J. Heat Transfer. 1966;88(2):147-152. doi:10.1115/1.3691494.

The effect of free convection on laminar forced flow heat transfer in a horizontal uniformly heated tube was investigated. The Grashof number was varied from 1000 down to the order of one, the low Grashof number runs agreeing with the prediction for pure forced convection within ±8 percent. The effect of the secondary flow created by free convection was observed as a decrease in the wall to bulk fluid temperature difference required to transfer heat as compared to the pure forced flow case in the region far from the tube inlet. This effect was found to increase as the ratio of Grashof number to Reynolds numbers increased. No appreciable effect of free convection was found in the thermal development region.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(2):154-159. doi:10.1115/1.3691498.

With thermal protective systems, the power transferred from an opaque layer to the skin or a skin simulant determines the temperature of the skin and in turn the degree of burn. The power input was calculated from the measured temperature of the simulant by expressing the power as a series of functions, with unknown constants, whose Laplace transforms were of the proper form for comparison with the measured temperatures and thus determine the constants. The lag of temperature behind the power causes some uncertainty in the latter, but practically adequate precision is attainable.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(2):161-167. doi:10.1115/1.3691501.

In the present study, the steady laminar forced convection problem of heat transfer in the fully developed constant property flow of liquids through a certain class of channels is analyzed by considering the contribution of heat due to viscosity. The effects of viscous dissipation on the heat transfer are emphasized. A class of sufficiently long straight channels with uniform cross-sectional area is chosen such that the solutions for velocity and temperature fields are deducible directly from the equations of the boundary curves. The wall temperature is allowed to vary linearly in the axial direction, and some heat-source distribution, other than that due to viscosity, is imagined to be present in the flow field. The general solution of the problem for the given class of channels is given directly by avoiding the details of the mathematical treatment of the governing equations. To illustrate the general mathematical derivations and to visualize the effects of viscous dissipation, some basic examples have been investigated and the graphical representation of several relevant results is given in a number of figures. In the last section of this study, various relevant results and figures have been discussed from the point of view of viscous dissipation phenomena.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(2):170-174. doi:10.1115/1.3691505.

An experimental investigation of the effect of asymmetrical heating on fully developed turbulent heat transfer has been carried out. The test apparatus was a rectangular duct of aspect ratio 5:1. The duct was constructed so that the two long sides of the rectangular cross section could be heated at different preselected rates, while the two short sides were unheated. Two cases of asymmetrical heating were studied: (a) One of the two long sides was heated, while the second was unheated; (b) both of the long sides were heated, with the heating rate at one side being twice that of the other. For the first case, the heat transfer coefficients are lower than those for the symmetrically heated duct. For the second case, the coefficients for the more strongly heated wall are also below the values for symmetrical heating, while the coefficients for the lesser-heated wall are greater than the symmetric heating results. These findings are in qualitative agreement with analytical predictions for the parallel-plate channel. Furthermore, by applying an analytically motivated correlation procedure (reference [10]), it was shown that overall Nusselt number results for asymmetric heating could be brought into virtual coincidence with those for symmetric heating.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(2):175-181. doi:10.1115/1.3691508.

The problem of fully developed laminar flow heat transfer in polygonal ducts with axially uniform wall heat flux is considered. The well-known analogy between laminar heat transfer in ducts and simply supported thin flat plates of the same shape under uniform lateral loading is used to obtain heat transfer characteristics. It is shown that both the fully developed laminar flow characteristics in noncircular ducts and the steady temperature distribution in infinitely long prismatical bars with uniform internal heat generation can also be obtained by the plate analogy based on the Dirichlet problem. The plate problem may be solved by the Moiré method and point-matching technique, and it is pointed out that the former can be applied to ducts of any shape. For a square duct, the results from these two approximate methods are given, and comparisons are made which show good agreement with the exact solution.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(2):183-193. doi:10.1115/1.3691510.

A simplified theoretical model for bubble nucleation stability has been proposed, and an approximate stability criterion has been developed. This criterion contains both fluid and surface properties, and it predicts that nucleation for sodium should be unstable. Commercial-grade sodium was boiled from a horizontal disk at pressures near 60 mm Hg absolute, with sodium temperatures near 1200 F. Heat fluxes as high as 236,000 Btu/hr ft2 were attained. Boiler surface finishes ranged from highly polished mirror finishes to coarse, porous coatings. The effects of surface material, chemical treatment, heat flux, and cavity geometry on nucleation stability were measured, and the experimental results agreed with the predictions of the proposed stability model.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(2):196-203. doi:10.1115/1.3691514.

Commercial grade sodium was boiled from a horizontal disk at pressures of 65 mm, 200 mm, and 400 mm Hg absolute, with sodium temperatures ranging from 1200 F to 1500 deg F. Heat fluxes as high as 236,000 Btu/hr sq ft were attained. Boiler surface finishes ranged from highly polished mirror finishes to coarse, porous coatings. By following a prescribed cleaning and filling procedure, nucleate-boiling results were generally reproducible for a given-type surface. The effect of roughness as well as any aging and hysteresis effects were experimentally determined. Incipient nucleate boiling results are discussed as well as the effect of pressure and pool depth on the nucleate-boiling curve.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(2):205-213. doi:10.1115/1.3691517.

The problem of simultaneous convection and radiation in the laminar boundary layer on a flat plate is formulated and solved. The plate surface is assumed black and the fluid medium is a perfect gas for which the mass absorption coefficient for radiation is considered to be independent of frequency and temperature. The solution is of the iterative type and includes effects of viscous dissipation, secondary emission and absorption, and incident external radiative fluxes. Illustrative examples of temperature profiles and local and average heat transfer rates are presented.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(2):214-222. doi:10.1115/1.3691518.

A numerical method was developed for the calculation of entrance flows in vertical tubes for the cases of upflow or downflow and constant wall heat flux or constant wall temperature. The solutions were in excellent agreement with experimental data obtained with water flowing upward in a vertical heated tube. The results show that both the density and the viscosity have to be treated as nonlinear functions of temperature. Consequently, for the constant heat flux condition, the velocity and temperature profiles constantly change and never reach “fully developed” states. The transition to turbulent flow was also studied. The experimental measurements demonstrated that the transition process depends on the developing velocity profiles. For the constant heat flux case, transition will always occur at some axial position. For a given entrance condition, the distance to transition is fixed by the fluid flow rate and the wall heat flux. For the experimental results, a tentative transition criterion was obtained, which depends only on the velocity profile shape, fluid viscosity, and the entrance Reynolds number.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(2):223-230. doi:10.1115/1.3691519.

Experiments have been performed which demonstrate that the directional distribution of reflected thermal radiation for moderate to large angles of incidence is not intermediate to the specular and diffuse limits as commonly assumed. Indeed, for such angles of incidence on roughened surfaces, maxima in the reflected intensity distribution occur at polar angles larger than the specular angle. In some cases, the intensity of this off-specular maximum is three or four times the intensity in the specular-ray direction. The materials studied were aluminum, nickel, copper, a nickel-copper alloy, and magnesium-oxide ceramic, thereby encompassing both metals and nonmetals. Controlled surface roughnesses of 0.23 to 5.8 microns were employed over a wavelength range extending from 0.5 to 6 microns. The angle of incidence was varied from 10 to 75 deg, while reflected radiation was collected in the plane of incidence at polar angles ranging from 0 to 89 deg. The experimental results are arranged on the basis of a surface-roughness-to-wavelength ratio, σm /λ. Certain trends of the off-specular peak with incident angle and σm /λ are noted.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(2):231-238. doi:10.1115/1.3691520.

An exact formulation of simultaneous radiation, conduction, and convection heat transfer for steady-state conditions in a one-dimensional, semi-infinite, isotropic, homogeneous, absorbing, and scattering porous bed is presented. Both diffuse and collimated radiant fluxes are incident on the bed causing absorption, scattering, emission, and heating of the bed which in turn heats a transparent, constant-property fluid flowing normal to the surface. Spectral selectivity is allowed for when the source energy is of shorter wavelength than the emitted energy. Exact and approximate numerical solutions and a linearized closed-form solution are given for inflow, as in a solar heat collector, and outflow, as with a heat shield.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1966;88(2):239-245. doi:10.1115/1.3691521.

The results of a semitheoretical and experimental investigation of the heat-transfer and frictional effects in air, nitrogen, and helium in steady flow in the downstream region of round tubes are presented. The constant-properties analysis for low Reynolds-number turbulent flow is evolved from an improved description of the adiabatic velocity profile, without modifying the Reynolds analogy assumption of equal eddy diffusivities. Data cover peak wall-to-bulk temperature ratios from near unity to 4.8 and entering Reynolds numbers from 1450 to 45,000. Low and moderate temperature-ratio data are used to confirm and to extend the analysis, while high temperature-ratio results are utilized for classification of flow regimes at high heating rates in the low Reynolds-number range.

Commentary by Dr. Valentin Fuster



J. Heat Transfer. 1966;88(2):246-247. doi:10.1115/1.3691522.
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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