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RESEARCH PAPERS

J. Heat Transfer. 1975;97(3):321-325. doi:10.1115/1.3450373.

The problems of the self-freezing of a wet substance were treated as a heat conduction problem with phase change in the case of multiphase substance. The solutions for this problem were derived from the analytical procedure of Neumann’s solution and were compared with the experimental results obtained through the self-freezing of the bed with wet glass powder.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):326-332. doi:10.1115/1.3450374.

A theoretical model describing the thermodynamics of intracellular ice nucleation is developed for red blood cells as a model biomaterial. Analytical expressions based on current theories of ice nucleation by both homogeneous and heterogeneous nucleation processes are coupled with a thermodynamic model for the loss of intracellular water during freezing. Numerical solutions for both modes of nucleation identify two cooling regions—high cooling rates and low cooling rates—separated by a sharp demarcation zone. The nucleation temperature for high cooling rates is approximately 20° K higher than the nucleation temperature for low cooling rates and is essentially independent of cooling rate in each region. The nucleation temperatures for heterogeneous nucleation are approximately 30° K higher than the nucleation temperatures for homogeneous nucleation in the two regions. For the case of heterogeneous nucleation, it is possible to increase the nucleation temperature by packing of catalysts via the concentration polarization effect. If the cell suspension is allowed to supercool before nucleation occurs in the extracellular medium, the sharp transition from low cooling rates to high cooling rates for heterogeneous nucleation shifts to much lower cooling rates. The dependence of the transition cooling rate on the degree of supercooling has been established for a typical freezing situation.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):333-340. doi:10.1115/1.3450375.

The basis of the enthalpy model for multidimensional phase change problems in media having a distinct phase change temperature is demonstrated, and subsequent numerical applications of the model are carried out. It is shown that the mathematical representation of the enthalpy model is equivalent to the conventional conservation equations in the solid and liquid regions and at the solid-liquid interface. The model is employed in conjunction with a fully implicit finite-difference scheme to solve for solidification in a convectively cooled square container. The implicit scheme was selected because of its ability to accommodate a wide range of the Stefan number Ste. After its accuracy had been established, the solution method was used to obtain results for the local and surface-integrated heat transfer rates, boundary temperatures, solidified fraction, and interface position, all as functions of time. The results are presented with SteFo (Fo = Fourier number) as a correlating parameter, thereby facilitating their use for all Ste values in the range investigated. At low values of the Biot number, the surface-integrated heat transfer rate was relatively constant during the entire solidification period, which is a desirable characteristic for phase change thermal energy storage.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):341-346. doi:10.1115/1.3450376.

Instantaneous drop-size distributions were measured during transient dropwise condensation onto an initially bare surface which forms the constituent process of the so-called steady dropwise condensation on a vertical surface. The measured distributions agreed satisfactorily with the prediction from the previous author’s theory.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):347-351. doi:10.1115/1.3450377.

An experimental study of laminar film condensation of steam on copper spheres of 1.90, 2.54, and 3.17 cm dia has been made. Experiments have been performed by submerging cold spheres in nearly stagnant water vapor at a saturation temperature of about 99° C. Values of Nusselt number based on average heat transfer coefficient are obtained for saturation to wall temperature differences of 5–65° C and for cp ΔT/hfg in the range of 0.009–0.12. The data are compared with the steady-state predictions of Dhir and Lien-hard and of Yang. Analysis has been made to show that it is valid to use steady-state solutions in quasi-steady condensation as long as the dimensionless thermal diffusion time constant is small, and the film does not move very slowly.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):352-359. doi:10.1115/1.3450378.

The characteristics of the various parameters affecting the films and overall heat transfer coefficients of horizontal evaporator-condenser elliptical tubes are presented for a representative range of operating conditions. Effects of the axis ratio of the tube are analyzed and compared with the equivalent circular tube. The study indicates that the ratio of the vertical to the horizontal axis of about 4 approaches the asymptotic solution for a vertical plane of constant wall temperature and the average overall transfer rate decreases at axis ratios above 4. Effects of the intermittent removal of the condensate film from the wall are presented. The effect of homogeneously distributed noncondensables is accounted for.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):360-365. doi:10.1115/1.3450379.

An analytical model for falling-film wetting of a hot surface has been developed to account for the effect of cooling by droplet-vapor mixture in the region immediately ahead of the wet front. The effect of precursory cooling is characterized by a heat transfer coefficient decaying exponentially from the wet front. Based on the present model, the wet front velocity, as well as the temperature profile along a thin slab, can be calculated. It is demonstrated that the precursory cooling can increase the wet front velocity by an order of magnitude. Existing experimental data with variable flow rates at atmospheric pressure are shown to be successfully correlated by the present model.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):366-371. doi:10.1115/1.3450380.

Heat transfer and fluid flow experiments were made in narrow vertical enclosures of varying aspect ratio (5 ≤ H/W ≤ 40) filled with non-Newtonian fluids whose consistencies ranged from near that of water to several orders of magnitude more. Temperature and velocity profiles were obtained for thermal conditions of low convection augmentation to fully developed turbulent flow. The tests were run over periods of as much as 60 days, during which time the flow index and the consistency of the fluids changed markedly according to their thermal histories. Local hot and cold wall and average enclosure heat transfer rates and wall shear stresses were evaluated. For all the fluids, including the abnormal fluids (those which thickened with increasing temperature) the heat transfer could be correlated by

Nu = C Rab
although the constant C differed for the two classes of fluids. These correlations were valid over the entire flow regimes studied even in the presence of multiple boundary layers and secondary vortices.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):372-377. doi:10.1115/1.3450381.

An experimental program was conducted to study natural convection heat transfer in an array of uniformly heated vertical cylinders in mercury. The cylinders were arranged in an equilateral triangular pattern, and three bundle spacings, P/D = 1.5, 1.3, and 1.1, were studied. The heat transfer results are presented as local Nusselt number—modified Grashof number correlations. The results indicate a strong dependence on cylinder spacing and the somewhat lesser effects of heat flux and circumferential position. In addition, mean radial temperature profiles were recorded for various conditions as well as the fluctuations in the fluid temperatures which were encountered. The influence of cylinder spacing and axial, radial, and circumferential position on these profiles and disturbances is discussed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):378-381. doi:10.1115/1.3450382.

Thermal instability of a thin horizontal layer of binary gas mixture subject to an adverse temperature gradient in a porous medium is experimentally determined by applying the Schmidt-Milverton principle for detecting the onset of convective currents. The binary gas mixture consists of helium and nitrogen gases at various composition, while a packed bed of tiny steel balls constitutes the porous medium. It is disclosed that the critical Rayleigh number for pure gas is lowered by the presence of another species of different molecular weight and has a minimum value at a certain composition of the binary mixture.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):382-386. doi:10.1115/1.3450383.

One promising device for protection of permafrost is the concentric tube thermosyphon. In the winter, the difference in temperature between the annulus and the tube provides a buoyant driving force to move the air down the tube and up the annulus. The resultant heat transfer freezes and subcools the permafrost. The paper describes in detail the flow and heat transfer by solving the boundary layer equations for velocity and temperature considering conduction and radiation at the boundaries. The predicted thermosyphon performance is compared with experimental data. The results for heat removal rate are generally within 10–20 percent.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):387-390. doi:10.1115/1.3450384.

Normal and hemispherical thermal emittances of cylindrical cavities closed by a circular diaphragm have been evaluated. Diaphragms are diffuse or specular reflectors, at the cavity temperature or at a very low temperature. Results are reported and discussed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):391-396. doi:10.1115/1.3450385.

Radiative transfer in an absorbing and linearly-anisotropic scattering gray medium is analyzed. The medium is confined between plane parallel, gray, diffuse walls and contains uniform heat generation. The problem is formulated in terms of coupled integral equations with the intensity-moments as the unknown variables. The set of equations is solved both numerically and in closed form. The closed-form solution consists of exact limiting solutions and approximate general solutions obtained by the kernel-substitution method. The case of combined radiation and conduction is also treated. The results reveal clearly the effects of anisotropic scattering on important characteristics such as heat flux and incident radiant energy per unit area. The approximate closed-form solutions which predict quite well these effects are very simple and convenient to use for engineering calculations.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):397-399. doi:10.1115/1.3450386.

Measurements have been made of the infrared emission of carbon dioxide in the 2.7 micron region. The measurements were carried out in a free piston shock tube at temperatures of 2400 and 3500° K. Results are reported for the mean line intensity to spacing ratio and for the emissivity.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):400-405. doi:10.1115/1.3450387.

A general and fundamental study of the effect of radiation between duct walls on the heat transfer performance of duct flows of nonradiating gas such as helium is made by an approximate analysis and numerical calculations. Laminar and turbulent flows in a duct simulating a coolant passage in an HTGR and flows in counterflow and parallel-flow heat exchangers in an HTGR heat transfer system are investigated. An approximate analytical solution, based on the assumption that radiation from a point of duct wall produces an effect only on the narrow region opposite the point, agrees well with numerical results. The increase of radiative heat transfer causes a decrease of temperature difference between the duct walls and improves the heat transfer performance. For heat exchangers the heat transfer effectiveness is shown to depend on three nondimensional parameters and can be improved by the increase of these parameters.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):406-410. doi:10.1115/1.3450389.

This paper investigates the transient temperature distribution in transpiration-cooled porous matrices, after sudden initiation of uniform internal heat generation. Analytic solutions are derived for the tube and plate geometries that include the effect of forced convection heat transfer at the gas-exit surface where the conventional heat-transfer coefficient is used to define the boundary condition.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):411-416. doi:10.1115/1.3450390.

The local heat transfer coefficient, for air flowing through a pipe with a swirling motion, was measured at various stations downstream of the swirling air inlet. The swirling motion of the air was produced by a single tangential slot, initially at 90 deg to the pipe axis, through which the air was introduced. The dimensions of the slot and the angle of tangency were varied and the resultant flow field inside the pipe was measured and expressed in the form of local “swirl numbers”. The augmentation of heat transfer was found to be a function of the swirl number and a correlation for this function is presented. At some locations, the augmentation can be as much as eight times the value for fully developed nonswirling turbulent flow.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):417-423. doi:10.1115/1.3450391.

The transient response of a fin of constant area of cross section and perimeter, with its end insulated, is analyzed using Laplace transforms. Solutions are developed for small and large values of times when the base is subjected to a step change in temperature or heat flux. Fins with base subjected to sinusoidal temperature or heat flux are also analyzed. Typical results are represented in graphical form.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):424-428. doi:10.1115/1.3450392.

Due to the geometric configurations of convectively cooled underground electric power cable systems, nonuniform cooling of the individual cables can occur. A numerical analysis has been performed on the effects of nonuniform surface cooling on the temperature distribution inside the insulation of a single cable. The results show that with the typical geometries considered, the coolant temperature would have to be lowered significantly in order to maintain a given amount of heat dissipation per unit length in comparison to uniform cooling. It is useful, therefore, to promote uniform cooling around the circumference of each cable by changing the fluid flow pattern and by the use of metal sheathing around the circumference. To evaluate this latter effect, a dimensionless parameter representing the relative magnitudes of heat conduction in the sheathing and in the insulation is proposed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):429-434. doi:10.1115/1.3450393.

When an electric field is applied to a system of electrically conducting particles in an insulating liquid, the rates of charge and heat transfer are augmented. Charged during collisions in the field, the particles execute field-induced excursions between the electrodes interrupted by collisions with other particles. Thus a combination of particle migration and particle-induced fluid convection results in the increase in heat transfer. Experimental values for the Nusselt number are obtained for heat transfer across the parallel electrode configuration. The model developed using these results consists of a well-mixed central region with thermal boundary layers about one particle diameter thick near each electrode.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):435-441. doi:10.1115/1.3450394.

Experiments were conducted upon a voltage pulsed coaxial argon plasma in a 1 cm dia, 13.6 cm long channel. Initial steady-state current and pressure were 81 A and 776 Torr, respectively. The final average current was about 1200 A. Rise times of current and center-line temperatures were about 200 μs. Using spectroscopic techniques, with data acquisition times of about 5 μs, radial distributions of temperature and pressure were obtained at various times into the transient. A final average temperature of about 18,000° K was obtained.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):442-450. doi:10.1115/1.3450396.

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

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):451-456. doi:10.1115/1.3450397.

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

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):457-462. doi:10.1115/1.3450398.

The purpose of this research was to measure threshold temperatures corresponding to the formation of minimum ophthalmoscopically visible lesions induced in rabbit ocular fundi by a 10-s exposure from an argon c. w. laser (4880 Å). The backside of the eye was surgically exposed and a specially designed microthermocouple with a 20-micron dia tip was inserted into the pigment epithelium to measure temperature rises. The mean threshold temperature for 30 measurements in 13 rabbits was 54° C and the standard deviation was 3° C. System error was estimated at 5 percent of temperature rise, or slightly less than ±1/2° C.

Commentary by Dr. Valentin Fuster

ERRATA

TECHNICAL BRIEFS

J. Heat Transfer. 1975;97(3):463-465. doi:10.1115/1.3450400.
Abstract
Topics: Temperature
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):467-469. doi:10.1115/1.3450402.

The least squares time-stepping algorithm, which has previously been shown by the authors to be competitive for one-dimensional problems, is applied to the solution of several two-dimensional examples having constant material properties. The results are compared against answers obtained using recurrence relationships based on the finite element and finite difference methods. Analytical results for one of the examples are also used for comparison. The least squares algorithm proved to be more accurate for equal values of time step especially in the large time step cases. It, however, requires more computer time and storage than the other methods used. Several other limitations of the scheme are also presented.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):469-471. doi:10.1115/1.3450403.
Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):472-474. doi:10.1115/1.3450404.

Experimental measurements for natural convection mass transfer adjacent to vertical and downward-facing inclined surfaces were performed using an electrochemical technique. The measurements yielded the time average and instantaneous mass transfer rates for the laminar, transition, and turbulent flow regimes along the test surface. The laminar mass transfer measurements were found to agree with both the analytical and experimental results for both the vertical and downward-facing inclined surfaces. The Rayleigh number marking the onset of the transition from laminar flow conditions depended heavily upon the angle of inclination of the test surface. In the turbulent regime the time average local mass transfer coefficient was correlated by the Rayleigh number to 1/3 power.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):476-478. doi:10.1115/1.3450406.

A model for turbulent natural convection based on the cyclic destruction and rebuilding of the boundary layer has been proposed by Howard [6]. A close look at more recent experimental data shows that the boundary layer is probably not destroyed as Howard postulated, but is stable with thermals growing upon it and producing the periodicity of the phenomenon. A modified model is proposed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):478-480. doi:10.1115/1.3450407.
Abstract
Topics: Gases , Slabs
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):480-482. doi:10.1115/1.3450408.
Abstract
Topics: Coatings , Emissivity
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):482-484. doi:10.1115/1.3450409.

Numerical solutions are described for the unsteady thermal boundary layer in incompressible laminar flow over a semi-infinite flat plate set impulsively into motion, with the simultaneous imposition of a constant temperature difference between the plate and the fluid. Results are presented for several Prandtl numbers.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):486-488. doi:10.1115/1.3450411.
Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):490-492. doi:10.1115/1.3450413.
Abstract
Topics: Heat exchangers
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):492-494. doi:10.1115/1.3450414.
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1975;97(3):494-495. doi:10.1115/1.3450415.
Abstract
Commentary by Dr. Valentin Fuster

DISCUSSIONS

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