bluuebunny/crossref_metadata_2025 huggingface dataset:
Condensation of Submerged Vapor Jets in Subcooled Liquids
Authors: Chen L-D. , Faeth G. M.
Published: October 2009

A theoretical investigation of turbulent condensing vapor jets submerged in subcooled liquids was conducted. A model of the process was developed employing the locally homogeneous flow approximation of two-phase flow in conjunction with a k-ε-g model of turbulence properties. The model was evaluated using existing data for turbulent condensing water, ethylene glycol and iso-octane vapor jets with liquid to vapor density ratios in the range 324–31,200, initial jet Reynolds numbers greater than 15,000 and negligible effects of buoyancy. Good predictions of vapor penetration lengths were obtained using conventional turbulence model constants established for single phase flows.
Performance of a Compact Cooling Unit Utilizing Air-Water Mist Flow
Authors: Aihara T. , Saga R.
Published: October 2009

Performance of a new compact cooling unit for semiconductors, being composed of an atomizer, a fan, and a heat-dissipating surface with no fin, has been measured over a wide range of the mass flow rate of spray water, m˙, and the wall heat flux. The heat transfer performance of the present compact, unit with m˙ = 0 to 1.05 g/s, attains 1.8 to 20 times that of the parallel-plate channel under the same thermal conditions.
Optimal Heat Transfer Assemblies With Thin Straight Fins
Authors: Kovarik M.
Published: October 2009

A simple criterion of optimality of finned duct assemblies for heat transfer is defined. A necessary condition of optimality in the defined sense is found for assemblies with straight thin fins. A reduction of design effort resulting from the application of this condition is demonstrated.
Influence of Free-Stream Turbulence on Turbulent Boundary Layer Heat Transfer and Mean Profile Development, Part I—Experimental Data
Authors: Blair M. F.
Published: October 2009

An experimental research program was conducted to determine the influence of free-stream turbulence on zero pressure gradient, fully turbulent boundary layer flow. Connective heat transfer coefficients and boundary layer mean velocity and temperature profile data were obtained for a constant free-stream velocity of 30 m/s and free-stream turbulence intensities ranging from approximately 1/4 to 7 percent. Free-stream multicomponent turbulence intensity, longitudinal integral scale, and spectral distributions were obtained for the full range of turbulence levels. The test results with 1/4 percent free-stream turbulence indicate that these data were in excellent agreement with classic two-dimensional, low free-stream turbulence, turbulent boundary layer correlations. For fully turbulent boundary layer flow, both the skin friction and heat transfer were found to be substantially increased (up to ∼ 20 percent) for the higher levels of free-stream turbulence. Detailed results of the experimental study are presented in the present paper (Part I). A comprehensive analysis is provided in a companion paper (Part II).
Heat Transfer From the Heated Convex Wall of a Return Bend With Rectangular Cross Section
Authors: Seki N. , Fukusako S. , Yoneta M.
Published: October 2009

An experimental investigation has been performed to clarify the turbulent heat transfer characteristics along the heated convex wall of a return bend which has a rectangular cross section with large aspect ratio for various heights of the duct. The experiments are carried out under the condition that the convex wall is heated at constant heat flux while the concave wall is insulated. Water is used as the working fluid with duct heights of 15, 40, 60 and 80 mm, Reynolds numbers of 8 × 103 to 8 × 104, and Prandtl numbers ranging from 6.5 to 8.5. The mean and the local heat transfer coefficients are always smaller than those for the straight parallel plates and straight ducts. Both the local and the mean heat transfer coefficients decrease as the duct height increases. Near the outlet region of the return bend the local heat transfer coefficient increases in the flow direction as the height decreases. Behavior is just the opposite at the inlet. Correlation equations for the mean and the local Nusselt numbers are determined in the range of parameters covered.
Radiative Heat Transfer in Fibrous Insulations—Part II: Experimental Study
Authors: Tong T. W. , Yang Q. S. , Tien C. L.
Published: October 2009

Two experiments have been conducted to study radiative heat transfer in lightweight fibrous insulations (LWFI). The spectral extinction coefficients for a commercial LWFI have been measured via transmission measurements, and a guarded hot plate apparatus has been used to measure the radiant heat flux as well as the total heat flux in the insulation. The experimental results are compared with the theoretical values calculated according to the analytical models presented in Part I of this paper. The comparisons reveal that the analytical models are useful in giving representative values for the radiative properties of typical LWFI. However, only qualitative agreements have been obtained for the heat transfer results.
Radiation and Smoke From the Gas Turbine Combustor Using Heavy Fuels
Authors: Najjar Y. S. H. , Goodger E. M.
Published: October 2009

Broadening of aviation fuel specifications has been simulated using blends of gas oil and residual fuel oil. Radiation, smoke, and temperature measurements in an experimental combustor at various air pressure, inlet temperture, and air/fuel ratios showed a diminishing rate of increase of radiation with soot concentration and reduced sensitivity of smoke to fuel hydrogen content at higher combustor pressures.
Freezing in a Vertical Tube
Authors: Sparrow E. M. , Broadbent J. A.
Published: October 2009

Fundamental heat transfer experiments were performed for freezing of an initially superheated or nonsuperheated liquid in a cooled vertical tube. Measurements were made which yielded information about the freezing front and the frozen mass, about the various energy components extracted from the tube, and about the decay of the initial liquid superheat. Four component energies were identified and evaluated from the experimental data, including the latent energy released by the phase change and sensible energies released from the subcooled frozen solid and the superheated liquid. Initial superheating of the liquid tended to moderately diminish the frozen mass and latent energy extraction at short freezing times but had little effect on these quantities at longer times. The extracted sensible energies associated with the superheating more than compensated for the aforementioned decrease in the latent energy. Although the latent energy is the largest contributor to the total extracted energy, the aggregate sensible energies can make a significant contribution, especially at large tube wall subcooling, large initial liquid superheating, and short freezing time. Natural convection effects in the superheated liquid were modest and were confined to short freezing times.
Effect of Transverse Misalignment on Natural Convection From a Pair of Parallel, Vertically Stacked, Horizontal Cylinders
Authors: Sparrow E. M. , Boessneck D. S.
Published: October 2009

Experiments were carried out to determine the effects of transverse misalignment on the natural convection heat transfer characteristics of a pair of equitemperature, parallel horizontal cylinders situated one above the other. During the course of the experiments, which were performed in air, the transverse offset was varied systematically at several fixed vertical separation distances, while the Rayleigh number ranged from 2 × 104 to 2 × 105. At small vertical separations, transverse offsetting causes an increase in the upper-cylinder Nusselt number (up to 27 percent) compared with that for the perfectly aligned case (i.e., no offset) and, furthermore, the Nusselt number is responsive to small offsets. On the other hand, at larger vertical separations, the offset-affected upper-cylinder Nusselt number is lower (by up to 20 percent) than the no-offset value but is quite insensitive to small offsets. At large transverse offsets, the upper-cylinder Nusselt number slightly exceeds that for a single cylinder, with the increase being due to a horizontal airflow induced by the acceleration of the lower cylinder’s plume. For all of the cases investigated, the lower-cylinder Nusselt number was virtually identical to that for a single cylinder.
Numerical Study of Droplet Evaporation in a High-Temperature Stream
Authors: Renksizbulut M. , Yuen M. C.
Published: October 2009

Numerical solutions for high-temperature air flowing past water and methanol droplets and solid spheres, and superheated steam flowing past water droplets were obtained in the Reynolds number range of 10 to 100. The coupled momentum, energy, and specie continuity equations of variable thermophysical properties were solved using finite difference techniques. The numerical results of heat transfer and total drag agree well with existing experimental data. Mass transfer decreases friction drag significantly but at the same time increases pressure drag by almost an equal amount. The net effect is that the standard drag curve for solid spheres can be used for evaporating droplets provided the density is the free stream density and the viscosity of the vapor mixture is evaluated at an appropriate reference temperature and concentration. Both the mass efflux and variable properties decrease heat transfer rates to the droplets.
Free Convection in a Vertical Annulus With Constant Heat Flux on the Inner Wall
Authors: Keyhani M. , Kulacki F. A. , Christensen R. N.
Published: October 2009

Heat transfer measurements are presented for free convection in a vertical annulus wherein the inner cylinder is at constant surface heat flux and the outer cylinder is at constant temperature. Overall heat transfer data are corrected for thermal radiation in the annulus. Rayleigh numbers span the conduction, transition and boundary layer regimes of flow, and average heat transfer coefficients are obtained with air and helium as the working fluids. The range of Rayleigh number is 103 < Ra < 2.3 × 106; the radius ratio is 4.33; and the aspect ratio (cylinder length divided by annular gap) is 27.6. Energy transferred by thermal radiation varies with Rayleigh number and working fluid. With air, thermal radiation can account for up to 50 percent of the heat transfer. With helium, radiation can account for up to 30 percent of the heat transfer rate. The results of the study provide data relevant to the design and performance assessment of spent fuel packages as part of the National Waste Terminal Storage Program for nuclear waste isolation.
Onset of Convection in a Horizontal Layer of Cold Water
Authors: Mollendorf J. C. , Jahn K. H.
Published: October 2009

Parabolic, cubic, and higher order expressions have been used in previous investigations to relate temperature to density in the vicinity of the density extremum. Another equation of state, based on the careful measurement of the density variations of both pure and saline water, has been used here to determine the onset of convection in a horizontally confined layer of water near its density extremum. The simplicity of this equation gives rise to a minimum number of problem particular parameters, and relatively easily allows for the inclusion of both pressure and salinity level effects (neglecting saline diffusion). The boundaries are considered to be rigid-rigid and of infinite thermal capacity. Present numerical results are compared with those previously calculated using other density relationships, including that embodied in the linear Oberbeck-Boussinesq approximation. Density extremum effects are seen to be stabilizing, with critical Rayleigh numbers calculated to be about 10 percent below those obtained using a parabolic density-temperature relationship and quite close to those found using a fifth-order polynomial. There is an associated increase in calculated wave number with the inclusion of density extremum effects.
An Interferometric Investigation of Separated Forced Convection in Laminar Flow Past Cavities
Authors: Aung W.
Published: October 2009

This study concerns the separated, laminar forced convection in cavities located on a flat plate in a low-speed wind tunnel. Temperature profiles and local heat transfer coefficients are measured by means of a Mach-Zehnder interferometer. With all walls maintained at a uniform temperature, experiments are conducted for cavity aspect ratios (length divided by depth) w/s = 4 and w/s = 1 at different Reynolds numbers. Results show that the temperature distribution outside of the cavity is little influenced by flow in the cavity. The local heat transfer distribution on the cavity floor attains a maximum value that is located between the midpoint of the cavity floor and the downstream wall. Everywhere on the cavity floor, the local heat transfer is substantially less than the value upstream of the cavity. Compared with attached flow obtained by setting the cavity depth to zero, the average heat transfer on the cavity floor is more than a factor of two lower for w/s = 4 and more than an order of magnitude lower for w/s = 1. The average Nusselt number on the cavity floor is correlated by an equation of the form, Nus = C(Res)m, where m is nearly 1/2 and C varies with the aspect ratio. Downstream of the cavity, the local heat transfer is less than the value that would prevail if the cavity depth was set equal to zero.
A Stochastic Approach to Thermal Modeling Applied to Electro-Discharge Machining
Authors: Pandit S. M. , Rajurkar K. P.
Published: October 2009

The usual method of making some simplifying assumptions and formulating thermal models that yield results confirmed by experiments does not work in many cases where the problem is complex and random. Electro-Discharge Machining (EDM) is such a process that is not only complicated and random but also physically little understood. The paper illustrates thermal modeling of this process with the help of a recently developed stochastic methodology called Data Dependent Systems (DDS). An equation to the melting iosthermal curve is defined from the DDS (stochastic empirical) model obtained from readily measurable surface profiles of actual machined surfaces created by the random superposition of electrical discharges. This equation of the melting isothermal curve is then combined with the heat conduction equation, under rather realistic and intuitively obvious assumptions, to develop a transient temperature distribution. The form of this (hybrid) thermal model is mathematically much simpler and yet its predictions are much closer to the experimental results, compared to the complicated models proposed in the literature.
Analysis of Mechanical-Draught Counterflow Air/Water Cooling Towers
Authors: Sutherland J. W.
Published: October 2009

This paper compares an accurate analysis of mechanical draught counterflow cooling towers, including water loss by evaporation, with the approximate common method based on enthalpy driving force developed by Merkel in 1925. Computer programs were developed for both the accurate analysis (TOWER A) and the approximate analysis (TOWER B). Substantial underestimates of tower volume of from 5 to 15 percent are obtained when the approximate analysis is used, indicating the possibility of quite serious consequences as far as cooling tower design is concerned. Computer predictions of cooling tower integral are shown to compare well with published values.
Boiling Heat Transfer With Freon 11 (R11) in Brazed Aluminum, Plate-Fin Heat Exchangers
Authors: Robertson J. M. , Lovegrove P. C.
Published: October 2009

The results of laboratory experiments with Freon 11 (R11) flowing in an electrically heated, serrated-fin test section to measure local boiling coefficients over a wide range of vapor quality, with mass fluxes up to 150 kg/m2 s, heat fluxes to 4 kW/m2, and pressure from 3–7 bar, are reported. These low mass and heat fluxes reflect the industrial process application of these heat exchangers where exceedingly small temperature differences may exist between streams. Results are compared with the very similar boiling characteristics previously reported elsewhere for the same test section, with liquid nitrogen as a test fluid under comparable flow conditions. A simple method using the Reynolds number of the total flow regarded as a liquid has been used to correlate boiling heat transfer coefficients with quality for both fluids. The use of a liquid-film flow model to produce a nondimensional correlation connecting the Nusselt, Reynolds, and Prandtl numbers of the film is discussed.
A Numerical Finite Difference Method for Performance Evaluation of a Periodic-Flow Heat Exchanger
Authors: Li Chung-Hsiung
Published: October 2009

A numerical finite difference method is presented for calculating the fluid and metal temperature distributions for the periodic-flow type heat exchanger, accounting for the effect of heat conduction in the wall in the direction of fluid flow. Unlike previous solution techniques that use the Gauss-Seidel method based on a single element calculation, the method presented here uses a column of elements to compute the fluids and metal temperature distributions, and it allows variable or constant thermal properties (specific heats, densities, heat transfer coefficients, and thermal conductivities). Nonuniform mass flow rates and a nonuniform grid spacing may be employed. The present method reduces the computational time required for convergence and improves the numerical stability while allowing an arbitrary metal temperature distribution as a starting case. After qualifying the numerical method, illustrative results are presented for counterflow and parallel flow rotary regenerators with three different surfaces in the flow direction and variable fluid and material properties.
Surface Microfouling During the Induction Period
Authors: Baier R. E. , Meyer A. E. , DePalma V. A. , King R. W. , Fornalik M. S.
Published: October 2009

The time during which newly installed or cleaned heat transfer surfaces remain free of fouling deposits thick enough to diminish heat transfer coefficients or energy efficiency is often called the “induction period,” a term disguising lack of knowledge of the microfouling events actually occurring. Using novel flow cells to conduct water of fresh, brackish, and oceanic quality, natural and treated with antifouling chemicals, over test surfaces of different clean and coated metals, it has been observed that the initial pattern of fouling deposits is remarkably similar in all circumstances. Rapid adsorption of protein-dominated films is followed by attachment of rodlike bacteria, bacterial exudation, colonization by a second wave of prosthecate microorganisms, additional secretion, and growth of debris-trapping filamentous appendages. Although inappropriate to extrapolate the noted rates of these processes to in-plant heat exchangers at present, this sequence of microfouling events seems universal enough to characterize the induction period of all water-side biofouling phenomena.
Stability of Steam-Water Countercurrent Flow in an Inclined Channel: Flooding
Authors: Lee S. C. , Bankoff S. G.
Published: October 2009

Flooding of stratified countercurrent steam-water flow in nearly-horizontal and in inclined flat-plate geometries is investigated. An envelope theory for onset of flooding in inclined stratified flow is developed, which agrees better with the experimental data than other theories. In addition, some basic flow parameters, such as mean film thickness and interfacial friction factor in the roll-wave regime (near-flooding) have been measured. Empirical correlations for these parameters were sought, which are essential in the flooding analysis.
Numerical Modeling of Wet Cooling Towers—Part 1: Mathematical and Physical Models
Authors: Majumdar A. K. , Singhal A. K. , Spalding D. B.
Published: October 2009

The paper discusses the limitations of current practices of evaluating thermal performance of wet cooling towers and describes a more advanced mathematical model for mechanical and natural draft cooling towers. The mathematical model computes the two-dimensional distributions of: air velocity (two components); temperature, pressure, and moisture content; and water temperature. The downward direction of water flow is presumed. The local interphase heat and mass transfer rates are calculated from empirical correlations for which two options are provided. In the first option, only one constant (Ka, based on Merkel’s approximations) is employed; in the second option, two separate constants for heat and mass transfer are used. Boundary conditions can be either of the prescribed cooling range or of the prescribed hot water temperature types. The governing equations are solved by a finite difference method. The model is embodied into a computer code (VERA2D) which is applicable for the natural and mechanical draft towers of both the crossflow and counterflow arrangements. Several applications of the code are described in Part II of the paper.
The Effect of Tube Layout on the Fluid-Elastic Instability of Tube Bundles in Crossflow
Authors: Soper B. M. H.
Published: October 2009

Fluid-elastic instability is widely recognized as a mechanism which can cause rapid failure of tubes in shell and tube heat exchangers. The shellside flow velocity for the onset of the fluid-elastic whirling is commonly calculated from Connors’ formula provided that the instability factor is known. The literature contains several reported values of the instability factor for different tube bundles but these have been obtained from a variety of test configurations and this has led to some large discrepancies. This paper describes a systematic study of the effect of tube layout on the instability factor for sixteen tube bundles. The results presented show that the instability factor varies by a factor of 3 over the range of tube layouts tested. This paper concludes with a comparison of the results of the present study with values taken from the open literature.
Natural Convective Heat Transfer on an Unheated Vertical Plate Attached to an Upstream Isothermal Plate
Authors: Kishinami K. , Seki N.
Published: October 2009

A numerical and experimental investigation on natural convective heat transfer with the coupling of heat conduction and thermal radiation from a vertical unheated plate connected to an upstream isothermal plate is carried out. The governing equations for conduction in the unheated plate and for convection in the boundary layer are written in finite difference form and are analyzed numerically by using an iterative technique coupled through the common heat flux with thermal radiation. The numerical results are discussed after comparing with the experimental results of temperature and velocity profiles and heat transfer coefficient. The coupling effects of heat conduction in the unheated plate and thermal radiation from the surface on laminar natural convective heat transfer from the plate connected to an isothermal heated upstream plate is greatly influenced by the plate-fluid thermal conductivity ratio and plate thickness, and the radiation emissivity of the plate.
Influence of Forced Flow on the He II-He I Transition in the Presence of Heat Flow
Authors: Caspi S. , Frederking T. H. K.
Published: October 2009

The influence of forced flow on the He I-He II, two-phase flow has been studied during heat transfer to superfluid He II in a U-shaped tube, at pressures from 2.4 bar to 10 bar, bath temperatures from 1.6 K to 2.1 K, and flow velocities from zero internally applied speed (“zero net mass flow”) to the order of 0.1 cm/s. Within this range of conditions, forced flow (i) did not influence heat transfer prior to phase transitions more than 10 percent; (ii) reduced temperature excursions at lambda phase transitions by a factor of 2 at most with respect to zero net mass flow; (iii) did not influence the limiting heat flux density at initiation of the lambda transition in the supercritical pressure range covered.
Enhanced Heat Transfer in a Flat Rectangular Duct With Streamwise-Periodic Disturbances at One Principal Wall
Authors: Sparrow E. M. , Tao W. Q.
Published: October 2009

Experiments were performed in a flat rectangular duct to determine the heat transfer and pressure drop response to periodic, rod-type disturbance elements situated adjacent to one principal wall and oriented transverse to the flow direction. In a portion of the experiments, heat transfer occurred only at the rodded wall, while in the remainder, heat was transferred at both principal walls of the duct. Highly detailed axial distributions of the local heat transfer coefficient were obtained. These distributions revealed the rapid establishment of a periodic (i.e., cyclic) fully developed regime as well as recurring local maxima and minima. Cycle-average, fully developed heat transfer coefficients were evaluated and were found to be much larger than those for a smooth-walled duct. Linear pressure distributions were measured between periodically positioned stations in the fully developed region, and the corresponding friction factors were several times greater than the smooth-duct values. The heat transfer and friction data were very well correlated using parameters that take account of the effective surface roughness associated with the disturbance rods.
Growth and Decay of a Thermal Pulse Predicted by the Hyperbolic Heat Conduction Equation
Authors: Vick B. , O¨zisik M. N.
Published: October 2009

The wave nature of heat propagation in a semi-infinite medium containing volumetric energy sources is investigated by solving the hyperbolic heat conduction equation. Analytic expressions are developed for the temperature and heat flux distributions. The solutions reveal that the spontaneous release of a finite pulse of energy gives rise to a thermal wave front which travels through the medium at a finite velocity, decaying exponentially while dissipating its energy along its path. When a concentrated pulse of energy is released, the temperature and heat flux in the wave front become severe. For situations involving very short times or very low temperatures, the classical heat diffusion theory significantly underestimates the magnitude of the temperature and heat flux in this thermal front, since the classical theory leads to instantaneous heat diffusion at an infinite propagation velocity.
An Experimental Study of Natural Convection in an Inclined Rectangular Cavity Filled With Water at Its Density Extremum
Authors: Inaba H. , Fukuda T.
Published: October 2009

An experimental investigation pertaining to the effect of the density inversion of water on steady natural convective flow patterns and heat transfer in an inclined rectangular cavity whose two opposing walls are kept at different temperatures is carried out. Water as a testing fluid has its maximum density at about 4 °C. The temperature of one wall is maintained at 0 °C, while that of the opposing hot wall is varied from 2 to 20 °C. Photographs of the flow patterns, temperature distribution in the water layer, and average Nusselt number are presented under various hot wall temperatures and inclination angles of the cavity. The present results could indicate that the density inversion of water has an influential effect on the natural convective heat transfer in the prescribed water layer. Moreover, the average Nusselt number is a peculiar function of the temperature difference between the cold and hot walls and inclination angle, unlike the previous results for common fluids without density inversion.
Heat Transfer During Melting From an Isothermal Vertical Wall
Authors: Ho C.-J. , Viskanta R.
Published: October 2009

This paper reports basic heat transfer data during melting of n-octadecane from an isothermal vertical wall of a rectangular cavity. The shadowgraph technique was used to measure local heat transfr coefficents at the heat source surface and the solid-liquid interface motion during phase change was recorded photographically. Experimental results clearly showed that, except in the very early stages of melting, the rates of melting and of heat transfer were greatly affected by the buoyancy-driven convection in the liquid. Initial subcooling of the solid substanially impeded the phase change process. A numerical simulation of the corresponding two-dimensional melting in the presence of natural convection was performed, and the numerical predictions are compared with experimental data.
Conductivity Models of Electrothermal Convection in a Plane Layer of Dielectric Liquid
Authors: Martin P. J. , Richardson A. T.
Published: October 2009

Experiments have demonstrated that a d-c voltage applied across a thermally stabilized plane layer of dielectric liquid can induce both stationary and oscillatory instabilities and thereby significantly augment heat transfer. While a unipolar charge injection model can explain both types of instability, the predictions of a conductivity model depend crucially upon the way the electrical conductivity varies with temperature. Here a conductivity model is derived from a dissociation and recombination model in an Ohmic limit, and its linear instabilities for linear, quadratic, and Arrhenius-type conductivity variations are investigated numerically. Oscillatory instability is usually predicted and an energy argument rules out stationary instability for the type of conductivity variation observed experimentally. This casts doubts on the experimental relevance of earlier quadratic conductivity models predicting stationary instability. The relative merits of conductivity and charge injection models are discussed in the light of empirical evidence.
Higher-Order Approximations for Darcian Free Convective Flow About a Semi-Infinite Vertical Flat Plate
Authors: Cheng P. , Hsu C. T.
Published: October 2009

Higher-order effects of Darcian free convection boundary-layer flow adjacent to a semi-infinite vertical flat plate with a power law variation of wall temperature (i.e., Tˆw αxˆλ for xˆ≥0) are examined theoretically in this paper. The method of matched asymptotic expansions is used to construct inner and outer expansions. The small parameter of the perturbation series is the inverse of the square root of the Rayleigh number. The leading term in the inner expansions is taken to be the boundary layer theory with the second-order term due to the entrainment effect, and the third-order term due to the transverse pressure gradient and the streamwise heat conduction. The ordering of the term due to the leading edge effect depends on the wall temperature distribution; this term is determinate within a multiplicative constant owing to the appearance of an eigenfunction in the inner expansion. Thus, the perturbation solutions are carried out up to this term. For the case of an isothermal vertical plate (λ = 0), the second-order corrections for both the Nusselt number and the vertical velocity are zero, with the leading edge effect appearing in the third-order term. For λ>0, both the second- and third-order corrections in the Nusselt number are positive. The increase in surface heat flux is due to the fact that the higher-order effects increase the velocity parallel to the heated surface. The boundary layer theory for the prediction of the Nusselt number is shown to be quite accurate even at small Rayleigh number for 0≤λ≤1/3. The higher order effects tend to have a stronger influence on the velocity distribution than the temperature distribution. These effects become more pronounced as λ is increased from λ=1/3, or as the Rayleigh number is decreased.
Convective Heat Transfer in a Rectangular Porous Cavity—Effect of Aspect Ratio on Flow Structure and Heat Transfer
Authors: Prasad V. , Kulacki F. A.
Published: October 2009

Two-dimensional steady natural convection in a porous rectangular cavity bounded by isothermal vertical walls at different temperatures and adiabatic horizontal walls has been studied numerically for aspect ratios less than unity and Rayleigh numbers up to 104. Results indicate the presence of multicellular flow. Also, the average Nusselt number based on cavity width is observed to be a maximum in a restricted range of aspect ratio, depending on the Rayleigh number. Effects of aspect ratio are summarized by a family of curves for constant Rayleigh number, based on cavity height, for aspect ratios from 0.05 to 100. For a cavity with fixed height, the heat transfer rate always increases as the aspect ratio is increased, except when the flow exhibits boundary layers on the vertical walls. Criteria in terms of aspect ratio and Rayleigh number have been established for the existence of different flow regimes.
Low Rayleigh Number Thermal Convection in a Saturated Porous Medium Bounded by Two Horizontal, Eccentric Cylinders
Authors: Bau H. H.
Published: October 2009

A two-term regular perturbation expansion is presented for two-dimensional, steady-state thermal convection in a fully saturated porous medium bounded by two horizontal, eccentric cylinders. Both cylinders are impermeable to fluid motion and are maintained at different, uniform temperatures. The complicated boundary conditions are handled through the use of bicylindrical coordinates. Three geometrical configurations are considered: an eccentric annulus; a pipe buried in a semi-infinite medium; and two cylinders, one outside the other, imbedded in an infinite medium. Detailed results, however, are presented only for the first case. It is demonstrated that eccentric insulations may be more effective under certain conditions and therefore more economical than the currently used concentric ones.
Application of the Local Assumption for the Design of Compact Heat Exchangers for Boiling Heat Transfer
Authors: Chen C. C. , Westwater J. W.
Published: October 2009

The design technique of interest here is the use of the local assumption, namely, that the local heat transfer coefficient during flow boiling is uniquely fixed by the local metal-to-liquid, ΔT, and the local fluid velocity. The object of this paper is to show the performance of two new compact heat exchangers that are specifically designed for boiling duty by this technique. These exchangers, from different manufacturers, were brazed aluminum, crossflow devices having core sizes of about 8 × 8 × 8 cm. The equivalent diameter of the flow passages on the boiling side, based on the wetted perimeter, was 0.167 cm. Offset fins gave excellent mixing of the boiling fluid, so homogeneous flow was assumed to prevail. Tests were made with Refrigerant-113 (R-113) at atmospheric pressure in these exchangers installed as thermosiphon reboilers. Heat was provided by condensing steam. The measured mass velocity of the R-113 was from 14 to 750 kg/s m2, the inlet velocity was 0.008 to 0.45 m/s, the calculated homogeneous exit velocity was 0.5 to 20 m/s, the calculated metal-liquid, ΔT, varied from 15 to 120 K, and the heat duty varied from 5.5 to 57 kW. On a volumetric basis, this upper duty is 120,000 kW/m3, a remarkably high duty for the exchange of heat between two fluids. For both exchangers, the agreement between predicted and measured duties was satisfactory as long as no dryout occurred. When dryout occurred, flow oscillations were observed, and the observed heat duty was as much as 40 percent below the predicted value.
Effect of Free-Stream Velocity Vector and Aspect Ratio on the Output of a Free-Standing Circular Disk Heat Flux Gage
Authors: Young M. F.
Published: October 2009

The effects of free-stream velocity, angle of attack, and aspect ratio on the output of a free-standing circular disk heat flux gage subjected to a combined radiative and convective heat flux are reported. The Reynolds number range investigated extends from 6000 to 25,000, while the gage angle of attack was varied from 0 to 90 deg. Results for three gage aspect ratios, 5.85, 8.77, and 11.76, are presented. The Nusselt number is used to represent the effects of convection on the gage output. The Nusselt number was found to increase with increasing Reynolds number and angles of attack. At an angle of attack of about 90 deg, however, a significant reduction in the Nusselt number was noted. A correlation relating the Nusselt number (based on the disk diameter) to the Reynolds number (based on the gage outside diameter) and the angle of attack is reported. This correlation represents the data to within ±5 percent.
Turbulent Heat Transport in Circular Ducts With Circumferentially Varying Heat Flux
Authors: Baughn J. W. , Hoffman M. A. , Launder B. E. , Takahashi R. K.
Published: October 2009

Experiments have been performed with turbulent air flow in a tube with uniform and with top-half heating; the flow was hydrodynamically fully developed at the start of the heated section, and there were negligible buoyancy effects. Numerical solutions of the mean momentum and energy equations which use the suggestion [1] that the ratio of radial-to-circumferential turbulent diffusivities is equal to the corresponding ratio of mean square velocity fluctuations in these directions agree well with the experimental results.
Thermal Instability of Forced Convection Boundary Layers
Authors: Chen K. , Chen M. M.
Published: October 2009

Thermal instability of forced convection boundary layers with nonzero streamwise pressure gradient is examined for moderate to high Prandtl numbers. The analysis is carried out for the family of Falkner-Skan flows, here viewed as the lowest order local similarity approximation of general forced convection boundary layers. Calculated critical Rayleigh numbers and wave numbers are found to be independent of the streamwise pressure gradient in the limiting case of infinite Prandtl number, and only weakly dependent on the streamwise pressure gradient for finite Prandtl number cases when the conduction thickness is employed as the reference length scale.
Experimental Study of Three-Dimensional Natural Convection High-Rayleigh Number
Authors: Bohn M. S. , Kirkpatrick A. T. , Olson D. A.
Published: October 2009

Natural convection in buildings is characterized by three-dimensional flow at high Rayleigh numbers (Ra ∼ 1010). At present, little is known about natural convection heat transfer in this regime, although a better understanding would allow more energy efficient usage of buildings. This paper presents results from the first phase of an experimental program aimed at improving our understanding of heat transfer and air flow in buildings. The experimental apparatus consists of a cubical enclosure filled with water in which each wall may be heated or cooled in a controlled manner. A transparent, adiabatic top and bottom provide flow visualization capability. Average heat transfer coefficients for the walls have been measured for several configurations of heating and cooling of the vertical isothermal walls. A unified Nu-Ra correlation has been computed which collapses the heat transfer coefficients of the various configurations to within 5.7 percent. The heat transfer and flow visualization results indicate that even at Rayleigh numbers as high as 6 × 1010, the heat transfer mechanism is laminar boundary-layer convection from one wall to the bulk fluid.
Effects of Corona Discharge on Free-Convection Heat Transfer Inside a Vertical Hollow Cylinder
Authors: Franke M. E. , Hutson K. E.
Published: October 2009

Vortex rolls induced inside a vertical hollow cylinder are found to increase the free-convection heat transfer rate from the inside surface. The vortex rolls are induced by the corona wind generated between 0.05-mm-dia wire electrodes placed vertically on the inside surface of the vertical hollow cylinder. The increase in heat transfer rate is determined experimentally and is based on the heat input required to maintain the inside surface of the cylinder at constant temperature. The experimental results without corona discharge are compared with an analytical heat balance. A Mach-Zehnder interferometer is used for boundary layer visualization.
Thermal Insulation in Flow Systems: Combined Radiation and Convection Through a Porous Segment
Authors: Wang K. Y. , Tien C. L.
Published: October 2009

The present work reports analytical findings on a new concept for thermal insulation in flow systems. The basic operating principles are illustrated by a duct flow system with a nonradiating gas passing through a porous segment, where convection and radiation take place. The radiative properties of the porous segment are computed from electromagnetic theory assuming that the porous medium is of homogeneous composition. The coupled energy and radiative transfer equations are solved numerically by iterative method in conjunction with over-relaxation. For the limiting case of no scattering, the present results based on the two-flux radiation model agree well with the exact calculations reported recently. It is found that in order to have higher recaptured radiation and temperature drop, a porous medium with large optical thickness and low scattering albedo is preferred. Two illustrative examples indicate that the pressure drop which resulted from installation of the porous segment is of little concern, especially in view of the resulting huge energy savings.
Simulation of Rapid Heating in Fusion Reactor First Walls Using the Green’s Function Approach
Authors: Hassanein A. M. , Kulcinski G. L.
Published: October 2009

The solution of the heat conduction probem in moving boundary conditions is very important in predicting accurate thermal behavior of materials when very high energy deposition is expected. Such high fluxes are encountered on first wall materials and other components in fusion reactors. A numerical method has been developed to solve this problem by the use of the Green’s function. A comparison is made between this method and a finite difference one. The comparison in the finite difference method is made with and without the variation of the thermophysical properties with temperature. The agreement between Green’s function and the finite difference method is found to be very good. The advantages and disadvantages of using the Green’s function method and the importance of the variation of material thermal properties with temperature are discussed.
Ice-Formation Phenomena for Water Flow Between Two Cooled Parallel Plates
Authors: Seki N. , Fukusako S. , Younan G. W.
Published: October 2009

Experiments have been performed to investigate the ice-formation phenomena and the heat transfer characteristics for water flow between two horizontal parallel plates. The experiments were carried out under the condition that the upper and lower plates were cooled at the same uniform temperature, which was less than the freezing and the temperature of the water. The temperature of the plates ranged from −7 to −14°C with inlet-water temperature varied from 2 to 5°C. The cooling-temperature ratio θc ranged from 1.4 to 7.0. By using three different values of height H, 16, 30, and 40 mm between the horizontal parallel plates, the Reynolds number ReH were varied from 3.8 × 103 to 3.2 × 104. As a result of the present investigation, two different types of ice-formation were observed. One was transition ice-formation type, and the other was smooth ice-formation type. It was found that the transition ice-formation type occurred for ReH/θc0.741 < 104, while the smooth ice-formation type occurred for ReH/θc0.741 > 104. The relation equations for the ice-transition position and the heat transfer coefficients along the water-ice interface were extensively determined.
Optimization of Finned Ducts in Laminar Flow
Authors: Kovarik M.
Published: October 2009

A simple necessary condition of optimality for a finned heat exchanger duct in laminar flow is derived. The criterion of optimality is maximum heat transfer from the fin per unit cost of the finned duct. The heat transfer is determined by the conjugate convection-conduction process rather than by the assumption of a given heat transfer coefficient on the fin surface. Both forced and natural convection are considered. Expressions comparing the performance of optimal assemblies of different materials are given. Approximate dimensions of optimal fins are derived. The relations between the present and earlier results are discussed.
Scaling Rules for Total Absorptivity and Emissivity of Gases
Authors: Edwards D. K. , Matavosian R.
Published: October 2009

Hottel’s Rule and Penner’s Rule for estimating the total absorptivity of a homogeneous gas from a total emissivity chart or expression are generalized. The generalized rule is developed from an examination of the functional relationships between total and spectral molecular gas radiation properties. It gives a rational prescription for finding the absorptivity or emissivity at arbitrary pressure from the one-atmosphere total emissivity. Calculations of total properties from band absorption data correlations are used to find the needed map of pressure scaling exponent versus path-length-pressure product and gas temperature. Also addressed is the question of allowing for reflecting walls in the calculation of radiation heat transfer between a homogeneous gas and its enclosing walls. Both exact and high-accuracy-approximate calculations are shown to be possible using only total properties.
An Experimental Performance Evaluation of a Disk and Doughnut Type Heat Exchanger
Authors: Goyal K. P. , Gupta B. K.
Published: October 2009

This paper reports the results of an experimental study in which 158-mm-dia disk and doughnut type 1-2 oil coolers were tested for various combinations of flow rates and clearances between the doughnut baffle and the shell. Oil coolers of 45 L per minute capacity were tested at the diametral clearances of 0.6 mm, 0.87 mm, and 1.25 mm between the doughnut baffle and shell for various flow rates of oil and water. It is found that the decrease in overall heat transfer coefficient with increasing clearance is not significant for most practical purposes. In another series of tests, oil coolers of 90 L per minute capacity with shell surface roughnesses of 4 and 19 microns and diametral clearances of 0.07 mm, 0.33 mm, and 0.59 mm were tested. The experimental results indicate that in this range of low clearances, the overall heat transfer coefficient increases with increasing clearance and surface roughness.
Swirl-Affected Turbulent Fluid Flow and Heat Transfer in a Circular Tube
Authors: Sparrow E. M. , Chaboki A.
Published: October 2009

Experiments were performed to study the fluid flow and heat transfer characteristics for turbulent airflow in a tube in which there is a decaying axisymmetric swirl. Measurements were made of the local swirl angle at the tube wall and of the local Nusselt number and friction factor, all as a function of position along the length of the tube. Supplementary flow visualization experiments were performed to establish the axisymmetry of the swirl and to explore the pattern of fluid flow at the inlet of the tube. The swirl angle was found to decay exponentially along the tube, with the decay being more rapid at lower Reynolds numbers. The swirl gave rise to substantial heat transfer enhancement in the initial portion of the tube. The enhancement prevailed over a greater length of the tube at higher Reynolds numbers than at lower Reynolds numbers. Compared with the enhancements encountered in the conventional thermal entrance region in a nonswirling pipe flow, those associated with swirl are substantially greater and longer lived.
Initiation of Waterhammer in Horizontal and Nearly Horizontal Pipes Containing Steam and Subcooled Water
Authors: Bjorge R. W. , Griffith P.
Published: October 2009

Localized slug formation from a stratified flow of steam and subcooled water in a pipe traps a steam bubble, which collapses rapidly and causes a waterhammer. This phenomenon was studied experimentally at low pressures. Several tests, including measurement of the critical conditions for waterhammer initiation, were performed. An analytical model was developed that can predict whether waterhammer initiation will occur for given flow conditions. Predictions of this model agree well with experimental results. The use of the model in evaluating the susceptibility of a piping system to condensation waterhammer is described.