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RESEARCH PAPERS

J. Heat Transfer. 1983;105(2):217-225. doi:10.1115/1.3245566.

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.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):226-234. doi:10.1115/1.3245567.

The melting process of a phase change material (PCM) enclosed in a horizontal, isothermal circular tube has been investigated analytically and by experiment for an interesting range of parameters. The physical process was analyzed by numerical methods, whereby the underlying mathematical model involves heat conduction as well as natural convection as the basic heat transport mechanisms. Difficulties associated with the complex and timewise changing melt region whose shape is also part of the solution, have been overcome by applying a numerical mapping technique. Computations and experiments were performed for Rayleigh numbers in the range 105 ≤ Ra ≤ 106 . For lower Rayleigh numbers the numerical calculations predict a streamlined design of the PCM at later times, similar to the experiment. At higher Rayleigh numbers, three-dimensional Bernard convection was observed in the bottom region of the melt layer, which was unsteady in their timewise behaviour. The appearance of several roll-cells have also been predicted by the calculations, although the mathematical model was restricted to two-dimensional flow. The experiments were performed with n-octadecane (Pr ≃ 50) as PCM. The test cell basically consists of a short tube filled with the PCM. The tube is closed with plexiglass disks on both ends, thus allowing the melting front to be recorded photographically with time. As a result, the interface positions as well as the overall and local heat transfer coefficients are presented as function of time. The agreement between experimental and numerical data is reasonably good.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):235-240. doi:10.1115/1.3245568.

Condensation-driven melting of an initially vertical wall is studied both analytically and experimentally. It is shown that a vertical surface undergoing simultaneous melting-condensation will not stay vertical and will go through a series of transient shapes before attaining a steady-state shape. Numerical solutions are obtained both for the transient shapes of the wall and the heat transfer. The steady-state shape of the wall is found to be the one which yields a constant melting rate along the wall. The total melting rate is shown to increase during the time the shape change occurs such that the steady-state shape yields about 35 percent more melting rate than the initial vertical wall. Experiments are conducted at one atmosphere pressure by condensing saturated steam on vertical surfaces of slabs made of naphthalene, biphenyl, and stearic acid. The heat transfer and shape change data are found to compare well with the predictions.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):241-247. doi:10.1115/1.3245569.

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.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):248-254. doi:10.1115/1.3245570.

The peculiar density variation of water with temperature makes the Boussinesq approximations invalid in the vicinity of density extremum conditions. The buoyancy force reversals which often arise from the density extremum have been studied in many recent investigations. The formulation of an accurate density relation has resulted in a simplified analysis for many convective motions. Two such analyses have dealt with the flow generated above a heated line source in cold water, around the extremum point. We present an experimental investigation of such flow. Temperature measurements have been carried out for ambient temperatures, t∞ ≥ tm , the temperature of density extremum, for pure water at atmospheric pressure. These measurements are in satisfactory agreement with the analyses. As the ambient temperature is successively increased above the density extremum temperature, the transformation of the flow behaviour from non-Boussinesq to Boussinesq is very clearly observed. Velocity measurements have been made at t∞ =4°C, the extremum temperature. For t∞ <tm , very complex flow patterns exist, due to the bidirectional buoyancy force. These patterns have been visualized. The influence of a bounding impermeable surface below the plume source has also been examined.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):255-260. doi:10.1115/1.3245571.

The onset of natural convection in a cylindrical volume of fluid bounded above and below by rigid, perfectly conducting surfaces and laterally by a wall of arbitrary thermal conductivity is examined. The critical Rayleigh number (dimensionless temperature difference) is determined as a function of aspect (radius to height) ratio and wall conductivity. The first three asymmetric modes as well as the axisymmetric mode are considered. Two sets of stream functions are employed to represent a velocity field that satisfies the no-slip boundary condition on all surfaces and conservation of mass everywhere. The Galerkin method is then used to reduce the linearized perturbation equations to an eigenvalue problem. The results for perfectly insulating and conducting walls are compared with the work of Charlson and Sani[9].

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):261-266. doi:10.1115/1.3245572.

Experimental data and correlations are presented for the time scales of developing and decaying thermal convection with volumetric heating in a horizontal layer. The layer is bounded by rigid surfaces, with an insulated lower boundary and an isothermal upper boundary. The time for complete flow development/decay, as a result of a step change in volumetric heat generation, is simply parameterized in terms of the Fourier number for the layer, the step change in Rayleigh number, ΔRa, and the initial/final dimensionless maximum core temperature. For developing flows, ΔRa > 0, results are in good agreement with existing experiments and an approximate boundary layer theory. In decaying flows, Fourier numbers are larger than those of previously reported experiments for a motionless final state. Data for turbulent-to-turbulent transitions when ΔRa < 0 suggests that the approximate boundary layer theory underestimates the Fourier number. Experimental uncertainties on measured Fourier numbers are generally well within the limits of uncertainty allowed by the approximate theory.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):267-272. doi:10.1115/1.3245573.

This paper presents theoretical results on natural convection in vertical air-filled enclosures with isothermal hot and cold walls. The flow is considered to be two-dimensional, laminar, and stationary. The effect of stratification of the fluid in the core region on the heat transfer and the natural convection flow is discussed. Local heat transfer relations considering this stratification are given. The Rayleigh number varied from 104 −106 , the aspect ratio from 1–18, and the side walls were both perfectly conducting and adiabatic.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):273-280. doi:10.1115/1.3245574.

The Galerkin finite element method was used to analyze the natural convection heat transfer in an irregular enclosure made by two isothermal concentric horizontal cylinders: the inner square cylinder and the outer circular cylinder. Two different aspect ratios, A/R = 0.2 and 0.4, are considered for two possible symmetric attitudes of the inner square cylinder. For the case of aspect ratio 0.4, experimental verification has also been made by obtaining field temperature measurement and streamline visualization. It is found that there is no boundary layer separation past the sharp edges of the inner cylinder in the range of Rayleigh numbers less than 105 , although this phenomenon plays a negative role in the local and overall heat transfer. Above the upper horizontal surface of the inner square cylinder, a well-defined symmetric plume is found despite its low flow speed and temperature gradient. For the geometry of stand-on-edge position of the inner cylinder, vortex cores exist in the enclosure in quadruple for Ra≤5.0×104 and A/R = 0.4, and in double for other cases including A/R = 0.2.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):281-287. doi:10.1115/1.3245575.

A mathematical model for predicting the course of a developing fire in a compartment is described. The model uses release rate data obtained from laboratory-scale tests to calculate the rate of heat and smoke generation within the compartment. From these data, the model predicts rate of involvement of combustible surfaces, upper layer temperatures, and smoke concentration as a function of time. The model is described by relationships used to determine: (i) ignition and rate of vertical fire propagation, (ii) release rates based on total heat released and incident flux, and (ii) heat losses by venting and accumulation within the boundaries of the compartment. Results of predicted by the model and observed in full-scale tests of furnished compartments are compared.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):288-294. doi:10.1115/1.3245576.

A calculational method is presented for the stationary thermal ignition of pulverized coal suspensions based on radiative energy transport in a heat generating medium. A diffusion-limited, Arrhenius model for heat generation is used in the description of the heterogeneous ignition and combustion of particles with the gases in which they are dispersed. The discrete ordinates method, which is used to solve numerically the radiative transfer equation, is combined with an iterative procedure to obtain both the temperature and radiation intensity distributions throughout the reacting system. Numerical examples are presented to show the variation in the critical behavior of a system in plane geometry with wall temperature and reflectivity, optical thickness of the system, particle size, optical parameters, anisotropy of the scattering, and the parameters of the heat generation model.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):295-301. doi:10.1115/1.3245577.

An approximate analytical method for treating parabolic type nonlinear heat diffusion equations is descibed in this study. The method involves transformation of the partial differential equations along with their initial and boundary conditions in terms of several pseudo-similarity variables followed by numerical solution of a system of quasi-ordinary differential equations. One obvious advantage of the approach is that the solution at a particular time can be found independently of the previous history of the temperature field. The simplicity and directness of the method are illustrated by solving the problem of combined conduction and thermal radiation in a large, heat-generating, particulate bed in contact with a solid. Comparison of the present analytical results is made with available finite difference solutions and found to be good.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):302-306. doi:10.1115/1.3245578.

Earlier papers by the authors developed a new set of parameters for characterizing heat transfer properties of single fins and fins in arrays of extended surface. The use of these parameters has facilitated the solutions to several interesting fin problems, namely: a more careful characterization of one-dimensional flow configurations, a method for accommodating continuously distributed heat sources along the fin, a perturbation approach for the approximate computation of the parameters, and new insights into the precepts of the optimal fin shape. These developments are reported in this paper.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):307-311. doi:10.1115/1.3245579.

The transient response of a straight fin composed of two different materials is analyzed. The Laplace transformation and eigenfunction expansion methods are used in the analysis. The inverse Laplace transform is solved by utilizing the Fourier series technique. It is shown that the conductivity ratio plays an important role on both the heat transfer rate and the time to reach the steady state. However, the effect of diffusivity ratio is found to be insignificant on the transient response when the conductivities are constant.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):312-318. doi:10.1115/1.3245580.

Mathematical models are developed for the response of surface mounted thermocouples on a thick wall. These models account for the significant causes of errors in both the transient and steady-state response to changes in the wall temperature. In many cases, closed form analytical expressions are given for the response. The cases for which analytical expressions are not obtainable can be easily evaluated on a programmable calculator or a small computer.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):319-324. doi:10.1115/1.3245581.

A primary objective of this work was to gather experimental convective heat transfer coefficient data for extended surfaces. The results were then compared with bare horizontal tubes in a similar flow environment. The finned tube configurations were considered an extension of the bare tube arrangements to enhance heat transfer. Heat transfer coefficients were computed from the heated tube surface temperature, the fluidized bed temperature, and the power input to the tube. Selected serrated finned tubes were used. The experimental heat transfer data were measured as a function of fluidized bed flow parameters and finned tube geometry. Several tests were performed using two different uniformly sized glass particles (.21 mm and .43 mm). Fin efficiency factors were determined and presented as a function of mass velocity and as a function of a fin length parameter. The finned tube demonstrated a better heat transfer capacity over bare tubes for similar fluidization conditions.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):325-332. doi:10.1115/1.3245582.

Radiative heat transfer through evacuated randomly packed beds of uniform-diameter spheres is considered. A Monte Carlo technique is used to simulate the energy bundle traveling through the voids of the bed. The randomly packed bed is assumed to be an absorbing-scattering medium with effective absorption and scattering coefficients. The packing pattern is modeled by a numerical simulation of rigid spheres slowly settling into a randomly packed assemblage. The Monte Carlo simulation of radiant energy transport through the packed beds generates the transmission curve as a function of bed height and sphere emissivity. The effective absorption and scattering coefficients of the randomly packed bed are evaluated by using the solution of the two-flux equations and Monte Carlo transmission results. Results show a strong dependence of the thermal radiative properties on the packing structure and the size and emissivity of constitutent spheres. Qualitative agreement is shown in comparison with other work which used regular cubic packing, and with existing experimental data.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):333-340. doi:10.1115/1.3245583.

Radiative energy transfer in a gray absorbing and emitting medium is considered in a two-dimensional rectangular enclosure using the P-N differential approximation. The two-dimensional moment of intensity partial differential equations (PDE’s) are combined to yield a single second-order PDE for the P-1 approximation and four coupled second-order PDE’s for the P-3 approximation. P-1 approximation results are obtained from separation of variables solutions, and P-3 results are obtained numerically using successive-over-relaxation methods. The P-N approximation results are compared with numerical Hottel zone results and with results from an approximation method developed by Modest. The studies show that the P-3 approximation can be used to predict emissive power distributions and heat transfer rates in two-dimensional media with opacities of unity or greater. The P-1 approximation is identical to the diffusion solution and is thus applicable only if the medium is optically dense.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):341-349. doi:10.1115/1.3245584.

An analysis is presented of forced convection heat transfer in spherical annuli bounded by isothermal surfaces at different temperatures. Flow enters the annulus through a port in the outer sphere and exits through a diametrically opposite port. The conservation equations of mass, momentum, and energy are reduced to dimensionless form, and the governing parameters of the problem are identified. Solutions are obtained for several values of each of the governing parameters via a numerical finite-difference procedure. It is found that very complex flow patterns can prevail within the annulus, particularly at high Reynolds numbers. Details of the flow field are presented by means of velocity and pressure profile plots. The effect of the flow patterns on the heat transfer phenomena is discussed by examining temperature profiles and variations of the local Nusselt number along the spherical surfaces. In addition, the circumferential average Nusselt numbers at the two spherical surfaces are presented as functions of the governing parameters of the problem. These graphs of average Nusselt numbers constitute information that could be used in the design of spherical annulus heat transfer equipment.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):350-357. doi:10.1115/1.3245585.

Transient forced convection heat transfer coefficients for both subcritical and supercritical helium in a rectangular flow channel heated on one side were measured during the application of a step in heat flux. Zero flow data were also obtained. The heater surface which served simultaneously as a thermometer was a fast response carbon film. Operating conditions covered the following range: Pressure, 1.0 × 105 Pa (1 bar) to 1.0 × 106 Pa (10 bar); Temperature, 4 K–10 K; Heat Flux, 0.1 W/cm2 −10 W/cm2 ; Reynolds number, 0–8 × 105 . The experimental data and a predictive correlation are presented.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):358-365. doi:10.1115/1.3245586.

As the efforts to produce more efficient heat transfer equipment continue, an increasing number of augmented surfaces are being produced commercially. Consequently, the designer faces an almost overwhelming task in comparing and evaluating the performance of various surfaces because of the many different ways in which the test data are currently presented in the literature. Thus, a uniform format for presenting pressure drop and heat transfer data for enhanced surfaces has become a necessity. This paper is concerned with one important aspect of this problem, namely, that of tubular enhanced surfaces used in shell-and-tube heat exchangers. As an initial step, the subject is limited to single-phase pressure drop and heat transfer; however, both tubeside and shellside flow are taken into consideration. A comprehensive list of commerical augmented tubes which may be considered for use in shell-and-tube exchangers is given, along with a survey of the performance data which are available in the literature. A standardized data format which uses the inside and outside envelope diameters as the basis for presenting the various geometrical, flow, and heat transfer parameters for all tubular enhanced surfaces is proposed and discussed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):366-373. doi:10.1115/1.3245587.

A mathematical model of the plate heat exchanger (PHE) cooling unit has been developed and solved using a digital computer. The equations of temperature distribution on each plate in a counterflow PHE cooling unit are derived using an energy balance analysis. The results are presented in the form of numerical values of the “overall effectiveness” of the heat exchanger. Factors affecting the effectiveness of the PHE cooling units have been investigated. The change of temperatures and humidity ratios of the air flows in the heat exchanger are also analyzed. Finally, the high performance of the PHE cooling unit is explained by introducing the concept of “enthalpy potential.” This unit is of particular interest as a component in solar-assisted cooling systems.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):374-378. doi:10.1115/1.3245588.

In a study of fouling of heat exchangers, aqueous solutions of CaSO4 and Li2 SO4 were circulated through electrically heated tubes at controlled conditions. Measured induction periods and fouling rates of both salts were found to be primarily functions of the supersaturation of the solutions. Secondary correlating parameters were surface temperature for the Li2 SO4 solutions and mass transfer coefficients for the CaSO4 solutions.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):379-383. doi:10.1115/1.3245589.

Examination of a large number of experiments dealing with flashing flows in converging and converging-diverging nozzles reveals that knowledge of the flashing inception point is the key to the prediction of critical flow rates. An extension of the static flashing inception correlation of Jones [16] and Alamgir and Lienhard [17] to flowing systems has allowed the determination of the location of flashing inception in nozzle flows with subcooled inlet conditions. It is shown that in all the experiments examined with subcooled inlet regardless of the degree of inlet subcooling, flashing inception invariably occurred very close to the throat. A correlation is given to predict flashing inception in both pipes and nozzles which matches all data available, but is lacking verification in intermediate nozzle geometries where turbulence may be important. A consequence of this behavior is that the critical mass flux may be correlated to the pressure difference between the nozzle inlet and flashing inception, through a single phase liquid discharge coefficient and an accurate prediction of the flashing inception pressure at the throat. Comparison with the available experiments indicate that the predicted mass fluxes are within 5 percent of the measurements.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):384-388. doi:10.1115/1.3245590.

Heat transfer rates to simulated and freely suspended liquid droplets were measured in an atmospheric hot air tunnel. The experiments were limited to water, methanol, and heptane droplets in a Reynolds number range of 25 to 2000, and a mass transfer number range of 0.07 to 2.79. The present experimental data together with data by others can best be correlated by Nuf (1+Bf ).7 = 2 + 0.57 ReM 1/2 Prf 1/3 , where properties are evaluated at film conditions except for the density in the Reynolds number which is the free-stream density. Thus the data shows that at higher temperatures, evaporation reduces heat transfer rates directly by a factor of (1 + Bf ).7 . Indirectly, evaporation affects heat transfer rates through the changes in both the composition and temperature of the surrounding gaseous medium.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):389-397. doi:10.1115/1.3245591.

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.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):401-403. doi:10.1115/1.3245593.
Abstract
Topics: Freezing
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):403-406. doi:10.1115/1.3245594.
Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):406-408. doi:10.1115/1.3245595.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):411-413. doi:10.1115/1.3245597.
Abstract
Topics: Dimensions , Fins
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):413-414. doi:10.1115/1.3245598.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1983;105(2):420-423. doi:10.1115/1.3245601.
Abstract
Commentary by Dr. Valentin Fuster

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