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RESEARCH PAPERS

J. Heat Transfer. 1966;88(1):1-8. doi:10.1115/1.3691463.

The experimentally determined pressure drops due to a sudden contraction in two-phase flow in round pipes is given as a function of system pressure, flowing mixture quality, contraction area ratio, and mass velocity. The theoretical equation derived for the resulting pressure drop is

ΔPc = G322gcρ [1 − σ2 + KTPC]
where K TPC is a parameter independent of mass velocity. This parameter was evaluated for three different two-phase flow models. It is shown that the fog-flow (homogeneous) model gives the best correlation of data over the whole range of conditions studied. The range of pressures studied was 200–500 psia; the area ratios varied from 0.144 to 0.398; the mass velocity varied from 0.52 × 106 to 4.82 × 106 lb/hr-ft2 . The fluid used in this study was water.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):10-17. doi:10.1115/1.3691453.

A total energy balance is employed in a single-component boiling flow system to obtain minimum limiting values of vapor volume content and show the effects of phase velocity distributions. Results are compared to data of various investigators in steam-water systems at pressures of 115 to 1000 psia. Limiting equations are used for derivation of more accurate relationships. A correlating function and equation are derived, from the generalized diffusion velocity for momentum, which relate voids, quality, and kw/liter. These are used to correlate Argonne’s steam voids data in a boiling channel at 163 and 614 psia with velocities in the range 1.83 to 5.94 ft/sec and steam qualities between 0.008 and 0.07. A simple, semitheoretical relationship between quality, vapor fraction, and energy addition/unit boiling volume is obtained which correlates all of the 163 psia data within about 5 percent, and a limited amount of data for 614 psia equally well.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):19-27. doi:10.1115/1.3691462.

The object of this investigation is to resolve the discrepancy between theory and experiment for the case of heat transfer during film condensation of liquid metal vapors. Calculations from kinetic theory show that with liquid metals a significant thermal resistance can exist at the liquid-vapor interface. This resistance increases with decreasing vapor pressure and is dependent on the value of an accommodation coefficient, named the “condensation coefficient” in this case. Experimental work verifying this hypothesis of a liquid-vapor interfacial resistance is presented here for mercury condensing at low pressures in the absence of noncondensable gases on a vertical nickel surface.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):29-36. doi:10.1115/1.3691466.

Heat transfer by simultaneous internal conduction and surface radiation is considered for two equal-length thin plates sharing a common edge. The external surfaces of the plates are insulated while the internal surfaces are gray, specular reflectors for thermal radiation. The problem is formulated in terms of a nonlinear integrodifferential equation which is converted to an integral equation and then solved numerically. Solutions have been obtained for a wide range of conditions including those for which diffuse reflection results are available. Temperature and local heat loss distributions as well as total heat loss calculations are presented and compared with those for diffuse reflectors. Temperatures are lower while local and total heat loss are greater for specular reflection than for diffuse reflection. With applications to radiating fins of rectangular profile in mind, fin effectiveness for specularly reflecting fins are presented and compared to the results for diffuse reflection. The effectiveness of specularly reflecting fins is greater than that of diffusely reflecting fins.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):37-43. doi:10.1115/1.3691468.

A method is presented for calculating radiative exchange in enclosures the reflectance of whose surfaces can be approximated by the sum of a diffuse and a specular component. As illustrations of application of the method, the radiative fluxes between the surfaces of two concentric spheres (or infinitely long concentric cylinders) and among the faces of a cube are calculated.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):45-49. doi:10.1115/1.3691472.

Steady-state heat transfer considerations have been used to determine the macroscopic solid-liquid interface shape in solidification processes such as floating zone melting and crystal pulling. It was found by means of computer solutions that the Biot number ha R/k, is the prime determinant of the shape of the interface. As the Biot number increases, the interface becomes increasingly concave into the solid. A uniform heat input model was formulated which gives analytical results close to the computer results. A one-dimensional analysis showed that the fractional error in the position of the isotherms caused by ignoring the heat carried by the motion of the crystal is approximately Vρcp−R/8hak. The effect of various heat transfer parameters on the dislocation generation caused by thermal stresses was also predicted and found to compare fairly well with experimental results.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):52-55. doi:10.1115/1.3691476.

The thermal conductivities of argon, neon, and krypton in the temperature range 1500 to 5000 deg Kelvin have been deduced from the measurement of heat transfer rates from the heated gases to the end wall in the reflected shock wave. Pressures ranged from approximately 1/2 atm to 3 atm. The relationship between thermal conductivity and temperature was assumed to be of the form k = aTb . The constant “b” was determined by a best fit to the data and the constant “a” by the known values of “k” below 1500 K. The effect of density variation in the thermal boundary layer was found to be significant in reducing the data; some previous investigations have neglected this effect.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):57-61. doi:10.1115/1.3691479.

The theory of nonequilibrium thermodynamics for inherently irreversible coupled processes is presented and the concept of heat is incorporated appropriately. The theory was applied to the problem of a solid carrying electric and heat currents in the presence of an external magnetic field. The principle of increase of entropy was employed to determine the reversibility or irreversibility of the macroscopic effects involved and to determine the limits on the material’s properties. The dynamic equations show that, in the one-dimensional thermoelectric case, the heat current is not coupled to the electrical phenomenon. In two and three-dimensional cases, the heat current is coupled to the electrical phenomenon only through the influence of the external magnetic field. Areas of disagreement with the literature are pointed out and discussed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):64-68. doi:10.1115/1.3691483.

An analysis of a thermal flowmeter is presented incorporating the normally neglected effect of axial conduction along the tube. It is assumed that heat flow from the tube to the fluid is proportional to the temperature difference between the tube wall and the bulk temperature of the fluid. The solution is given in analytical form, and a numerical example is included.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):69-76. doi:10.1115/1.3691484.

A theoretical and experimental study of the heat transfer and flow friction characteristics of matrices of high porosity, with incident radiation from one side resulting in an exponential heat source, and with air as a coolant, is reported. In the theory, a transient solution of simultaneous convection and radiation heat transfer equations has been worked out. Used with experimental data taken in the unsteady state, it resulted in the calculation of volumetric heat transfer coefficients by convection in the matrices. Correlations with Reynolds numbers, based on a characteristic length obtained by equating pressure drops to the sum of viscous and inertia resistance terms, were obtained. Using the more familiar hydraulic radius did not result in reducing the relationships to a unified form. The matrices used in the experiments were formed from slit-and-expanded aluminum foils, blackened to high radiant absorptivity. The results of the investigation are believed useful in many solar, nuclear, and space applications.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):77-79. doi:10.1115/1.3691485.

The thickness of a laminar liquid film draining from a vertical surface is found analytically under the assumption that the evaporation rate from the surface of the film is a known constant. The transient is studied as well as the steady solution. Expressions are found for the location where the film vanishes as well as for the rate of evaporation and total mass evaporated until any time.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):80-86. doi:10.1115/1.3691486.

Heat transfer coefficients on smooth plate rotating evaporator-condensers are reliably predicted by equation (2). Radial machine grooving of the condensing surface improves the heat transfer coefficient in filmwise condensation on this surface by reducing the resistance up to 65 percent. The overall coefficient was improved some 13 percent. Surfaces radially scratched by coarse sandpaper exhibited higher coefficients than smooth surfaces. Sanding the condensation side improved the overall coefficient about 8 percent, and sanding the evaporation side improved it about 10 percent. Care should be used in applying grooves to the evaporation side, however, as they increase the tendency toward local overevaporation and, hence, scale formation. Machined grooves on the evaporation side reduced overall coefficients.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):87-90. doi:10.1115/1.3691487.

The kinematics of vapor removal from a sphere has been investigated during film boiling in saturated liquid nitrogen. New experimental data are presented concerning the bubble frequency f and diameter D. In spite of film boiling conditions, the results may be correlated with the nucleate boiling relation, f(D)1/2 ≈ 17.5 (cm)1/2 sec, proposed by McFadden and Grassmann.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):94-99. doi:10.1115/1.3691491.

The peak nucleate boiling heat flux has been observed for five fluids during saturated pool boiling on horizontal wire heaters, ranging in radius from 0.0025 in. to 0.0254 in., over a reduced pressure range from 0.0010 to 0.0197. A scheme for correlating the peak and minimum heat fluxes is developed heuristically and successfully applied to these data. The result is a single three-dimensional surface which represents all of the data. The surface can be represented as the product of a function of geometric scale, and a function of pressure. The function of pressure appears to be the same in any configuration.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):101-107. doi:10.1115/1.3691449.

Local as well as average heat transfer coefficients between an isothermal flat plate and impinging two-dimensional jets were measured for both single jets and arrays of jets. For a large and technologically important range of variables the results have been correlated in relatively simple terms, and their application to design is briefly considered.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):109-116. doi:10.1115/1.3691452.

Combined free and forced convection inside inclined circular tubes is studied theoretically. The case considered is that of fully developed laminar flow with constant-pressure gradient and constant-heat flux. Fluid properties are considered constant except for the variation of density in the buoyancy terms. Upward flow only is considered. Velocity and temperature fields are calculated by perturbation analysis in terms of power series of Rayleigh numbers. A detailed analysis of the final equations is made to determine the range of values of nondimensional parameter such as Rayleigh and Reynolds numbers over which the mathematical results are valid. Nusselt numbers are calculated based on bulk temperature difference and in final form are also expressed in terms of power series of Rayleigh numbers. Rayleigh number appears to be the dominant parameter in equations of velocity and temperature fields and Nusselt number. However Rayleigh and Reynolds number product and Prandtl number also influence the equations independently. As the tube inclination varies from horizontal, the Nusselt number increases up to a maximum which may occur before the vertical position is reached. The angle at which this maximum occurs appears to be a function of Rayleigh, Reynolds, and Prandtl number, and in most instances lies between 20 and 60 deg of tube inclination.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):117-124. doi:10.1115/1.3691454.

The general problem of turbulent flow heat transfer in parallel rod arrays is considered. To accommodate the complexity introduced by this configuration, a method of analysis is developed using the technique of superposition of fundamental solutions. Fundamental solutions are determined experimentally which may be used to predict heat transfer in parallel rod arrays of various spacings and with arbitrary power distribution from rod to rod and around the periphery of the rods. The experimental investigation was conducted with airflow (Pr = 0.70) past electrically heated rods. Rod center-to-center spacing to rod diameter ratios of 1.15 and 1.25 were investigated for fully developed turbulent flow. Experimentally determined fundamental solutions are presented for Reynolds numbers from 7000 to 200,000.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):125-130. doi:10.1115/1.3691455.

Predictions of the heat loss from animal systems under the influence of environmental air temperature using thermal modeling techniques are found to agree with available experimental results. To perform the necessary experiments on heat loss, over a variety of environmental conditions for all species of interest, would be a formidable task. The thermal modeling approach circumvents these difficulties by the use of basic heat-transfer equations and properties and is suggested and exemplified as an alternative.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):131-136. doi:10.1115/1.3691456.

Experiments were performed to determine the effect of flow separation on the heat-transfer characteristics of a turbulent pipe flow. The flow separation was induced by an orifice situated at the inlet of an electrically heated circular tube. The degree of flow separation was varied by employing orifices of various bore diameters. Water was the working fluid. The Reynolds number and the Prandtl number, respectively, ranged from 10,000 to 130,000 and from 3 to 6. The measurements show that the local heat-transfer coefficients in the separated, reattached, and redevelopment regions are several times as large as those for a fully developed flow. For instance, at the point of reattachment, the coefficients were 3 to 9 times greater than the corresponding fully developed values. In general, the increase of the heat-transfer coefficient owing to flow separation is accentuated as the Reynolds number decreases. The point of flow reattachment, which corresponds to a maximum in the distribution of the heat-transfer coefficient, was found to occur from 1.25 to 2.5 pipe dia from the onset of separation.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):137-139. doi:10.1115/1.3691457.

The Lagrangian method of description was used, as opposed to the Eulerian coordinate system, in studying the dynamic response of a single fluid heat exchanger. Experimental measurements are reported for a heated thin walled stainless steel tube. Comparison of the analytical and experimental results is given.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(1):140-146. doi:10.1115/1.3691458.

A study of the cooling effect of secondary fluid injection on the heat transfer between a shrouded rotating disk and a radially inward main flow stream is presented. The investigation is intended as a model study of film-cooled, radial-flow gas turbines. The film-cooling method is reviewed, and the nondimensional parameters governing the heat transfer are obtained. Experimental results, covering the range of radial-flow, gas-turbine operating conditions, were obtained from a film-heated, rotating-disk facility. The heat-transfer behavior of the main stream only was determined separately, and the film-cooling results are presented as ratios of the heat transfer obtained with film cooling to the heat transfer obtained with only the single radial inflow.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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