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RESEARCH PAPERS

J. Heat Transfer. 1977;99(2):163-168. doi:10.1115/1.3450663.

Results are presented for a series of solar collector experiments in which the incident solar flux was concentrated by a single-axis tracking parabolic trough mirror. The concentrated solar flux was directed onto an absorber tube whose axis coincided with the focal axis of the concentrator. The performance of the collector was evaluated using three different absorbers; a black painted tube designed to operate near ambient temperature, a heat pipe which had a selective solar absorber coating applied to its surface, and a heat pipe which had its surface coated with a nonselective black paint. The peak efficiency for the collector in the absence of heat losses is approximately 62 percent when the incoming solar energy is normal to the collector aperture. The heat losses which occurred at elevated temperatures (300°C) decreased the peak efficiencies to 50 and 30 percent, respectively, for the selectively coated and black painted tubes. The experimental results establish the technical feasibility of using parabolic trough collectors for applications requiring thermal energy at temperatures up to 300°C.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):169-173. doi:10.1115/1.3450664.

A glass tube honeycomb solar collector, composed of a conventional single-glazed flat-plate water cooled nonselective black absorber with a cylindrical glass honeycomb mounted between the plate and cover glass, was designed, fabricated, and tested. The test procedure followed the National Bureau of Standards Method of Testing for Rating Solar Collectors. The honeycomb consists of individual cylindrical thin-wall glass tubes standing on end on the absorber plate in a hexagonal close-packed pattern. The tubes are 9.5-mm ID, 0.2-mm wall thickness, 5.3 length to diameter ratio made of glass with mean solar absorptive index (k), 2.6 × 10−6 μ−1 , evaluated from spectral transmittance-reflectance measurements on a tubing specimen. The collector performance equalled or surpassed theoretical predictions for measurements made over a broad range of collector inlet temperatures and environmental conditions. Performance comparisons are made with a baseline double-glazed solar collector tested alongside the honeycomb collector. For applications requiring a working fluid temperature of 65°C above the ambient air temperature, honeycomb collector efficiencies of 35–55 percent may be expected for approximately a six hour period on clear days; for fluid temperature 40° C above ambient air temperature, efficiencies of 50–65 percent may be expected.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):174-179. doi:10.1115/1.3450665.

The optimization of the design of a solid sensible heat storage unit initially at a uniform-temperature is presented. The storage unit is composed of a number of rectangular cross-sectional channels for the flowing fluid, connected in parallel and separated by the heat storage material. The complex method for constrained nonlinear optimization as presented by M. J. Box is utilized, with some modifications. The design optimization is based upon achieving maximum utilization of the heat storage or removal capabilities of the material for a given set of operating conditions. This is achieved by varying the storage unit’s geometry while placing constraints on the maximum and minimum length of the unit, fluid channel size, storage material thickness, maximum and minimum outlet fluid temperature, and the minimum amount of heat to be stored.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):180-186. doi:10.1115/1.3450666.

The concepts of fully developed flow and heat transfer have been generalized to accommodate ducts whose cross-sectional area varies periodically in the streamwise direction. The identification of the periodicity characteristics of the velocity components and of a reduced pressure function enables the flow field analysis to be confined to a single isolated module, without involvement with the entrance region problem. A similar modular analysis can be made for the temperature field, but the periodicity conditions are of a different nature depending on the thermal boundary conditions. For uniform wall temperature, profiles of similar shape recur periodically. On the other band, for prescribed wall heat flux which is the same for all modules, the temperature field itself is periodic provided that a linear term related to the bulk temperature change is subtracted. The concepts and solution procedure for the periodic fully developed regime were applied to a heat exchanger configuration consisting of successive ranks of isothermal plate segments placed transverse to the mainflow direction. The computed laminar flow field was found to be characterized by strong blockage effects and massive recirculation zones. The fully developed Nusselt numbers are much higher than those for conventional laminar duct flows and show a marked dependence on the Reynolds number.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):187-195. doi:10.1115/1.3450667.

Experiments based on the naphthalene sublimation technique were carried out to determine the local and average transfer characteristics for flow in a corrugated wall channel. The range of the experiments encompassed the laminar, transition, and low-Reynolds-number turbulent regimes. Local mass transfer measurements were made both in the spanwise (i.e., cross stream) and streamwise directions, and overall transfer rates were also determined. The experiments demonstrated the existence of a variety of complex transfer processes and related fluid flow phenomena. These included secondary flows and associated spanwise mass transfer variations, suppression of the secondary flow by counteracting centrifugal forces, and destruction of the secondary flow by the onset of turbulence. Flow separation on the leeward facets of the corrugated wall caused a sharp decrease in the local transfer rates, but relatively high transfer rates were in evidence in the reattachment region. In the laminar range, the average transfer coefficients for the corrugated wall channel were only moderately larger than those for a parallel-plate channel. On the other hand, in the low-Reynolds-number turbulent regime, the wall corrugations were responsible for an increase of nearly a factor of three in the average coefficient compared with the smooth wall channel.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):196-202. doi:10.1115/1.3450668.

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.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):203-207. doi:10.1115/1.3450669.

The transfer of heat in a gas filled enclosure can be calculated by the zone method put forward by Hottel and Cohen [1, 2]. For a shape which can be divided into cylindrical or cubic zones, tabulated and graphical data on exchange areas are available, however, insufficient data exist for subdivision into rectangular zones. The present contribution provides a mathematical solution for the gas-to-surface exchange area between a rectangular parallelepiped gas volume and an adjacent face. The rules for manipulating and scaling of exchange areas are reviewed, and their application to the zoning of a rectangular furnace chamber into concentric rectangular volume elements is demonstrated.

Topics: Heat , Furnaces , Shapes
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):208-211. doi:10.1115/1.3450670.

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.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):212-220. doi:10.1115/1.3450671.

An experimental and theoretical investigation of the interaction of gaseous thermal radiation with natural convection was made for a laminar methane-air diffusion flame in the lower stagnation region of a horizontal porous cylinder. The exponential wide-hand gas radiation model was employed in this nonhomogeneous (nonuniform in temperature and composition) problem through the use of scaling techniques. Using a numerical scheme, the compressible energy, flow, and species-diffusion equations were solved simultaneously with and without the radiative component. In the experiment, methane was blown uniformly from the surface of the porous cylinder, setting up (upon ignition) a diffusion flame within the free-convection boundary layer. Using a Mach-Zehnder interferometer and a gas chromatograph, temperature and composition measurements were obtained along the stagnation line. Excellent agreement was found between the results based on the nongray wide-band model and the experimental data. Furthermore, it was found that the wide-band model yielded results that were superior to those results that excluded radiation-interaction effects. Thus, this study demonstrates that the exponential wide-band model can be accurately applied to nonhomogeneous combustion situations in order to account for the radiation-convection interactions.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):221-226. doi:10.1115/1.3450672.

Non-gray radiation described by the exponential model for molecular gas bands was added to the numerical solution of turbulent combustion of methane in a planar, enclosed, jet-diffusion flame. The planar jet of methane is injected with velocity ufuel into a stream of air flowing with velocity uair parallel to the fuel. Diffusion-controlled combustion occurs in the mixing region of the jet. Plane-parallel, isothermal, black walls symmetrically located above and below the jet form the combustion chamber. A soot-free flame is assumed to exist so that molecular gas bands determine the thermal radiative transfer to the walls. Velocity, composition, and temperature fields and heat flux at the wall are obtained numerically. Approximately 40 percent of the requisite computation time is expended on the radiation calculation. Solutions are obtained to show the effect of channel size, air preheat, and product recirculation. Also the effect of reaction zone thickness was examined by varying an effective first Damköhler or mixing number which parameterizes the mixing-controlled reaction rate. It is found that a given reduction in maximum combustion temperature to reduce nitric oxide formation can be accomplished with a much less detrimental reduction on heat transfer by recirculating exhaust product into the combustion air than by reducing air preheat.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):227-232. doi:10.1115/1.3450673.

The energy fluxes that exist in an ice sheet exposed to a collimated beam of radiant energy were examined. A theoretical model was used which includes the effects of anisotropic scattering as well as the spectral dependence of the absorption coefficient of ice and of the incident radiation beam. Laboratory measurements were also made which generally confirm the predictions of the model. The results calculated from the model are primarily intended for use in analyzing two particular problems involving radiative transfer in ice. These are: (a) the assessment of the feasibility of using radiant energy sources as a means of removing ice from structures, and (b) the prediction of temperatures and internal melting in ice covers on lakes and rivers due to the absorption of solar radiation.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):233-238. doi:10.1115/1.3450674.

The penetration of a saturated liquid (a liquid at its freezing temperature) into a tube that is initially empty and maintained at a temperature below the freezing temperature of the liquid is treated theoretically and experimentally. A convenient approximate method is introduced which involves postulating a reasonable functional form for the instantaneous shape of the frozen layer along the tube wall. Graphical velocity-time and penetration distance-time curves are presented displaying the principal effects of a single dimensionless parameter. In the limit of negligible liquid inertia, shown to be relevant to high Prandtl number materials, a closed-form expression for the liquid penetration length is obtained. The expression compares well with the experimental results.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):239-245. doi:10.1115/1.3450675.

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.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):246-249. doi:10.1115/1.3450676.

A theoretical model has been developed to predict the effect of cavity size (both radius and depth), and superheat on frequency of bubble departure by considering the effect on waiting time (time between the last bubble departure and appearance of the next one on the surface) and bubble growth time. An increase in cavity size or decrease in surface superheat results in longer waiting time and bubble growth time, thus causing a lower frequency. The model explains qualitatively the observed effect of superheat and cavity size on bubble departure frequency during pool boiling experiments with water on artificial cavities drilled by laser.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):250-256. doi:10.1115/1.3450677.

Experimental observations of the dryout heat fluxes for inductively heated particulate beds have been made. The data were obtained when steel and lead particles in the size distribution 295–787 microns were placed in a 4.7-cm dia pyrex glass jar and inductively heated by passing radio frequency current through a 13.3-cm dia multiturn work coil encircling the jar. Distilled water, methanol and acetone were used as coolants in the experiments, while the bed height was varied from 1.9 to 8.9 cm. Different mechanisms for the dryout in deep and shallow beds have been identified. Dryout in shallow beds is believed to occur when the vapor velocity in the gas jets exceeds a certain critical velocity at which choking of the vapor, leading to obstruction in the flow of the liquid towards the bed occurs. However, deep beds dry out when gravitational force can no longer maintain a downward coolant flow rate necessary to dissipate the heat generated in the bed. Finally, the heat flux data of the present investigation and that from two previous investigations made at Argonne Laboratory and at UCLA have been correlated with semitheoretical correlations based on the proposed hydrodynamic models.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):257-262. doi:10.1115/1.3450678.

Experiments on film condensation including noncondensable gas in an enclosed chamber have been carried out to clarify the effects of molecular weights of vapor and noncondensable gas and the convective motion induced by the vapor flow. From the experimental results of R113-air and CH3 OH-mixed gas of He and Ar, it is shown that the separation of vapor and gas in the main flow is realized when the direction of gas flow in free convective boundary layer driven by concentration distribution of gas is the same as that of supplied vapor, whereas the homogeneous main flow occurs in the case of counter direction. It is also shown that in case of the separation of vapor and gas in the main flow the heat transfer coefficient is higher than that for an homogeneous main flow.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):263-268. doi:10.1115/1.3450679.

This paper presents results from a research program conducted a number of years ago on the problem of flashing flow of water in nozzles. In a previous paper [1] we presented results for the case of stagnation states in the low quality two-phase region. The present paper reports results for stagnation states in the subcooled region at pressures up to 9.05 × 103 kN/m2 and subcooling from 0 to 60° C. Pressure profiles and flow rates are reported. The results are compared with limiting cases of Bernoulli flow (meta-stable liquid flow) and homogeneous equilibrium flow. As expected neither was able to predict the experimental results. A two-step model based upon nucleation delay, “discontinuous” transition to two-phase flow followed by frozen composition gave reasonable predictions of the flowrates and pressure profiles in the convergent section.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):269-273. doi:10.1115/1.3450680.

A circulating fluid motion is generated by an electric field imposed on a dielectric drop in another dielectric liquid. The motion of the drop surface may be from the poles to the equator or from the equator to the poles. Transient heat or mass transfer results in response to a sudden change in the temperature difference or concentration difference between the drop and the surrounding fluid. The low Reynolds number, high Peclet number response is analyzed. The boundary layer equations are solved exactly using a similarity transformation. Results are obtained for both directions of circulation. While local fluxes differ greatly when the flow reverses, and despite a lack of symmetry, the overall transfer rate is independent of the direction of flow. This result applies to the transient as well as the steady state.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):274-280. doi:10.1115/1.3450681.

The relation between the Spray Energy Release (SER) and the spray nozzle efficiency (η) is considered with the view toward increasing the utility of previous spray thermal performance information. Through the approximate analysis of an assumed counter-flow process, the relevant parameters that η depends upon have been identified as the total heat transfer factor c′ /cw , the sensible heat factor φ, and the SER. In general η cannot be correlated with wind speed alone. Similarities and differences between the NTU and SER methods are also considered. Values of SER are established from data obtained from a prototype spray system and a laboratory scale single column spray system. A simplified drift loss prediction model which is in good agreement with experimental data is proposed for an open atmosphere spray system.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):281-286. doi:10.1115/1.3450682.

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.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):287-293. doi:10.1115/1.3450683.

An analysis is presented which predicts the heat transfer across fluid layers bounded laterally by vertical isothermal surface and adiabatic surfaces on the top and bottom. The vertical temperature distribution in the core of the cavity is also predicted. Extensive comparisons of average Nusselt number and temperature distribution are made with experimental data for aspect ratios greater than 5. Good agreement between analysis and experiment is found. The heat-transfer equations for vertical layers are generalized to include layers which are tilted up to 20° from the vertical, making the results useful for the design of solar collectors.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):294-299. doi:10.1115/1.3450684.

A finite difference technique was used to analyze steady, laminar natural convection due to stripwise heating on an infinite, horizontal surface. The stripwise heating was accomplished by an array of alternately heated and unheated strips. Plots of the stream function and temperature field within a two-dimensional cell are given for a variety of heating and spacing configurations. From these results, the average Nusselt number was determined as a function of the Grashof number for a Prandtl number of 0.7. A plot of this dependence indicates diffusion, transition and plume modes exist, depending upon the value of the Grashof number. The present results are compared to previous experimental results for the same system, as well as results for uniformly heated surfaces. Higher heat transfer rates for the stripwise-heated surfaces compared to uniformly-heated surfaces are demonstrated for a wide range of Grashof numbers.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):300-306. doi:10.1115/1.3450685.

A single comprehensive equation is developed for the rate of heat and mass transfer from a circular cylinder in crossflow, covering a complete range of Pr (or Sc) and the entire range of Re for which data are available. This expression is a lower bound (except possibly for RePr < 0.2); free-stream turbulence, end effects, channel blockage, free convection, etc., may increase the rate. In the complete absence of free convection, the theoretical expression of Nakai and Okazaki may be more accurate for RePr < 0.2. The correlating equation is based on theoretical results for the effect of Pr in the laminar boundary layer, and on both theoretical and experimental results for the effect of Re. The process of correlation reveals the need for theoretical results for the effect of Pr in the region of the wake. Additional experimental data for the effect of Pr at small Pe and for the effect of Re during the transition in the point of separation are also needed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):307-313. doi:10.1115/1.3450686.

An analysis technique applicable to the problem of leeward vortex-induced heat transfer on a sharp cone at high angles of incidence under hypersonic laminar flow conditions is presented. The analysis, a three-dimensional hypersonic viscous shock layer approach in conjunction with a numerical solution procedure, is shown to be both applicable and accurate based on comparisons of heat-transfer distributions, surface pressure distributions, and leeward meridian flow-field profile measurements taken in a hypersonic wind tunnel. Detailed calculations of the embedded vortex flow field on the leeward side of the cone are presented in such a manner as to clearly portray exactly how embedded vortex flow influences local heating rates.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):314-321. doi:10.1115/1.3450687.

This paper presents a method for estimating the parameters appearing in heat transfer models. The method involves minimizing a function that is more general than that utilized in least squares. One of the unique features of the method is that it is sequential. Some of the advantages of this feature are that the basic equations are simple in that no matrix inverses are required, computer programs can be easily written to have an arbitrary number of parameters, and the sequential procedure provides information for development for better mathematical models for describing complex phenomena. Some examples are given.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):322-329. doi:10.1115/1.3450688.

A one-dimensional model has been developed for diffusion transport in a binary liquid solution with a moving semipermeable boundary. The governing equations are basically Fick’s First and Second Laws in which the solute concentrations are replaced by the logarithms of the solute volume fractions. In the limit of negligible solute volume fraction, the analysis reduces to the classical one-dimensional diffusion equation. The complete form has been employed to describe the concentration polarization of solutes within human erythrocytes during freezing. The results show that the water transport process across the cell membrane is significantly affected by both the water permeation characteristics of the membrane and the diffusion of water within the intracellular medium. These results are consistent with experimental observations of red cell survival during freezing.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):335-338. doi:10.1115/1.3450691.
Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):338-339. doi:10.1115/1.3450692.
Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):340-342. doi:10.1115/1.3450693.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1977;99(2):343-345. doi:10.1115/1.3450695.
Abstract
Topics: Heat conduction
Commentary by Dr. Valentin Fuster

DISCUSSIONS

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