor, effect of shell nozzle orientation, local coefficient of the multipass exchangers with tube side in laminar flow and flow instability phenomenon across the viscous flow coolers.
The Application of the Collocation Method Using Hermite Cubic Splines to Nonlinear Transient One-Dimensional Heat Conduction Problems
Authors: Chawla T. C. , Leaf G. , Chen W. L. , Grolmes M. A.
Published: November 2010

A collocation method for the solution of one-dimensional parabolic partial differential equations using Hermite splines as approximating functions and Gaussian quadrature points as collocation points is described. The method consists of expanding dependent variables in terms of piece-wise cubic Hermite splines in the space variable at each time step. The unknown coefficients in the expansion are obtained at every time step by requiring that the resultant differential equation be satisfied at a number of points (in particular at the Gaussian quadrature points) in the field equal to the number of unknown coefficients. This collocation procedure reduces the partial differential equation to a system of ordinary differential equations which is solved as an initial value problem using the steady-state solution as the initial condition. The method thus developed is applied to a two-region nonlinear transient heat conduction problem and compared with a finite-difference method. It is demonstrated that because of high-order accuracy only a small number of equations are needed to produce desirable accuracy. The method has the desirable characteristic of an analytical method in that it produces point values as against nodal values in the finite-difference scheme.
Convective Instability in a Melt Layer Heated From Below
Authors: Sparrow E. M. , Lee L. , Shamsundar N.
Published: November 2010

Consideration is given to the onset of convective motions in a horizontal melt layer created by solid-to-liquid phase change. The melt layer is heated at its lower bounding surface either due to convective transfer from an adjacent fluid medium or to a step change in wall temperature. The analysis is carried out for liquid melts whose densities decrease with increasing temperature. Linear stability theory is employed to determine the conditions marking the onset of motion. The results of the analysis are expressed in terms of two Rayleigh numbers. One of these, the internal Rayleigh number, is based on the instantaneous thickness and instantaneous temperature difference across the layer. The other, the external Rayleigh number, is more convenient to use in applications problems since it contains quantities which are constant and a priori prescribable. For a melting problem where the external Rayleigh number is large, instability occurs soon after the start of heating. At smaller external Rayleigh numbers, the duration time of the regime of no motion increases markedly. At large times, the stability results for convective heating coincide with those for stepped wall temperature. In addition to the results for the stability problem, results for conduction phase change (in the absence of motion) are also presented for the surface convection boundary condition.
Wave Effects on the Transport to Falling Laminar Liquid Films
Authors: Seban R. A. , Faghri A.
Published: November 2010

Existing data for the transport to falling liquid films are reviewed to show the effect of augmented transport by surface waves in the cases of heating of the film, absorption by the film from the surrounding gas, and evaporation from the film. It is shown that, while the effect of the waves can be partially rationalized, the nature of the waves themselves is not known exactly enough to provide a consistent specification for all of the available data.
Combined Conductive and Radiative Heat Transfer in an Absorbing and Scattering Infinite Slab
Authors: Roux J. A. , Smith A. M.
Published: November 2010

Simultaneous radiation and conduction heat transfer results are presented for an absorbing and isotropically scattering medium having negligible emission. The radiatively participating medium is assumed to be one-dimensional and bounded by an opaque substrate and by a semi-transparent top interface. The boundary interfaces are assumed to reflect and transmit radiation in accordance with Fresnel’s equations and Snell’s law, respectively. A diffuse radiative flux, along with a conductive flux, is assumed incident upon the participating medium at the top interface. The Chandrasekhar solution to the transport equation is employed, then the solution of the governing energy equation is formulated for the radiatively participating medium. Heat transfer to the substrate is presented as a function of the governing parameters: albedo, optical thickness, and substrate and medium refractive indices. Finally, dimensionless temperature profiles are shown. Solutions for a convective boundary condition are also derived.
An Analysis of Critical Heat Flux in Flow Reversal Transients
Authors: Smith R. A. , Price F. A. , Griffith P.
Published: November 2010

A large inlet break Loss of Coolant Accident in a Pressurized Water Reactor (PWR) would cause the flow through the core to reverse within milliseconds. Currently approved methods of analysis conservatively assume that vapor blanketing of core heat transfer surfaces occurs upon this first reduction to zero flow. A coordinated experimental and analytical study has been conducted to determine when and where the vapor blanketing or Critical Heat Flux (CHF) conditions actually do develop in constant pressure rapid flow reversals. The results indicate that first occurrence of CHF is due not to low coolant velocities, but to flow stagnation in the channel interior with associated rapid channel voiding. Calculations indicate that good cooling should persist over large regions of the core for about 1 s longer than is currently assumed.
Experimental and Analytical Study of Axial Turbulent Flows in an Interior Subchannel of a Bare Rod Bundle
Authors: Carajilescov P. , Todreas N. E.
Published: November 2010

Reactor fuel elements generally consist of rod bundles with the coolant flowing axially through the bundles in the space between the rods. Heat transfer calculations form an important part in the design of such elements, which can only be carried out if information of the velocity field is available. A one-equation statistical model of turbulence is applied to compute the detailed description of velocity field (axial and secondary flows) and the wall shear stress distribution of steady, fully developed turbulent flows with incompressible, temperature-independent fluid, flowing through triangular arrays of rods with different aspect ratios (P/D). Also experimental measurements of the distributions of the axial velocity, turbulence kinetic energy, and Reynolds stresses were performed using a laser Doppler anemometer (LDA), operating in a “fringe” mode with forward scattering, in a simulated interior subchannel of a triangular rod array with P/D = 1.123 and L/DH = 77. From the experimental results, a new mixing length distribution is proposed. Comparisons between the analytical results and the results of this experiment as well as other experimental data available in the literature are presented. The results are in good agreement.
On the Prediction of Heat Transfer Across Turbulent Liquid Films
Authors: Brumfield L. K. , Theofanous T. G.
Published: November 2010

The film hydrodynamics determined by Dukler and coworkers, together with standard heat transfer considerations, provide a coherent description of heat transfer across turbulent liquid films. Predictions are found to be in agreement with overall heat transfer measurements for nonsheared (falling) films. Qualitative features are deduced for heat transfer across sheared films.
Mixed Convection On a Vertical Plate With an Unheated Starting Length
Authors: Abdel-Wahed R. M. , Sparrow E. M. , Patankar S. V.
Published: November 2010

The effect of an unheated starting length on combined forced and natural convection adjacent to a vertical plate has been investigated by solving the nonsimilar laminar boundary layer equations. The solutions were carried out numerically for prescribed values of the governing parameters which include the starting length Reynolds number Re0, a mixed convection parameter gβ(ΔT)ν/U∞3, and the Prandtl number (which was assigned a value of 0.7). The local heat transfer results show that the presence of the unheated starting length can significantly accentuate the effects of buoyancy relative to the case of no starting length. The degree of accentuation of the buoyancy effects is strongly influenced by the magnitude of gβ(ΔT)ν/U∞3. When this parameter is on the order of 10−3, the natural convection contribution to the heat transfer coefficient is markedly increased owing to the starting length. On the other hand, when gβ(ΔT)ν/U∞3 is about 10−5 the buoyancy contribution is essentially unaffected by the starting length. The shape of the velocity profile is also found to be highly responsive to the interaction between the buoyancy and the starting length. As a by-product of the research, the accuracy of a well-known integral momentum/energy solution for pure forced convection with a starting length was established. In addition, velocity profiles for mixed convection without a starting length were compared with those of experiment in order to appraise a proposed explanation for a disparity that had been previously identified in the literature.
An Analysis of Laminar Forced Convection Between Concentric Spheres
Authors: Astill K. N.
Published: November 2010

A numerical solution for predicting the behavior of laminar flow and heat transfer between concentric spheres is developed. Axial symmetry is assumed. The Navier-Stokes equations and energy equation are simplified to parabolic form and solved using finite-difference methods. Hydrodynamic and energy equations are uncoupled, which allows the hydrodynamic problem to be solved independently of the heat-transfer problem. Velocity and temperature are calculated in terms of the two spatial coordinates. Solutions depend on radius ratio of the concentric spheres, Reynolds number of the flow, Prandtl number, initial conditions of temperature and velocity, temperature distribution along the spherical surfaces, and azimuthal position of the start of the flow. The effect on flow and heat transfer of these variables, except surface temperature distribution, is evaluated. While the computer solution is not restricted to isothermal spheres, this is the only case treated. Velocity profiles, pressure distribution, flow losses, and heat-transfer coefficients are determined for a variety of situations. Local and average Nusselt numbers are computed, and a correlation is developed for mean Nusselt number on the inner surface as a function of Reynolds number, Prandtl number, and radius ratio. Flow separation is predicted by the analysis. Separation is a function of Reynolds number, radius ratio, and azimuthal location of the initial state. Separation was observed at the outer surface as well as from the inner surface under some conditions. In cases where separation occurred, the solution was valid only to the point of separation.
Combined Radiation—Convection for a Real Gas
Authors: Nakra N. K. , Smith T. F.
Published: November 2010

A study of interaction of radiative transfer with convective transfer is presented for slug flow of an absorbing-emitting gas in a circular tube with an isothermal black wall. The zone method of solution is utilized to evaluate axial gas temperature and wall heat flux distributions using recently developed direct exchange areas for arbitrary zone width to radius ratio. Gas radiative properties are evaluated from the weighted sum of gray gases model with weighting factors and gray gas absorption coefficients applicable for an equimolal mixture of carbon dioxide and water vapor. Results are presented for several values of the governing parameters which are the Boltzmann and Stanton numbers, inlet gas and tube wall temperatures, as well as tube length to diameter ratio. Effects of cooling and heating of the gas are examined.
Heat and Mass Transfer in Rotary Heat Exchangers With Nonhygroscopic Rotor Materials
Authors: Holmberg R. B.
Published: November 2010

Heat and mass transfer in rotary heat exchangers with nonhygroscopic rotor materials have been investigated. A numerical method of the finite-difference type is applied to the steady-state performance under conditions of finite rotational speed and finite longitudinal heat conduction. Temperature and absolute humidity distributions are calculated for a set of rotary heat exchanger parameters typical in air conditioning, and temperature and humidity efficiencies are evaluated for different inlet air conditions.
Influence of Substrate Properties on the Apparent Emittance of an Isothermal Isotropically Scattering Medium
Authors: Armaly B. F. , El-Baz H. S.
Published: November 2010

The apparent directional and hemispherical emittances of an isothermal, isotropically scattering, emitting, and absorbing medium that is bounded by a diffusely emitting and reflecting substrate has been investigated. The exponential kernel approximation is used to develop a closed-form algebraic expression which describes the apparent directional and hemispherical emittances as a function of the optical thickness, substrate reflectance and emittance, and scattering albedo of the medium. The approximation also provides a closed-form solution for the intensity and flux distribution within the medium. Comparison, when possible, with exact solutions indicates very good agreement.
Study of Frost Properties Correlating With Frost Formation Types
Authors: Hayashi Y. , Aoki A. , Adachi S. , Hori K.
Published: November 2010

Frost formation process was studied by photographic observation, and frost formation types were classified into several groups according to their structure in the temperature range of 0 ∼ −25°C. Frost properties, density and effective thermal conductivity, were clarified in connection with the classified frost formation types, and the prediction of the thermal conductivity was performed by the presented structural model of a frost layer.
Laser Beam-Hygroscopic Aerosol Interactions
Authors: Caledonia G. E. , Teare J. D.
Published: November 2010

A model for the prediction of the temperature and vapor fields created about a small water droplet undergoing irradiation by a laser beam has been developed. Time-dependent and steady-state solutions of the model are discussed. Estimates of characteristic phase shifts to be expected in propagating through standard atmospheric aerosol distributions are also presented. While the model is quite general, the calculations are limited to DF laser wavelengths.
Effective Thermal Diffusivity for a Multimaterial Composite Laminate
Authors: Schimmel W. P. , Beck J. V. , Donaldson A. B.
Published: November 2010

This paper discusses the development of an “effective thermal diffusivity” which can be used to estimate the temperature response at the insulated rear surface of a multilayer composite to a step in temperature at the front surface of the composite. An example is considered using the effective value along with the mathematics of a single layer problem, and results thereof are compared with both those of an exact solution, and those which use an effective diffusivity computed from a “lumped” parameter model.
Transient Heat and Mass Transfer in Soils in the Vicinity of Heated Porous Pipes
Authors: Slegel D. L. , Davis L. R.
Published: November 2010

This paper presents an analysis which describes the time dependent heat and mass transfer in soils. Local effective thermal conductivity as a function of soil material, moisture content and temperature were used from experimental data. Diffusion of liquid and vapor are both accounted for. Local thermodynamic equilibrium between liquid and vapor is assumed. Boundary conditions were chosen to represent a subsurface soil warming and irrigation system. Surface heat exchange was included as a function of varying atmospheric and surface conditions. The spacing and depth of the pipes were varied to find their effect on moisture and temperature distribution within the soil for both summer and winter environmental conditions. The result of expressing the governing equations in finite difference form and solving them numerically on a computer are presented in the form of temperature and moisture content distribution curves for summer and winter conditions. The results agree well with existing laboratory data. A steady-state closed form conduction solution with surface convection is also presented. Seasonal soil temperature variations are also presented for three climates for heated and unheated soils.
Transient Pool Boiling Heat Transfer—Part 2: Boiling Heat Transfer and Burnout
Authors: Sakurai A. , Shiotsu M.
Published: November 2010

Transient boiling heat transfer for exponential heat input to a platinum wire supported horizontally in a pool of water was investigated. Transient boiling heat transfer coefficient, transient DNB heat flux, and transient maximum heat flux were obtained for exponential periods ranging from 5 ms to 10 s and for system pressures ranging from 0.1 to 2.1 MPa. Transient boiling heat transfer coefficient after the commencement of boiling becomes lower than the steady boiling heat transfer coefficient at the same heat flux. This was explained to be as a result of the time lag of the activation of originally flooded cavities for the increasing rate of the heat input. Initial heat flux was varied from zero to near the steady maximum heat flux. Effect of initial boiling condition on transient DNB and maximum heat fluxes was negligible. Mechanism of transient boiling heat transfer beyond steady DNB heat flux was suggested.