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RESEARCH PAPERS

J. Heat Transfer. 1974;96(4):435-442. doi:10.1115/1.3450223.

A rapid computation procedure is described for the prediction of heat transfer in laminar free convection boundary layers, either two-dimensional or axisymmetrical, over isothermal smooth objects with fairly arbitrary shape. The analysis employs suitable coordinate transformation which makes it possible to express the solutions of the governing conservation equations in terms of a sequence of universal functions that depend on the fluid Prandtl number and a configuration function. The latter is completely determined by the body contour and its orientation relative to the body force that generates the motion. Several of the leading universal functions have been evaluated and tabulated. The theory was applied to a number of body configurations and the results compared well with published analytical and/or experimental information. Some new results are also obtained for the local Nusselt number over horizontal elliptical cylinders and ellipsoids or revolution.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):443-447. doi:10.1115/1.3450224.

Natural convection adjacent to horizontal surfaces of circular, square, rectangular, and right triangular planforms has been studied experimentally. Electrochemical techniques were employed involving a fluid with a Schmidt number of about 2200. The results encompass a wide range of Rayleigh numbers thus providing information on both the laminar and the turbulent regimes. The data for all planforms are reduced to a single correlation in the laminar and turbulent regimes using the characteristic length, as recommended by Goldstein, Sparrow, and Jones. L* = A/p, where A is the surface area and p is the surface perimeter. The laminar data for all planforms are correlated by the expression

Sh = 0.54 Ra1/4
  (2.2 × 104 ≤ Ra ≤ 8 × 106)
and the data for the turbulent regime are correlated by the expression
Sh = 0.15 Ra1/3
  (8 × 106 ≤ 1.6 × 109)
Transition is found to occur at about Ra = 8 × 106 . The present work thus significantly extends the Rayleigh number range of validity for the use of L* through the 1/4 power laminar regime into the turbulent 1/3 power regime. It also demonstrates the validity of the use of L* to correlate natural convection transfer coefficients for highly unsymmetrical planforms, which heretofore had not been demonstrated. Comparisons to analytical solutions and other experimental heat and mass transfer data are presented.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):448-454. doi:10.1115/1.3450225.

An experimental program was conducted to study the heat transfer characteristics of mercury in laminar natural convection flow within a vertical open-ended channel over a range of channel widths. Two sets of boundary conditions were investigated separately: (1) uniform heat flux at one wall with the other insulated, and (2) both walls symmetrically and uniformly heated. A decrease in channel width caused a decrease in channel wall temperature in the developing portion of the flow. This unexpected phenomenon persisted until the channel height-to-width ratio, Ar, reached a value greater than 18. Hence, the buoyancy induced flow of a low Prandtl number fluid in a channel is more thermally efficient than a single heated plate. Temperature data have been correlated into local Nusselt versus modified Grashof number plots, based on streamwise position, for several aspect ratios. The effect of aspect ratio on channel temperature is displayed on NuL versus Ar curves for several GrL*. The infinite spacing limit is compared to previous work with temperature profiles and local heat transfer results. Expressions for local and average heat transfer correlations are presented, with suggested limits on their application. The effect of flow in from the sides of the channel was investigated by affixing plastic side plates to the channel.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):455-458. doi:10.1115/1.3450226.

An experimental investigation of laminar natural convection heat transfer from a uniformly heated vertical cylinder immersed in an effectively infinite pool of mercury is described. A correlation was developed for the local Nusselt number as a function of local modified Grashof number for each cylinder. A single equation incorporating the diameter-to-length ratio was formulated that satisfied the data for all three cylinders. An expression derived by extrapolation of the results to zero curvature (the flat plate condition) was found to agree favorably with others’ work, both analytical and experimental. The influence of curvature upon the heat transfer was found to be small but significant. It was established that the effective thermal resistance through the boundary layer is less for a cylinder of finite curvature than for a flat plate. Consequently, local heat transfer coefficients for cylinders are larger than those for flat plates operating under identical conditions.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):459-462. doi:10.1115/1.3450227.

Heat transfer measurements are made in the separated, reattached, and redeveloped regions of the two-dimensional air flow on a flat plate with blunt leading edge. The flow reattachment occurs at about four plate thicknesses downstream from the leading edge and the heat transfer coefficient becomes maximum at that point and this is independent of the Reynolds number which ranged from 2720 to 17900 in this investigation. The heat transfer coefficient is found to increase sharply near the leading edge. The development of flow is shown through the measurements of the velocity and temperature in the separated, reattached, and redeveloped regions.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):463-466. doi:10.1115/1.3450228.

A simple computational procedure is described for ascertaining the heat or mass transfer in laminar forced convection over a rotating body of revolution. The analysis is applicable to nonuniform surface condition and for fluids having a large or a moderate value of the Prandtl (Schmidt) number. Examples are given to illustrate the usefulness of the analysis as well as to expose its limitation.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):467-473. doi:10.1115/1.3450229.

The exact solution is obtained for the transient thermal response of toroidal coils of rectangular cross section with orthotropic constant thermal conductivity, constant density, and specific heat, and linear boundary conditions. The solution is a rapidly converging doubly infinite eigenfunction expansion whose leading term is generally accurate to within 5 percent. No conclusive results were obtained from our evaluation of the applicability of previously obtained solutions for the infinite rod approximation for the toroidal coils. In some cases, the infinite rod approximation is accurate even for large curvatures, but in other cases it is in substantial error for relatively small curvatures. Hence, the solution presented here is generally recommended to predict the temperature distribution in toroidal coils and a number of design curves are provided for prediction purposes.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):474-477. doi:10.1115/1.3450230.

The problem of heat conduction in solids with random initial condition is studied. A general theory is first discussed and several examples are considered. It is observed that the homogeneity of the random initial condition is sufficient for the homogeneity of the temperature field in an unbounded domain. But in bounded domains the random temperature field becomes nonhomogeneous even though the initial condition is homogeneous.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):478-482. doi:10.1115/1.3450232.

Heat transfer from an acrosol aggregate composed of two touching spheres is investigated analytically. In the range of interest, the Knudsen number is small and the Peclet number negligible. The Nusselt number of a sphere is found to be reduced by the presence of a neighbor and by temperature jump. Expressions for the Nusselt number are obtained.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):483-488. doi:10.1115/1.3450233.

Radiative equilibrium temperature and surface heat flux distributions are calculated for an absorbing-emitting gray medium in an infinite plane layer bounded by gray diffuse walls with arbitrary temperature distributions. Superposition is used to obtain the solution for the differential approximation, which yields good accuracy for the optically thick medium. To also obtain accurate results for optically thin and intermediate regimes, the differential approximation is subsequently improved by a number of geometrical parameters, which are derived from the exact expression for the intensity. As an example, the case of constant temperature at the upper wall and a temperature step at the lower wall without heat generation in the medium is presented. Comparison with other available results shows excellent agreement.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):489-495. doi:10.1115/1.3450234.

This paper finds by an exact method the temperature distribution in a viscous fluid undergoing Poiseuille flow between two infinite parallel plates. The upstream portion of the plates is assumed to be at temperature T = T− and downstream portion of the plates to be at temperature T = T+ . Results are obtained numerically for the “entrance region” temperature profiles. These tend rapidly to zero away from the point where the wall temperature changes abruptly. Using asymptotic expansions for the functions involved estimates are made for the number of terms required to achieve a given level of accuracy for a given Peclet number (Pe). Typical results for Pe = 1 and 10 are shown graphically.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):496-503. doi:10.1115/1.3450235.

Experimental research on highly dispersed, two-phase, turbulent flows was performed employing Freon 12 at different pressures up to the critical value. By means of visualization techniques it was possible to study the droplet size distribution, their spatial concentration, and the relationships among the deduced law of distribution and the main thermo-hydraulic parameters for different thermo-hydraulic conditions (pressure, mass velocity, and quality). Simple relations were developed which make it possible to determine, at least for some reference thermo-hydraulic situations, all of the characteristics of the liquid dispersed phase.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):504-510. doi:10.1115/1.3450236.

This paper presents experimental data on the dynamic behavior of diabatic two-phase flow in a vertical tube with Refrigerant-11 as the working fluid. A detailed description is included of the experimental test facility as well as the instrumentation used for monitoring the variables of pressure, flow, heat flux, and void fraction. Experimental data are presented in frequency response form for inlet impedance (ΔP1 /ΔW1 ) and exit void fraction (Δα3 /ΔW1 ) at constant heat flux over a frequency range of 0.01 to 10.0 Hz. The data cover inlet subcooling conditions of 14°F and 79°F and two heat flux levels. The experimental results show that the inlet impedance characteristics have fluctuations in amplitude and phase lag with frequency which lead to resonant peaks in the overall frequency response behavior. Exit void fraction characteristics show similar resonant behavior with large phase lag at frequencies above 1 Hz.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):511-517. doi:10.1115/1.3450237.

A new way of presenting the heat transfer data is shown. This leads to a dimensionless performance plot between a “heat transfer performance factor” and a “pumping power factor” with a nondimensional “flow length between major boundary layer disturbances” as a varying parameter. This approach leads to the possibility of approximately presenting all surface geometries on a single “idealized” performance plot, the nondimensional “flow length” being a geometrical characteristic of each surface. The method can be used to predict approximately the heat transfer performance characteristics of a new, untested surface. The plot permits the rapid assessment and comparison of various heat transfer geometries for a given application. The performance plot is valid only in the turbulent flow regime. The method will prove invaluable in optimizing a design accounting for space limitations, economic restraints, and system considerations such as pumping power and effectiveness tradeoffs.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):518-523. doi:10.1115/1.3450238.

The concept of regeneration is successfully demonstrated for the heat processing of sorptive materials in a continuous-flow heat exchanger. Data are presented for oats, cracked corn, and black peppercorns. Regeneration efficiency depends on the relative flow rates of the air and the product. Maximum efficiency was attained with the ratio of the air-to-product heat capacity fluxes near unity. Regeneration efficiency is also dependent on the moisture content of the product entering the heat exchanger. A maximum efficiency of 57 percent was obtained for black peppercorns that entered the heat exchanger with moisture contents of 5 to 8 percent (dry basis) and were processed to a holding temperature of 175° F (79.5° C). Significant drying of the product was realized in the heat exchanger/regenerator. For oats, processed at 200° F, approximately half the moisture was removed in a single pass when the inlet moisture content was 13.7 percent. The amount of drying decreased as the moisture content of the product entering the heat exchanger was lowered. Drying also decreased when the processing temperature was lowered. Considerable energy is consumed by drying, and thus the regeneration effect for high moisture products is not as apparent.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):524-529. doi:10.1115/1.3450239.

Experiments were conducted to determine the film cooling effectiveness and convective heat transfer coefficient distributions on the endwall of a large-scale turbine vane passage. The vane test models employed simulated the passage geometry and upstream cooling slot geometry of a typical first stage turbine. The test models were constructed of low thermal conductivity foam and foil heaters. The tests were conducted at a typical engine Reynolds number but at lower than typical Mach numbers. The film cooling effectiveness distribution for the entire endwall and the heat transfer distribution for the downstream one-half of the endwall were characterized by large gapwise variations which were attributed to a secondary flow vortex.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):530-535. doi:10.1115/1.3450240.

The thermal diffusion flame model for a bimolecular reaction under stoichiometry conditions of the fresh mixture was examined. The structure of the flame tip of the Bunsen cone was studied. A local breakdown in the stoichiometry in the vicinity of the reaction zone was found such that the light component is always insufficient. For Lewis numbers greater than unity, the flame front is continuous. The temperature at the exit from the reaction zone exceeds the adiabatic temperature of the combustion products. For a Lewis number of the light component less than unity, either a flame with a continuous front, the temperature of which is less than the adiabatic temperature, or a flame with an exposed tip is possible. The problem is solved on the assumption of a strong temperature dependence of the reaction rate.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):536-540. doi:10.1115/1.3450241.

The heat transfer relationships for shapes that approximate animal appendages have been experimentally determined. Finite length hollow cylinders, arcs, and cones with different amounts of closure were tested over a wide range of pitch and yaw angles at different wind speeds. The data for all of these shapes are within ±70 percent of the standard correlation for circular cylinders. Pitch and yaw variations have little effect on the heat transfer coefficient. Shorter length geometries and those with less enclosure have higher heat transfer than the longer and more enclosed geometries. The application of these results to modeling the heat transfer from animal appendages is illustrated.

Commentary by Dr. Valentin Fuster

ERRATA

TECHNICAL BRIEFS

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):544-545. doi:10.1115/1.3450243.
Abstract
Topics: Flow (Dynamics) , Heat
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):545-547. doi:10.1115/1.3450244.
Abstract
Topics: Optimization , Fins
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):547-549. doi:10.1115/1.3450245.
Abstract
Topics: Slabs
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):549-551. doi:10.1115/1.3450246.
Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):551-553. doi:10.1115/1.3450247.
Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):553-555. doi:10.1115/1.3450248.
Abstract
Topics: Pressure , Boiling
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):555-557. doi:10.1115/1.3450249.
Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):557-558. doi:10.1115/1.3450250.
Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):558-560. doi:10.1115/1.3450251.
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1974;96(4):562-564. doi:10.1115/1.3450253.
Abstract
Commentary by Dr. Valentin Fuster

DISCUSSIONS

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