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RESEARCH PAPERS

J. Heat Transfer. 1965;87(1):1-12. doi:10.1115/1.3689039.

A cool slab of metal when dipped into the bath of a molten metal first freezes metal from the bath; then—if kept there long enough—the frozen crust and the slab melt out. The same result is obtained in a continuous process where the slab is pulled through the melt. In this paper a theory is developed for the process, assuming that the material properties of bath and slab are the same. The governing partial differential equation is established, and is approximated by four-node (“3-channel”) and two-node (“1-channel”) difference-differential equations. It is shown that when the slab is passed through the bath at a speed exceeding a value 5 of the Peclet number p, it is adequate to regard the slab in the calculations as suddenly dipped into the bath and then kept there for a time equal to the time of travel through the bath. The solutions of the 1-channel equations are presented in the form of dimensionless curves which give the mean temperature of the slab as function of position and show the growth and decrease of the slab thickness. Good agreement is obtained with available test results for dip-formed copper.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):17-27. doi:10.1115/1.3689038.

A photographic study was made of saturated nucleate pool boiling at a pressure of one atmosphere. Over 1000 still photographs and 12 high-speed motion pictures were taken of water boiling from a 2-in-dia flat horizontal surface facing upward. Two surfaces were studied, a 2/0 polished platinum surface and a 4/0 polished copper surface. The platinum surface was studied in the heat flux range of 14,700 to 176,000 Btu/hr, sq ft, and the copper surface from the incipient boiling heat flux of 10,500 Btu/hr, sq ft to the maximum flux of 493,000 Btu/hr, sq ft. Data were obtained for the breakoff diameters of discrete bubbles, and for the populations of active sites at heat fluxes up to 58,600 Btu/hr, sq ft. At least three, and possibly four, heat-transfer regions were found to exist in nucleate boiling, depending upon the mode of vapor generation. The vapor structures on the surface progressed through a sequence of first discrete bubbles, then vapor columns and vapor mushrooms, and finally vapor patches, as the surface temperature was increased. These individual vapor structures, or combinations of them, determine the mechanism of heat transfer in the four nucleate boiling regions. It was concluded that any heat-transfer model or design equation which is based on the dynamics of individual bubbles, or on any other single mechanism, must be in serious error.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):30-39. doi:10.1115/1.3689043.

This paper describes a series of closely controlled experiments made to investigate the performance of the closed thermosyphon. All the regimes previously observed in the open system were identified, and suggestions are made concerning the nature of the process by which the heated and cooled regions of the thermosyphon are hydrodynamically coupled together. A theoretical analysis of the laminar boundary layer regime is given and comparisons made with the experimental results.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):41-46. doi:10.1115/1.3689046.

Hydrogen heat-transfer data in the supercritical region has been compared with an analysis based on fully developed turbulent pipe flow with variable fluid properties. The comparison indicated an additional variable property effect not included in the analysis. However, this approach led to the correlation of the data over the full range of experimental conditions. These results indicate that the mechanism of supercritical heat transfer with hydrogen can be explained on the basis of variable fluid property effects without postulating a new mechanism for heat transfer, as done in previous investigations. It was also found that the pipe flow equation with fluid properties based on the film temperature can be made to correlate the data by correcting the calculated values with a simple function of wall to bulk kinematic viscosity ratio. This method provides a rapid means for determining supercritical hydrogen heat transfer with accuracy sufficient for most purposes.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):49-52. doi:10.1115/1.3689049.

Transient heat conduction in a copper rod was studied using an arc-imaging furnace to supply pure radiant thermal energy at flux levels up to 1000 cal/cm2 -sec. No significant effects were observed attributable to the rate of heating up to and through melting at the surface. Transient temperature profiles agree well with theory and melting was initiated at its equilibrium temperature. The dynamics of the vaporization process are more uncertain.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):53-57. doi:10.1115/1.3689050.

An analytical model to predict two-phase critical flow rate is proposed. The model is based upon thermal equilibrium, a “lumped” treatment of the two-phase velocity (each phase is represented by a single mean velocity), and upon the neglect of frictional and hydrostatic pressure losses. A comparison of the proposed predictions with available test results and previous analyses shows that: (a) The present model agrees very well with the published test data; (b) In contrast to all other analyses, the model requires no assumption about the gas void fraction.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):59-66. doi:10.1115/1.3689053.

This study deals with fully developed laminar forced convection in rectangular channels that are heated on the broad sides. The analysis determines the effect of peripheral heat conduction within the heated walls on the wall temperature distributions. The unheated short side walls are assumed nonconducting. The heat conduction within the broad walls was formulated in terms of an integral equation and coupled with the convective energy equation within the fluid. Analytical solutions were obtained where the heating extends over the entire width of the broad side, is removed from the corner region, or extends beyond the corner into the side wall. Transverse wall conduction produced substantial decreases in the peak wall temperature and in the temperature gradients along the long side.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):67-73. doi:10.1115/1.3689054.

The results of an experimental investigation of the frictional and heat transfer effects in air, nitrogen, and helium in steady, turbulent flow in round tubes are presented. Wall-to-bulk temperature ratios extend from near unity to 2.5, entering Reynolds numbers from 15,000 to 233,000. Dependence of the thermodynamic and transport properties on temperature is shown to be significant in both heat transfer and wall friction and is reflected in the empirical correlations for local and average coefficients which are developed. The results of other investigators who have analyzed or measured variable properties effects are recalculated where necessary to facilitate comparisons.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):77-82. doi:10.1115/1.3689057.

This paper presents results of an experimental investigation of convective heat transfer in liquids confined by two parallel plates and inclined at various angles with respect to the horizontal. The experiments covered a range of Rayleigh numbers between 5(10)4 and 7.17(10)8 , and Prandtl numbers between 0.02 and 11,560. Tests were made in rectangular and circular containers having copper plates and insulating walls. The liquids used were water, silicone oils, and mercury. The test results indicate that the heat transfer coefficients for all liquids investigated at the various angles, from horizontal to vertical, may be determined from the relationship

Nu = C(Ra)1/3(Pr)0.074
The constant, C, is a function of the angle of inclination. It varies from C = 0.069 for the horizontal case when heated from below to C = 0.049 for the vertical case. For the test cells used, no effect on the Nusselt number had been detected for the vertical case by the change of the ratio of height of cell to distance between plates. The ratio for these tests was varied from 4.41 to 16.56.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):85-93. doi:10.1115/1.3689061.

A detailed experimental study has been carried out to examine the influence of surface roughness conditions on the reflection characteristics of metal surfaces for monochromatic thermal radiation. Surfaces used were prepared by standard optical grinding techniques using a range of sizes of grit of the grinding compounds. Various definitions of reflectances are presented to facilitate in the discussion of the results. Biangular, specular, and hemispherical-angular reflectance measurements are discussed in terms of the optical root-mean-square surface roughness, wavelength of reflected radiation, and surface material. The experimental results are compared with the available predictions from theoretical analysis.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):95-102. doi:10.1115/1.3689064.

The analysis of Bankoff and Jain [10] of film condensation on a vertical porous plate with uniform suction velocity is extended to the case of a horizontal porous tube. Integral momentum and energy balances are written for the system, including the effects of interface drag and condensate heat capacity, and the dimensionless equations are solved using a perturbation technique. All dependent variables are expressed in a double power series in the two perturbation parameters, ξ = kΔt/μλ (acceleration parameter) and α (dimensionless suction velocity), and the resulting equations are solved up to the second order perturbation. An asymptotic solution valid for high values of α is derived, and this solution together with the perturbation solution describes the system for a wide range of α. The case of heat transfer in a zero gravity field is treated, and the Nusselt number is found to be directly proportional to the suction velocity. Based on the results it is concluded that significant increases in heat transfer are possible with the use of suction.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):103-109. doi:10.1115/1.3689018.

A variational expression is devised from which the governing equations are derivable for all problems of radiant interchange between diffusely emitting and reflecting surfaces. This correspondence between the variational expression and the equations of radiant interchange serves as the basis of an approximate solution method for radiation heat transfer problems. The solution method is discussed in general and then applied to specific physical situations. It is shown that the variational method yields results with remarkable ease, especially when compared with the formidable computational task inherent in a direct numerical assault on the governing integral equations.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):110-114. doi:10.1115/1.3689021.

The heat transferred through vertical plane layers by free convection was measured as a function of the temperature difference across the layer, the height of the layer, and its thickness. Heat transfer coefficients are reported for fluids having Prandtl numbers from 3 to 30,000. An analysis of the problem by means of integral equations yielded results which differed by no more than 12 percent from the measured data in the range in which the equations were applicable.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):117-130. doi:10.1115/1.3689025.

The transient, one-dimensional temperature distribution is determined for a slab, insulated on one face, and subjected to thermal radiation at the other face. The slab is initially at a uniform temperature and is assumed to be homogeneous, isotropic, and opaque; the physical properties are assumed to be independent of temperature. Transient temperature distributions for both heating and cooling situations are obtained by means of a thermal-electrical analog computer. A diode limiter circuit is used to simulate the nonlinear radiant heat flux. The transient temperature distributions are presented in a dimensionless, graphical form for a wide range of variables. Approximate analytical solutions are also given which complement and extend the solution charts over ranges of parameters not covered in the charts.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):134-141. doi:10.1115/1.3689029.

A theoretical model is developed for predicting the maximum flow rate of a single component, two-phase mixture. It is based upon annular flow, uniform linear velocities of each phase, and equilibrium between liquid and vapor. Flow rate is maximized with respect to local slip ratio and static pressure for known stagnation conditions. Graphs are presented giving maximum steam/water flow rates for: local static pressures between 25 and 3,000 psia, with local qualities from 0.01 to 1.00; local stagnation pressures and enthalpies which cover the range of saturation states.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):143-150. doi:10.1115/1.3689035.

Heat transfer by simultaneous conduction and radiation in thermal radiation absorbing, emitting, and scattering materials is investigated theoretically. Consideration is given to a one-dimensional system consisting of two diffuse, nonblack, isothermal parallel plates separated by a finite distance. The space between the two plates is filled with an isotropically scattering material. The problem is formulated exactly in terms of integrodifferential and integral equations. The results define as well as illustrate several mechanisms of radiant energy transfer and show how one mode of heat transfer influences the other. The numerical results reveal the effect of the system parameters on the heat transfer characteristics. In particular, it is shown that the effect of albedo on the heat transfer is small. Albedo being the parameter which represents the fraction of the incident pencil of radiation which has been scattered.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):151-156. doi:10.1115/1.3689036.

Recent numerical solutions of Spalding’s form of the thermal energy equation are compared to other, more limited, analytic solutions of the energy equation that have been used for situations in which the temperature at the wall or the heat flux at the wall varies with distance along the wall. For Prandtl numbers near unity the two kinds of solutions are comparable and they predict well the heat transfer for flow along a flat plate. For variable free stream velocity the discrepancies found between experiment and the older solutions remain the same with the new ones. Another model of the thermal boundary layer is presented by which better agreement with experiment is obtained for accelerated flows.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):157-160. doi:10.1115/1.3689037.

An analytical investigation of the effects of an initial splitter plate boundary layer on the flow field associated with the slot injection of a gas in laminar flow is presented. The analysis is based on the method of collocation, using profiles generated by a modified Oseen approximation to the momentum equation, and the results are presented in terms of the effects on skin friction and heat transfer coefficients. It is shown that the initial boundary layer thickness can be an important parameter in describing the flow field.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

J. Heat Transfer. 1965;87(1):12-13. doi:10.1115/1.3689026.
FREE TO VIEW
Abstract
Topics: Heat transfer
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1965;87(1):13-16. doi:10.1115/1.3689030.
FREE TO VIEW
Abstract
Topics: Heat transfer
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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