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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Drag measurements of an axisymmetric nacelle mounted on a flat plate at supersonic speeds

An experimental investigation was conducted to determine the effect of diverter wedge half-angle and nacelle lip height on the drag characteristics of an assembly consisting of a nacelle fore cowl from a typical high-speed civil transport (HSCT) and a diverter mounted on a flat plate. Data were obtained for diverter wedge half-angles of 4.0 deg, 6.0 deg, and 8.0 deg and ratios of the nacelle lip height above a flat plate to the boundary-layer thickness (h(sub n)/delta) of approximately 0.87 to 2.45. Limited drag data were also obtained on a complete nacelle/diverter configuration that included fore and aft cowls. Although the nacelle/diverter drag data were not corrected for base pressures or internal flow drag, the data are useful for comparing the relative drag of the configuration tested. The tests were conducted in the Langley Unitary Plan Wind Tunnel at Mach numbers of 1.50, 1.80, 2.10, and 2.40 and Reynolds numbers ranging from 2.00 x 10(exp 6) to 5.00 x 10(exp 6) per foot. The results of this investigation showed that the nacelle/diverter drag essentially increased linearly with increasing h(sub n)/delta except near 1.0 where the data showed a nonlinear behavior. This nonlinear behavior was probably caused by the interaction of the shock waves from the nacelle/diverter configuration with the flat-plate boundary layer. At the lowest h(sub n)/delta tested, the diverter wedge half-angle had virtually no effect on the nacelle/diverter drag. However, as h(sub n)/delta increased, the nacelle/diverter drag increased as diverter wedge half-angle increased.

Flamm, Jeffrey D.↗
NASA NTRS2018

Impedance Eduction in a Duct Using the Linearized Euler Equations

An impedance eduction technique that is based upon a numerical solution to the linearized Euler equations coupled with the minimization of an objective function is presented. The linearized Euler equations are solved numerically using a cubic finite element method and the minimum of the objective function is obtained via a gradient based optimizer. The mean flow is allowed to have a gradient in two coordinate directions and the impedance of the liner may vary arbitrarily over the liner surface. A new regularized wall impedance boundary condition presented by Rienstra which contains the effects of the mean boundary layer thickness is implemented. Impedances are educed for a perforate over honeycomb liner using test data acquired in the Langley Grazing Flow Impedance Tube. The impedance of the liner is educed both with an upstream source and a downstream source. The method is validated by comparing the educed impedance to a benchmark method. The primary conclusion of the study is that the impedances educed for upstream and downstream sources are not well matched and that the primary effect of the boundary thickness is to reduce the resistance of the liner.

Watson, Willie R.↗
NASA NTRS2013

Wake Instabilities Behind Discrete Roughness Elements in High Speed Boundary Layers

Computations are performed to study the flow past an isolated, spanwise symmetric roughness element in zero pressure gradient boundary layers at Mach 3.5 and 5.9, with an emphasis on roughness heights of less than 55 percent of the local boundary layer thickness. The Mach 5.9 cases include flow conditions that are relevant to both ground facility experiments and high altitude flight ("cold wall" case). Regardless of the Mach number, the mean flow distortion due to the roughness element is characterized by long-lived streamwise streaks in the roughness wake, which can support instability modes that did not exist in the absence of the roughness element. The higher Mach number cases reveal a variety of instability mode shapes with velocity fluctuations concentrated in different localized regions of high base flow shear. The high shear regions vary from the top of a mushroom shaped structure characterizing the centerline streak to regions that are concentrated on the sides of the mushroom. Unlike the Mach 3.5 case with nearly same values of scaled roughness height k/delta and roughness height Reynolds number Re(sub kk), the odd wake modes in both Mach 5.9 cases are significantly more unstable than the even modes of instability. Additional computations for a Mach 3.5 boundary layer indicate that the presence of a roughness element can also enhance the amplification of first mode instabilities incident from upstream. Interactions between multiple roughness elements aligned along the flow direction are also explored.

Choudhari, Meelan↗
NASA NTRS1984

Aerothermal loads analysis for high speed flow over a quilted surface configuration

Attention is given to hypersonic laminar flow over a quilted surface configuration that simulates an array of Space Shuttle Thermal Protection System panels bowed in a spherical shape as a result of thermal gradient through the panel thickness. Pressure and heating loads to the surface are determined. The flow field over the configuration was mathematically modeled by means of time-dependent, three-dimensional conservation of mass, momentum, and energy equations. A boundary mapping technique was then used to obtain a rectangular, parallel piped computational domain, and an explicit MacCormack (1972) explicit time-split predictor corrector finite difference algorithm was used to obtain steady state solutions. Total integrated heating loads vary linearly with bowed height when this value does not exceed the local boundary layer thickness.

Olsen, G. C.↗
NASA NTRS1984

Aerothermal loads analysis for high speed flow over a quilted surface configuration

Attention is given to hypersonic laminar flow over a quilted surface configuration that simulates an array of Space Shuttle Thermal Protection System panels bowed in a spherical shape as a result of thermal gradients through the panel thickness. Pressure and heating loads to the surface are determined. The flow field over the configuration was mathematically modeled by means of time-dependent, three-dimensional conservation of mass, momentum, and energy equations. A boundary mapping technique was then used to obtain a rectangular, parallelepiped computational domain, and an explicit MacCormack (1972) explicit time-split predictor-corrector finite difference algorithm was used to obtain steady state solutions. Total integrated heating loads vary linearly with bowed height when this value does not exceed the local boundary layer thickness.

Olsen, G. C.↗
NASA NTRS1995

Bleed Roughness Mechanism

Suction applied through wall bleed is expected to reduce boundary-layer thickness and lead to a profile that can resist separation. However, experiments with rows of suction holes or slots have shown that the benefits of suction are not realized under certain circumstances. Lee, Sloan and Paynter attributed this to a 'bleed roughness', and modeled the phenomena using a modified inner-length scale with convective lag for the eddy viscosity. Test information was required to determine the roughness values at each Mach number and bleed rate. The present work used numerical calculation, subsonic and supersonic experimentation, and physical modeling were used to explore bleed roughness. It was found that the phenomena can exist in the absence of bleed, that it is a function of geometry and Mach number, and that it does not appear in low subsonic flow. The inner-length scale/convective lag approach was found to be inconsistent with recent physical observation. Alternate steady models for the roughness effect disagreed with mass flux trends and the choked flow limit, and suggested that non-steady mechanisms are present. While new supersonic experiments did exhibit low-frequency plenum oscillations, high-frequency unsteadiness associated with the orifice flow scale appears to be the cause of bleed roughness. In fact, boundary-layer calculations with an oscillatory orifice flow produced the same effect in the time-averaged downstream profile for incompressibile flow. A new empirical turbulence-model was proposed which increased the eddy viscosity throughout the entire boundary-layer by a constant which was calibrated using the zero-bleed profile. Preliminary calculations agreed with the experimental data. The model significantly reduced the test information required to determine roughness values for turbulence modeling, and provided prediction capability for supersonic bleed flows. An abstract of a thesis entitled 'Boundary-Layer Bleed Roughness' is included.

Russell, David A.↗
NASA NTRS2002

Review of Research on Low-Profile Vortex Generators to Control Boundary-Layer Separation

An in-depth review of boundary-layer flow-separation control by a passive method using low-profile vortex generators is presented. The generators are defined as those with a device height between 10% and 50% of the boundary layer thickness. Key results are presented for several research efforts, all of which were performed within the past decade and a half where the majority of these works emphasize experimentation with some recent efforts on numerical simulations. Topics of discussion consist of both basic fluid dynamics and applied aerodynamics research. The fluid dynamics research includes comparative studies on separation control effectiveness as well as device-induced vortex characterization and correlation. The comparative studies cover the controlling of low-speed separated flows in adverse pressure gradient and supersonic shock-induced separation. The aerodynamics research includes several applications for aircraft performance enhancement and covers a wide range of speeds. Significant performance improvements are achieved through increased lift and/or reduced drag for various airfoils-low-Reynolds number, high-lift, and transonic-as well as highly swept wings. Performance enhancements for non-airfoil applications include aircraft interior noise reduction, inlet flow distortion alleviation inside compact ducts, and a more efficient overwing fairing. The low-profile vortex generators are best for being applied to applications where flow-separation locations are relatively fixed and the generators can be placed reasonably close upstream of the separation. Using the approach of minimal near-wall proturbances through substantially reduced device height, these devices can produce streamwise vortices just strong enough to overcome the separation without unnecessarily persisting within the boundary layer once the flow-control objective is achieved. Practical advantages of low-profile vortex generators, such as their inherent simplicity and low device drag, are demonstrated to be critically important for many applications as well.

Lin, John C.↗
NASA NTRS2016

Nonlinear Wakes Behind a Row of Elongated Roughness Elements

This paper is concerned with the high Reynolds number flow over a spanwise periodic array of roughness elements with inter-element spacing of the order of the local boundary-layer thickness. While earlier work by Goldstein, Sescu, Duck and Choudhari (2010) and Goldstein, Sescu, Duck and Choudhari (2011) was mainly concerned with smaller roughness heights that produced relatively weak distortions of the downstream flow, the focus here is on extending the analysis to larger roughness heights and streamwise elongated planform shapes that together produce a qualitatively different, nonlinear behavior of the downstream wakes. The roughness scale flow now has a novel triple-deck structure that is somewhat different from related studies that have previously appeared in the literature. The resulting flow is formally nonlinear in the intermediate wake region, where the streamwise distance is large compared to the roughness dimensions but small compared to the downstream distance from the leading edge, as well as in the far wake region where the streamwise length scale is of the order of the downstream distance from the leading edge. In contrast, the flow perturbations in both of these wake regions were strictly linear in the earlier work by Goldstein et al (2010, 2011). This is an important difference because the nonlinear wake flow in the present case provides an appropriate basic state for studying the secondary instability and eventual breakdown into turbulence.

Boundary layer control↗
NASA NTRS1999

A Study of Nucleate Boiling with Forced Convection in Microgravity

The ultimate objective of basic studies of flow boiling in microgravity is to improve the understanding of the processes involved, as manifested by the ability to predict its behavior. This is not yet the case for boiling heat transfer even in earth gravity, despite the considerable research activity over the past 30 years. The elements that constitute the nucleate boiling process - nucleation, growth, motion, and collapse of the vapor bubbles (if the bulk liquid is subcooled) - are common to both pool and flow boiling. It is well known that the imposition of bulk liquid motion affects the vapor bubble behavior relative to pool boiling, but does not appear to significantly influence the heat transfer. Indeed, it has been recommended in the past that empirical correlations or experimental data of pool boiling be used for design purposes with forced convection nucleate boiling. It is anticipated that such will most certainly not be possible for boiling in microgravity, based on observations made with pool boiling in microgravity. In earth gravity buoyancy will act to remove the vapor bubbles from the vicinity of the heater surface regardless of how much the imposed bulk velocity is reduced, depending, of course, on the geometry of the system. Vapor bubbles have been observed to dramatically increase in size in pool boiling in microgravity, and the heat flux at which dryout took place was reduced considerably below what is generally termed the critical heat flux (CHF) in earth gravity, depending on the bulk liquid subcooling. However, at heat flux levels below dryout, the nucleate pool boiling process was enhanced considerably over that in earth gravity, in spite of the large vapor bubbles formed in microgravity and perhaps as a consequence. These large vapor bubbles tended to remain in the vicinity of the heater surface, and the enhanced heat transfer appeared to be associated with the presence of what variously has been referred to as a liquid microlayer between the bubble and the heater surface. The enhancement of the boiling process with low velocities in earth gravity for those orientations producing the formation of a liquid macrolayer described above, accompanied by "sliding" vapor bubbles, has been demonstrated. The enhancement was presented as a function of orientation, subcooling, and heated length, while a criterion for the heat transfer for mixed natural/forced convection nucleate boiling was given previously. A major unknown in the prediction and application of flow boiling heat transfer in microgravity is the upper limit of the heat flux for the onset of dryout (or critical heat flux - CHF), for given conditions of fluid-heater surfaces, including geometry, system pressure and bulk liquid subcooling. It is clearly understood that the behavior in microgravity will be no different than on earth with sufficiently high flow velocities, and would require no space experimentation. However, the boundary at which this takes place is still an unknown. Previous results of CHF measurements were presented for low velocity flow boiling at various orientations in earth gravity as a function of flow velocity and bulk liquid subcooling, along with preliminary measurements of bubble residence times on a flat heater surface. This showed promise as a parameter to be used in modeling the CHF, both in earth gravity and in microgravity. The objective of the work here is to draw attention to and show results of current modeling efforts for the CHF, with low velocities in earth gravity at different orientations and subcoolings. Many geometrical possibilities for a heater surface exist in flowing boiling, with boiling on the inner and outer surfaces of tubes perhaps being the most common. If the vapor bubble residence time on and departure size from the heater surface bear a relationship to the CHF, as results to be given indicate, it is important that visualization of and access to vapor bubble growth be conveniently available for research purposes. In addition, it is desirable to reduce the number of variables as much as possible in a fundamental study. These considerations dictated the use of a flat heater surface, which is rectangular in shape, 1.91 cm by 3.81 cm (0.75 x 1.5 inches), consisting either of a 400 Angstrom thick semi-transparent gold film sputtered on a quartz substrate which serves simultaneously as a heater and a resistance thermometer, or a copper substrate of the same size. The heater substrate is a disc which can be rotated so that the heated length in the flow direction can be changed from 1.91 to 3.81 cm (0.75 to 1.5 inches). The fluid is R-113, and the velocities can be varied between 0.5 cm/s and 60 cm/s. For a sufficiently low velocity the CHF can be modeled reasonably well at various orientations by the correlation for pool boiling corrected for the influence of bulk liquid subcooling, multiplied by the square root of q, the angle relative to horizontal. This arises from equating buoyancy and drag forces in the inverted positions where the vapor bubbles are held against the heater surface as they slide. A distortion of the measurements relative to pool boiling occurs as the flow velocity increases. In modeling this effect at different levels of subcooling it appeared appropriate to estimate the volumetric rate of vapor generation, using measurements of bubble frequency (or residence time), void fraction and average bubble boundary layer thickness. These were determined with the use of a platinum hot wire probe 0.025 mm in diameter by 1.3 mm long, applying a constant current to distinguish between contact with liquid or vapor. Two-dimensional spatial variations are obtained with a special mechanism to resolve displacements in increments of 0.025 mm. From such measurements it was determined that the fraction of the surface heat transfer resulting in evaporation varies inversely with the subcooling correction factor for the CHF. The measured inverse bubble residence time is normalized relative to that predicted for an infinite horizontal flat plate at the CHF, and is correlated well with the CHF normalized relative to that for pool boiling, for various orientation angles and subcooling levels. This correspondence is then combined with a normalizing factor for the energy flux leaving the heater surface at the CHF and the computed bubble radius at departure, determined from the balance between the outward velocity of the interface due to evaporation and the buoyance induced velocity of the center of mass of the bubble. The product of the CHF and the corresponding residence time was determined to be a constant for all orientations at a given bulk flow velocity and liquid subcooling, and must be determined empirically for each velocity and subcooling at present. It then becomes possible to predict the CHF for the different orientations, velocities, and subcoolings. These are compared with normalized measurements of the CHF for velocities ranging from 4 cm/s to 55 cm/s, subcoolings from 2.8 to 22.2 K, over orientations angles of 360 degrees.

Merte, Herman, Jr.↗
DOE OSTI2026

Mechanistic mass transfer in hollow fiber membrane solvent extraction for bio-based isobutanol

Membrane solvent extraction (MSE) has emerged as a promising method for selectively recovering bioproducts from complex aqueous streams. Bio-isobutanol, a next-generation feedstock for biofuel, remains challenging to recover because of its low concentration and the presence of inhibitory substances. This study explores the potential of hollow fiber (HF) MSE for bio-isobutanol recovery and systematically examines the coupled effects of fiber packing, shell-side flow dynamics, and aqueous chemistry on performance. A resistance-in-series model is applied to understand mass transfer in the HF MSE modules, quantify local resistances, and validate overall performance. The results show that increasing the fiber packing provides a larger interfacial area but induces poor flow distribution and channeling, hindering effective isobutanol transport. Meanwhile, increasing the shell-side velocity improves isobutanol recovery due to reductions in the boundary layer thickness. The presence of salts, added to mimic fermentation broth, increases the partition coefficient through salting-out effects, further improving isobutanol flux. A modified correlation for the shell-side mass transfer coefficient (k s,ϕ+v ), integrating geometric and hydrodynamic effects, was developed and validated. The proposed model achieves highly predictive accuracy (r 2 = 0.9808) across a wide range of conditions, outperforming previous models. The findings provide mechanistic insight into the interaction of geometric packing, hydrodynamics, and chemistry in governing mass transfer in HF MSE. Overall, this work demonstrates the potential of HF MSE for efficient bio-isobutanol recovery and also provides practical guidelines on critical factors (packing fraction, partition coefficient, and shell-side velocity), aiding in the design and scaling of MSE systems for resource recovery.

Aqueous chemistry↗
DOE OSTI2022

Heat transport and temperature boundary-layer profiles in closed turbulent Rayleigh–Bénard convection with slippery conducting surfaces

Here, we report direct numerical simulations (DNS) of the Nusselt number Nu , the vertical profiles of mean temperature Θ(z) and temperature variance Ω(z) across the thermal boundary layer (BL) in closed turbulent Rayleigh–Bénard convection (RBC) with slippery conducting surfaces ( z is the vertical distance from the bottom surface). The DNS study was conducted in three RBC samples: a three-dimensional cuboid with length L=H and width W=H/4 ( H is the sample height), and two-dimensional rectangles with aspect ratios Γ≡L/H=1 and 10. The slip length b for top and bottom plates varied from 0 to ∞ . The Rayleigh numbers Ra were in the range 10 6 $⩽$Ra$⩽$10 10 and the Prandtl number Pr was fixed at 4.3 . As b increases, the normalised Nu/Nu 0 ( Nu 0 is the global heat transport for b =0 ) from the three samples for different Ra and Γ can be well described by the same function Nu/Nu 0 = N 0 tanh( b /λ 0 )+1 , with N 0 =0.8±0.03 . Here λ 0 ≡ L /(2 Nu 0 ) is the thermal boundary layer thickness for b =0 . Considering the BL fluctuations for Pr >1, one can derive solutions of temperature profiles Θ(z) and Ω(z) near the thermal BL for b $⩾$ 0 . When b =0 , the solutions are equivalent to those reported by Shishkina et al. ( Phys. Rev. Lett. , vol. 114, 2015, 114302) and Wang et al. ( Phys. Rev. Fluids , vol. 1, 2016, 082301(R)), respectively, for no-slip plates. For b >0, the derived solutions are in excellent agreement with our DNS data for slippery plates.

42 ENGINEERING↗
DOE OSTI2025

Tracking Local pH Dynamics during Water Electrolysis via In-Line Continuous Flow Raman Spectroscopy

The performance of electrochemical devices, which play a critical role in decarbonization efforts, is often governed by proton-coupled electron transfer reactions at the electrode–electrolyte interface. These reactions are highly sensitive to the complex and dynamic microenvironment present at the electrode surface. However, characterizing this environment─particularly monitoring interfacial pH and its evolution under reaction conditions─remains challenging, necessitating the development of advanced analytical tools. Here, in this study, we introduce in-line continuous flow Raman spectroscopy (CFRS) as a spectroelectrochemical platform for quantifying interfacial pH swings generated during water-splitting. By monitoring phosphate ion speciation and controlling the hydrodynamics with a flow cell, we measure pH swings as a function of current density, flow rate, and distance from the electrode. Comparison with theoretical models reveals the impact of bulk pH, boundary layer thickness, and bubble dynamics at high current densities. Collectively, these findings establish CFRS as a platform for quantitatively investigating pH dynamics, offering critical insights for advancing electrochemical energy conversion technologies.

Marquez, Raul A. [Univ. of Texas, Austin, TX (Unit↗
DOE OSTI2026

Spatially Mapping the CO 2 Alkaline Sorbent Diffuse Microenvironment Using Operando Raman Spectroscopy

When designing a chemical process, the local balance of transport and kinetics, collectively referred to as the diffuse microenvironment, plays a critical role in performance but is difficult to directly observe. This work demonstrates a method of two-dimensional spatial chemical mapping of the diffuse microenvironment in the context of alkali metal hydroxide direct air capture of carbon dioxide using a custom operando gas-absorption flow cell along with confocal Raman spectroscopy. Notably, we observe the concentration boundary layer near the gas–liquid interface and elucidate the interplay of carbonate and bicarbonate ions within it while inferring local hydroxide depletion through continuum modeling. These first of their kind observations provide a technique to compare the performance of direct air capture solvents based on diffuse microenvironment dynamics while also providing metrics important for air contactor design such as boundary layer thickness. Overall, this work showcases a new experimental platform to study interfacial diffuse microenvironments in and outside of the field of direct air capture of carbon dioxide.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

The Cascade Effectiveness of 3-Terminal Tandem Photocathode Architectures as Applied to CO 2 Reduction

Cascade catalysis for photoelectrochemical CO 2 reduction (CO 2 R) decouples the overall reaction into sequential steps occurring on separately optimized catalysts (for example, Ag and Cu) between which an intermediate species such as CO is transferred. A 3-terminal tandem (3TT) photovoltaic architecture advantageously holds two different catalytic regions at different potentials under a single illumination source, but its overall efficiency is low. Using a stochastic reaction-diffusion model, we have examined 3TT photocathode design principles, focusing on the coupling of surface chemistry and transport of CO both inside the boundary layer and outward, into the bulk electrolyte. We find that ensuring that the lateral diffusion distance within the boundary layer is short compared to the boundary layer thickness and controlling bulk flow are key, with interdigitated designs showing an overall conversion efficiency improvement by 2 orders of magnitude compared to the side-by-side case without flow. These findings can be adapted for other cascaded architectures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Low-temperature Leidenfrost-like jumping of sessile droplets on microstructured surfaces

The Leidenfrost effect—the levitation and hovering of liquid droplets on hot solid surfaces—generally requires a sufficiently high substrate temperature to activate liquid vaporization. Here, in this paper, we report the modulation of Leidenfrost-like jumping of sessile water microdroplets on micropillared surfaces at a relatively low temperature. Compared to traditional Leidenfrost effect occurring above 230 °C, the fin-array-like micropillars enable water microdroplets to levitate and jump off the surface within milliseconds at a temperature of 130 °C by triggering the inertia-controlled growth of individual vapour bubbles at the droplet base. We demonstrate that droplet jumping, resulting from momentum interactions between the expanding vapour bubble and the droplet, can be modulated by tailoring of the thermal boundary layer thickness through pillar height. This enables regulation of the bubble expansion between the inertia-controlled mode and the heat-transfer-limited mode. The two bubble-growth modes give rise to distinct droplet jumping behaviours characterized by constant velocity and constant energy regimes, respectively. This heating strategy allows the straightforward purging of wetting liquid droplets on rough or structured surfaces in a controlled manner, with potential applications including the rapid removal of fouling media, even when located in surface cavities.

42 ENGINEERING↗
DOE OSTI2024

Validation of predictive performance models for supersonic gas-jet nozzles at the Laboratory for Laser Energetics

We present results characterizing the neutral-density distributions produced by the supersonic nozzles used in experiments on the OMEGA-60 and OMEGA-EP laser systems at the University of Rochester’s Laboratory for Laser Energetics (LLE). Axisymmetric Fluent® simulations using LLE nozzle specifications capture the viscous effects, gas expansion, and shock waves that complicate flow predictions for offsets above the nozzle exit. Here, these simulations show good agreement with neutral-density measurements obtained using a four-wave shearing interferometer. An analytical form is given for the plateau length. Fits to simulation data for boundary layer thickness, mean plateau density, and density ramps are given as functions of nozzle offset and nozzle backing pressure for a number of nozzles and gases.

47 OTHER INSTRUMENTATION↗
NASA NTRS1956

An Engineering Approach to the Variable Fluid Property Problem in Free Convection

An analysis is made for the variable fluid property problem for laminar free convection on an isothermal vertical flat plate. For a number of specific cases, solutions of the boundary layer equations appropriate to the variable property situation were carried out for gases and liquid mercury. Utilizing these findings, a simple and accurate shorthand procedure is presented for calculating free convection heat transfer under variable property conditions. This calculation method is well established in the heat transfer field. It involves the use of results which have been derived for constant property fluids, and of a set of rules (called reference temperatures) for extending these constant property results to variable property situations. For gases, the constant property heat transfer results are generalized to the variable property situation by replacing beta (expansion coefficient) by one over T sub infinity and evaluating the other properties at T sub r equals T sub w minus zero point thirty-eight (T sub w minus T sub infinity). For liquid mercury, the generalization may be accomplished by evaluating all the properties (including beta) at this same T sub r. It is worthwhile noting that for these fluids, the film temperature (with beta equals one over T sub infinity for gases) appears to serve as an adequate reference temperature for most applications. Results are also presented for boundary layer thickness and velocity parameters.

Gregg, J. L.↗