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At least 955 records · Page 53

Integrated Bosch Process System Models for In-Situ Oxygen and Carbon Production

In-Situ Resource Utilization (ISRU) technology is a vital component to NASA’s mission of a sustainable presence on the Moon and Mars. Local resources can be leveraged to reduce resupply frequency and mass. Elements of the Bosch process, combined with the carbothermal reduction process, can produce oxygen on the lunar surface with minimal consumables. The Bosch process can also produce oxygen on the Martian surface by using the CO 2 -rich environment. Between both systems, adsorption pump, solar thermal energy, carbon formation reactor, and water recovery subsystems are modeled and integrated to create a functional model in MATLAB software. The model is used to simulate performance of the system and reduce mass, power, and volume requirements. This integrated system model provides a tool to scale ISRU technologies for oxygen and carbon production. The MATLAB model is created by developing a system of independent subsystem models that are solved for their quasi-steady state values which can be integrated with respect to time to determine the change in current states. A flexible time stepping method is used to ensure a high level of accuracy during periods of rapid change while still making use of a simple explicit integration method. The flexible time step is calculated for each independent subsystem and the minimum value from those is used as the overall time step. A flexible time step is calculated by dividing a resolution value, or the maximum change per time step, by the variables current rate of change. The maximum value from all points in space is used for subsystem models that contain multiple values. The process is done for every variable that is being monitored in each subsystem and the global minimum is used as that iteration’s timestep. Several assumptions used in the MATLAB model for fluid flow dynamics, such as 1-D gas flow through the sorption pump, are supported by modeling in Ansys Fluent software. The Lunar oxygen production system is outlined in Fig. 1. The carbothermal reduction subsystem uses solar energy to heat a mixture of lunar regolith and carbon powder to produce carbon monoxide. To begin, the carbon monoxide feeds to the modified Bosch subsystem along with hydrogen gas. The reactants then enter the carbon formation reactor where water and carbon powder are produced. Solar thermal energy is used to add energy to the reactor, but waste heat from the carbothermal process is another potential heat source. The water is collected and electrolyzed to produce hydrogen which reenters the Bosch subsystem, and the oxygen is stored for downstream use. The carbon powder is collected and feeds back into the carbothermal subsystem. The Martian oxygen production system uses the full Bosch process and is outlined in Fig 2. A CO 2 adsorption pump thermally cycles to scrub and pressurize CO 2 from the environment. Along with an initial supply of hydrogen, the reactants enter the Reverse Water Gas Shift Reactor (RWGSR) which produces carbon monoxide and water. Carbon monoxide and unreacted hydrogen enter the carbon formation reactor to produce water and carbon powder. The water is collected from both reactors and electrolyzed to reintroduce hydrogen and store oxygen for propellant production or life support. Carbon is removed from the carbon formation reactor and stored. The adsorption pump utilizes rapid cycle temperature swings within a stack of zeolite coated surfaces. The subsystem model solves 1-D quasi-steady conservation laws of the quasi-steady form, shown in Eq. 1, for the gas stream and heat exchange liquid to predict performance parameters such as breakthrough capacity and optimum cycle time. The source term S is used to capture interactions between the fluid flows and the sorbent. A quasi-steady-state scheme is used where no time derivatives appear in the governing equations, except for those in the source terms. This results in an autonomous system, where ∂F/∂x = ƒ(F). The fluxes F are provided at the inlet, and an explicit method is used to solve for the spatial distribution of F. The heat and mass flows to the sorbent are then extracted from the source terms. These flows are numerically integrated to produce a 1-D solution for the system’s state as a function of both time and space. The body of the adsorption pump is separated into two semi-independent models: the heat exchanger fluid flow and gas flow through the zeolite coated surfaces. Both models are solved using the above-described method to find a 1-D solution as a function of space and interact only once a timestep is taken. The interaction point is the sorbent through which all heat transfer between the two models must occur. Sorbent mass adsorption is calculated using the Lagergren model, shown in Eq. 2, where the transfer coefficient, λ D , is found by solving a system of nondimensionalized equations derived by using the heat and mass transfer analogy for transport phenomena. Using Grade 544 Type 13X zeolite as the sorbent material, the equilibrium concentration, θ eq , is calculated using the k-site Langmuir isotherm and fit parameters. Additionally, the enthalpy of adsorption used in the model is computed by interpolation of available data [1]. The subsystem model was validated using the Rapid Cycle Temperature Swing Adsorption (RC-TSA) pump. The solar thermal energy subsystem focuses on a solar concentrator concept with a heat exchanger to heat the reactants before entering the carbon formation reactor. The subsystem model assumes a fixed solar flux and reflector efficiency to calculate the reactant temperature given the incoming temperature, pressure, and exchanger geometry. The receiver is a custom manufactured series of copper blocks with serpentine channels to increase its surface area and the residence time of the reactants to heat up to 550 °C. The subsystem model was validated using a heat exchanger developed at NASA Glenn Research Center (GRC). The solar thermal energy subsystem focuses on a solar concentrator concept with a heat exchanger to heat the reactants before entering the carbon formation reactor. The subsystem model assumes a fixed solar flux and reflector efficiency to calculate the reactant temperature given the incoming temperature, pressure, and exchanger geometry. The receiver is a custom manufactured series of copper blocks with serpentine channels to increase its surface area and the residence time of the reactants to heat up to 550 °C. The subsystem model was validated using a heat exchanger developed at NASA Glenn Research Center (GRC).

In situ Resource Utilization↗

Analog Phase Holograms by Electron Beam Lithography

Phase holograms have been created on the surface of a thin film of poly-methyl methacrylate (PMMA, Plexiglas) by direct-write electron beam (E-Beam) lithography. The process involves delivering a patterned exposure dose followed by partial development with a strong developer. The patterned dose derives from arbitrary computer-calculated holograms, which must be corrected for the sensitivity characteristic of the PMMA and for the effective point-spread function of the E-Beam.

phase↗

An investigation of potential applications of OP-SAPS: Operational sampled analog processors

The impact of charge-coupled device (CCD) processors on future instrumentation was investigated. The CCD devices studied process sampled analog data and are referred to as OP-SAPS - operational sampled analog processors. Preliminary studies into various architectural configurations for systems composed of OP-SAPS show that they have potential in such diverse applications as pattern recognition and automatic control. It appears probable that OP-SAPS may be used to construct computing structures which can serve as special peripherals to large-scale computer complexes used in real time flight simulation. The research was limited to the following benchmark programs: (1) face recognition, (2) voice command and control, (3) terrain classification, and (4) terrain identification. A small amount of effort was spent on examining a method by which OP-SAPS may be used to decrease the limiting ground sampling distance encountered in remote sensing from satellites.

Parrish, E. A.↗

An efficient algorithm for estimating noise covariances in distributed systems

An efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochatic-dynamic systems is presented. Such systems arise typically by discretizing distributed-parameter systems, and their size renders computational efficiency a major consideration. The proposed adaptive filtering algorithm is based on the ideas of Belanger, and is algebraically equivalent to his algorithm. The earlier algorithm, however, has computational complexity proportional to p to the 6th, where p is the number of observations of the system state, while the new algorithm has complexity proportional to only p-cubed. Further, the formulation of noise covariance estimation as a secondary filter, analogous to state estimation as a primary filter, suggests several generalizations of the earlier algorithm. The performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction.

Dee, D. P.↗

A theoretical study of the excited states of Ag3

Recently there was considerable interest in the properties and reactivities of small metal clusters. However, for the transition metal trimers, gas phase spectroscopy exists only for Cu3. Calculations are reported for the excited states of the Ag3 molecule. The excitation energies, geometries, derived harmonic frequencies, and transition moments are presented. The electronic structure of these states is very similar to the analogous states of Cu3. From the VCI wave functions transition moments were calculated between each of the Rydberg excited states and the ground state for an equilateral triangle geometry with R sub Ag-Ag = 5.3 a sub 0. One state was computed for the configuration 4d29 5sa sup prime 2 sub 1 5se sup prime 1 sub x 5se sup prime 1 sub y. This configuration was considered since the corresponding configuration for Cu3 is low-lying. Calculations were carried out for a quartet wavefunction in which the 4d hole was localized on the central Ag atom. The spectrum for Ag3 is expected to be simpler than for Cu3 since the 5s2 4d9 states are shifted to higher energy.

Walch, Stephen P.↗

Reconfigurable HIL Testing of Earth Satellites

In recent years, hardware-in-the-loop (HIL) testing has carved a strong niche in several industries, such as automotive, aerospace, telecomm, and consumer electronics. As desktop computers have realized gains in speed, memory size, and data storage capacity, hardware/software platforms have evolved into high performance, deterministic HIL platforms, capable of hosting the most demanding applications for testing components and subsystems. Using simulation software to emulate the digital and analog I/O signals of system components, engineers of all disciplines can now test new systems in realistic environments to evaluate their function and performance prior to field deployment. Within the Aerospace industry, space-borne satellite systems are arguably some of the most demanding in terms of their requirement for custom engineering and testing. Typically, spacecraft are built one or few at a time to fulfill a space science or defense mission. In contrast to other industries that can amortize the cost of HIL systems over thousands, even millions of units, spacecraft HIL systems have been built as one-of-a-kind solutions, expensive in terms of schedule, cost, and risk, to assure satellite and spacecraft systems reliability. The focus of this paper is to present a new approach to HIL testing for spacecraft systems that takes advantage of a highly flexible hardware/software architecture based on National Instruments PXI reconfigurable hardware and virtual instruments developed using LabVIEW. This new approach to HIL is based on a multistage/multimode spacecraft bus emulation development model called Reconfigurable Hardware In-the-Loop or RHIL.

Source record↗

Conducting Research on the International Space Station Using the EXPRESS Rack Facilities

Conducting Research on the International Space Station using the EXPRESS Rack Facilities. Sean W. Thompson and Robert E. Lake. NASA Marshall Space Flight Center, Huntsville, AL, USA. Eight "Expedite the Processing of Experiments to Space Station" (EXPRESS) Rack facilities are located within the International Space Station (ISS) laboratories to provide standard resources and interfaces for the simultaneous and independent operation of multiple experiments within each rack. Each EXPRESS Rack provides eight Middeck Locker Equivalent locations and two drawer locations for powered experiment equipment, also referred to as sub-rack payloads. Payload developers may provide their own structure to occupy the equivalent volume of one, two, or four lockers as a single unit. Resources provided for each location include power (28 Vdc, 0-500 W), command and data handling (Ethernet, RS-422, 5 Vdc discrete, +/- 5 Vdc analog), video (NTSC/RS 170A), and air cooling (0-200 W). Each rack also provides water cooling (500 W) for two locations, one vacuum exhaust interface, and one gaseous nitrogen interface. Standard interfacing cables and hoses are provided on-orbit. One laptop computer is provided with each rack to control the rack and to accommodate payload application software. Four of the racks are equipped with the Active Rack Isolation System to reduce vibration between the ISS and the rack. EXPRESS Racks are operated by the Payload Operations Integration Center at Marshall Space Flight Center and the sub-rack experiments are operated remotely by the investigating organization. Payload Integration Managers serve as a focal to assist organizations developing payloads for an EXPRESS Rack. NASA provides EXPRESS Rack simulator software for payload developers to checkout payload command and data handling at the development site before integrating the payload with the EXPRESS Functional Checkout Unit for an end-to-end test before flight. EXPRESS Racks began supporting investigations onboard ISS on April 24, 2001 and will continue through the life of the ISS.

Thompson, Sean W.↗

Conducting Research on the International Space Station Using the EXPRESS Rack Facilities

Eight "Expedite the Processing of Experiments to Space Station" (EXPRESS) Rack facilities are located within the International Space Station (ISS) laboratories to provide standard resources and interfaces for the simultaneous and independent operation of multiple experiments within each rack. Each EXPRESS Rack provides eight Middeck Locker Equivalent locations and two drawer locations for powered experiment equipment, also referred to as sub-rack payloads. Payload developers may provide their own structure to occupy the equivalent volume of one, two, or four lockers as a single unit. Resources provided for each location include power (28 Vdc, 0-500 W), command and data handling (Ethernet, RS-422, 5 Vdc discrete, +/- 5 Vdc analog), video (NTSC/RS 170A), and air cooling (0-200 W). Each rack also provides water cooling (500 W) for two locations, one vacuum exhaust interface, and one gaseous nitrogen interface. Standard interfacing cables and hoses are provided on-orbit. One laptop computer is provided with each rack to control the rack and to accommodate payload application software. Four of the racks are equipped with the Active Rack Isolation System to reduce vibration between the ISS and the rack. EXPRESS Racks are operated by the Payload Operations Integration Center at Marshall Space Flight Center and the sub-rack experiments are operated remotely by the investigating organization. Payload Integration Managers serve as a focal to assist organizations developing payloads for an EXPRESS Rack. NASA provides EXPRESS Rack simulator software for payload developers to checkout payload command and data handling at the development site before integrating the payload with the EXPRESS Functional Checkout Unit for an end-to-end test before flight. EXPRESS Racks began supporting investigations onboard ISS on April 24, 2001 and will continue through the life of the ISS.

Thompson, Sean W.↗

Conducting Research on the International Space Station using the EXPRESS Rack Facilities

Eight "Expedite the Processing of Experiments to Space Station" (EXPRESS) Rack facilities are located within the International Space Station (ISS) laboratories to provide standard resources and interfaces for the simultaneous and independent operation of multiple experiments within each rack. Each EXPRESS Rack provides eight Middeck Locker Equivalent locations and two drawer locations for powered experiment equipment, also referred to as sub-rack payloads. Payload developers may provide their own structure to occupy the equivalent volume of one, two, or four lockers as a single unit. Resources provided for each location include power (28 Vdc, 0-500 W), command and data handling (Ethernet, RS-422, 5 Vdc discrete, +/- 5 Vdc analog), video (NTSC/RS 170A), and air cooling (0-200 W). Each rack also provides water cooling for two locations (500W ea.), one vacuum exhaust interface, and one gaseous nitrogen interface. Standard interfacing cables and hoses are provided on-orbit. One laptop computer is provided with each rack to control the rack and to accommodate payload application software. Four of the racks are equipped with the Active Rack Isolation System to reduce vibration between the ISS and the rack. EXPRESS Racks are operated by the Payload Operations Integration Center at Marshall Space Flight Center and the sub-rack experiments are operated remotely by the investigating organization. Payload Integration Managers serve as a focal to assist organizations developing payloads for an EXPRESS Rack. NASA provides EXPRESS Rack simulator software for payload developers to checkout payload command and data handling at the development site before integrating the payload with the EXPRESS Functional Checkout Unit for an end-to-end test before flight. EXPRESS Racks began supporting investigations onboard ISS on April 24, 2001 and will continue through the life of the ISS.

Thompson, Sean W.↗

Plasmon Resonances of Metal Nanoparticles in an Absorbing Medium

We study the behavior of plasmon resonances of metal nanospheres embedded in an absorbing medium. First-principles far-field computations based on the general Lorenz–Mie theory show that increasing absorption in the host medium broadens and suppresses plasmon resonances in the extinction and effective scattering efficiency factors and suppresses resonance features in the phase function. These effects of absorption are analogous to those on the morphology-dependent resonances of dielectric particles with large size parameters.

Mishchenko, Michael I.↗

Real-time demonstration hardware for enhanced DPCM video compression algorithm

The lack of available wideband digital links as well as the complexity of implementation of bandwidth efficient digital video CODECs (encoder/decoder) has worked to keep the cost of digital television transmission too high to compete with analog methods. Terrestrial and satellite video service providers, however, are now recognizing the potential gains that digital video compression offers and are proposing to incorporate compression systems to increase the number of available program channels. NASA is similarly recognizing the benefits of and trend toward digital video compression techniques for transmission of high quality video from space and therefore, has developed a digital television bandwidth compression algorithm to process standard National Television Systems Committee (NTSC) composite color television signals. The algorithm is based on differential pulse code modulation (DPCM), but additionally utilizes a non-adaptive predictor, non-uniform quantizer and multilevel Huffman coder to reduce the data rate substantially below that achievable with straight DPCM. The non-adaptive predictor and multilevel Huffman coder combine to set this technique apart from other DPCM encoding algorithms. All processing is done on a intra-field basis to prevent motion degradation and minimize hardware complexity. Computer simulations have shown the algorithm will produce broadcast quality reconstructed video at an average transmission rate of 1.8 bits/pixel. Hardware implementation of the DPCM circuit, non-adaptive predictor and non-uniform quantizer has been completed, providing realtime demonstration of the image quality at full video rates. Video sampling/reconstruction circuits have also been constructed to accomplish the analog video processing necessary for the real-time demonstration. Performance results for the completed hardware compare favorably with simulation results. Hardware implementation of the multilevel Huffman encoder/decoder is currently under development along with implementation of a buffer control algorithm to accommodate the variable data rate output of the multilevel Huffman encoder. A video CODEC of this type could be used to compress NTSC color television signals where high quality reconstruction is desirable (e.g., Space Station video transmission, transmission direct-to-the-home via direct broadcast satellite systems or cable television distribution to system headends and direct-to-the-home).

Bizon, Thomas P.↗

Volcanic Signatures in Estimates of Stratospheric Aerosol Size, Distribution Width, Surface Area, and Volume Deduced from Global Satellite-Based Observations

Volcanic signatures in the stratospheric aerosol layer are revealed by two independent techniques which retrieve aerosol information from global satellite-based observations of particulate extinction. Both techniques combine the 4-wavelength Stratospheric Aerosol and Gas Experiment (SAGE) II extinction measurements (0.385 <= lambda <= 1.02 microns) with the 7.96 micron and 12.82 micron extinction measurements from the Cryogenic Limb Array Etalon Spectrometer (CLAES) instrument. The algorithms use the SAGE II/CLAES composite extinction spectra in month-latitude-altitude bins to retrieve values and uncertainties of particle effective radius R(sub eff), surface area S, volume V and size distribution width sigma(sub R). The first technique is a multi-wavelength Look-Up-Table (LUT) algorithm which retrieves values and uncertainties of R(sub eff) by comparing ratios of extinctions from SAGE II and CLAES (e.g., E(sub lambda)/E(sub 1.02) to pre-computed extinction ratios which are based on a range of unimodal lognormal size distributions. The pre-computed ratios are presented as a function of R(sub eff) for a given sigma(sub g); thus the comparisons establish the range of R(sub eff) consistent with the measured spectra for that sigma(sub g). The fact that no solutions are found for certain sigma(sub g) values provides information on the acceptable range of sigma(sub g), which is found to evolve in response to volcanic injections and removal periods. Analogous comparisons using absolute extinction spectra and error bars establish the range of S and V. The second technique is a Parameter Search Technique (PST) which estimates R(sub eff) and sigma(sub g) within a month-latitude-altitude bin by minimizing the chi-squared values obtained by comparing the SAGE II/CLAES extinction spectra and error bars with spectra calculated by varying the lognormal fitting parameters: R(sub eff), sigma(sub g), and the total number of particles N(sub 0). For both techniques, possible biases in retrieved-parameters caused by assuming a unimodal functional form are removed using correction factors computed from representative in situ measurements of bimodal size distributions. Some interesting features revealed by the LUT and PST retrievals include: (1) Increases in S and V (but not R(sub eff)) after the Ruiz and Kelut injections, (2) Increases in S, V, R(sub eff) after Pinatubo, (3) Post-Pinatubo increases in S, V, and R(sub eff) that are more rapid in the tropics than elsewhere, (4) Mid-latitude post-Pinatubo increases in R(sub eff) that lag increases in S and V, (5) S and V returning to pre-Pinatubo values sooner than R(sub eff) does, (6) Sharp increases in sigma(sub g), after Pinatubo and slight increases in sigma(sub g) after Ruiz, Etna, Kelut, Spurr and Rabaul, and (7) Gradual declines in the heights at which R(sub eff), S and V peak after Pinatubo.

Bauman, J. J.↗

Separated flow over a body of revolution

A method is developed to determine the flowfield of a body of revolution in separated flow. The technique employed is the use of the computer to integrate various solutions and solution properties of the sub-flowfields which make up the entire flowfield without resorting to a finite difference solution to the complete Navier-Stokes equations. The technique entails the use of the unsteady cross flow analogy and a new solution to the required two-dimensional unsteady separated flow problem based upon an unsteady discrete-vorticity wake. Data for the forces and moments on bodies of revolution at high angle of attack (outside the range of linear inviscid theories) such that the flow is substantially separated are produced which compare well with experimental data at low speeds. In addition, three-dimensional steady separation regions and wake vortex patterns are determined.

Marshall, F. J.↗

Theoretical research program to study chemical reactions in AOTV bow shock tubes

Effort continued through this period to refine and expand the SIRIUS/ABACUS program package for CASSCF and RASSCF second derivatives. A new approach to computing the Gaussian integral derivatives that require much of the time in gradient and Hessian calculations was devised. Several different studies were undertaken in the area of application calculations. These include a study of proton transfer in the HF trimer, which provides an analog of rearrangement reactions, and the extension of our previous work on Be and Mg clusters to Ca clusters. In addition, a very accurate investigation of the lowest-lying potential curves of the O2 molecule was completed. These curves are essential for evaluating different models of the terrestrial atmosphere nightglow. The most effort this year was devoted to a large scale investigation of stationary points on the C4H4 surface, and the thermochemistry of acetylene/acetylene reaction.

Taylor, Peter↗

Neural node network and model, and method of teaching same

The present invention is a fully connected feed forward network that includes at least one hidden layer 16. The hidden layer 16 includes nodes 20 in which the output of the node is fed back to that node as an input with a unit delay produced by a delay device 24 occurring in the feedback path 22 (local feedback). Each node within each layer also receives a delayed output (crosstalk) produced by a delay unit 36 from all the other nodes within the same layer 16. The node performs a transfer function operation based on the inputs from the previous layer and the delayed outputs. The network can be implemented as analog or digital or within a general purpose processor. Two teaching methods can be used: (1) back propagation of weight calculation that includes the local feedback and the crosstalk or (2) more preferably a feed forward gradient decent which immediately follows the output computations and which also includes the local feedback and the crosstalk. Subsequent to the gradient propagation, the weights can be normalized, thereby preventing convergence to a local optimum. Education of the network can be incremental both on and off-line. An educated network is suitable for modeling and controlling dynamic nonlinear systems and time series systems and predicting the outputs as well as hidden states and parameters. The educated network can also be further educated during on-line processing.

Parlos, Alexander G.↗

Differential equation of exospheric lateral transport and its application to terrestrial hydrogen

The differential equation description of exospheric lateral transport of Hodges and Johnson is reformulated to extend its utility to light gases. Accuracy of the revised equation is established by applying it to terrestrial hydrogen. The resulting global distributions for several static exobase models are shown to be essentially the same as those that have been computed by Quessette using an integral equation approach. The present theory is subsequently used to elucidate the effects of nonzero lateral flow, exobase rotation, and diurnal tidal winds on the hydrogen distribution. Finally it is shown that the differential equation of exospheric transport is analogous to a diffusion equation. Hence it is practical to consider exospheric transport as a continuation of thermospheric diffusion, a concept that alleviates the need for an artificial exobase dividing thermosphere and exosphere.

Hodges, R. R., Jr.↗

Application of the vortex-lattice technique to the analysis of thin wings with vortex separation and thick multi-element wings

Two techniques for extending the range of applicability of the basic vortex-lattice method are discussed. The first improves the computation of aerodynamic forces on thin, low-aspect-ratio wings of arbitrary planforms at subsonic Mach numbers by including the effects of leading-edge and tip vortex separation, characteristic of this type wing, through use of the well-known suction-analogy method of E. C. Polhamus. Comparisons with experimental data for a variety of planforms are presented. The second consists of the use of the vortex-lattice method to predict pressure distributions over thick multi-element wings (wings with leading- and trailing-edge devices). A method of laying out the lattice is described which gives accurate pressures on the top and part of the bottom surface of the wing. Limited comparisons between the result predicted by this method, the conventional lattice arrangement method, experimental data, and 2-D potential flow analysis techniques are presented.

Smith, C. W.↗

An analysis of laminar free-convection flow and heat transfer about a flat plate paralled to the direction of the generating body force

The free-convection flow and heat transfer (generated by a body force) about a flat plate parallel to the direction of the body force are formally analyzed and the type of flow is found to be dependent on the Grashof number alone. For large Grashof numbers (which are of interest in aeronautics), the flow is of the boundary-layer type and the problem is reduced in a formal manner, which is analogous to Prandtl's forced-flow boundary-layer theory, to the simultaneous solution of two ordinary differential equations subject to the proper boundary conditions. Velocity and temperature distributions for Prandtl numbers of 0.01, 0.72, 0.733, 1, 1, 10, 100, and 1000 are computed, and it is shown that velocities and Nusselt numbers of the order of magnitude of those encountered in forced-convection flows may be obtained in free-convection flows. The theoretical and experimental velocity and temperature distributions are in good agreement. A flow and a heat-transfer parameter, from which the important physical quantities such as shear stress and heat-transfer rate can be computed, are derived as functions of Prandtl number alone.

Ostrach, Simon↗